  The study of protostellar collapse or infall has proven unusually difficult
and controversial. Some historical context will be provided, against which
recent advances can be measured. We now have a substantial number of objects
with signatures that can be interpreted in terms of collapse, but a number of
issues remain. One issue is the effect of chemical variations, especially
depletion in the dense, cold interiors of cores that are likely to form low
mass stars. Strategies for dealing with this issue depend on using dust
emission to constrain the density and temperature distribution, leaving
molecular line observations to constrain dynamics and abundance distributions.
Recent progress in this area will be described and we will consider the next
challenges to be overcome. Interferometeric observations, especially with
future instruments, will provide a powerful tool. In combination with chemical
studies coupled with dynamical models, the observations made possible by
interferometers should finally put this subject on a firm foundation.


  We use equivariant surgery to classify all involutions on closed surfaces, up
to isomorphism. Work on this problem is classical, dating back to the
nineteenth century, but some questions seem to have been left unanswered. We
give a modern treatment that leads to a complete classification.


  We study the rapidity window dependences of higher order cumulants of
conserved charges observed in relativistic heavy ion collisions. The time
evolution and the rapidity window dependence of the non-Gaussian fluctuations
are described by the diffusion master equation. Analytic formulas for the time
evolution of cumulants in a rapidity window are obtained for arbitrary initial
conditions. We discuss that the rapidity window dependences of the non-Gaussian
cumulants have characteristic structures reflecting the non-equilibrium
property of fluctuations, which can be observed in relativistic heavy ion
collisions with the present detectors. It is argued that various information on
the thermal and transport properties of the hot medium can be revealed
experimentally by the study of the rapidity window dependences, especially by
the combined use, of the higher order cumulants. Formulas of higher order
cumulants for a probability distribution composed of sub-probabilities, which
are useful for various studies of non-Gaussian cumulants, are also presented.


  An increasing number of potentially habitable terrestrial planets and planet
candidates are found by ongoing planet search programs. The search for
atmospheric signatures to establish planetary habitability and the presence of
life might be possible in the future. We want to quantify the accuracy of
retrieved atmospheric parameters which might be obtained from infrared emission
spectroscopy. We use synthetic observations of hypothetical habitable planets,
constructed with a parametrized atmosphere model, a high-resolution radiative
transfer model and a simplified noise model. Classic statistical tools such as
chi2 statistics and least-square fits were used to analyze the simulated
observations. When adopting the design of currently planned or proposed
exoplanet characterization missions, we find that emission spectroscopy could
provide weak limits on surface conditions of terrestrial planets, hence their
potential habitability. However, these mission designs are unlikely to allow to
characterize the composition of the atmosphere of a habitable planet, even
though CO2 is detected. Upon increasing the signal-to-noise ratios by about a
factor of 2-5 (depending on spectral resolution) compared to current mission
designs, the CO2 content could be characterized to within two orders of
magnitude. The detection of the O3 biosignature remains marginal. The
atmospheric temperature structure could not be constrained. Therefore, a full
atmospheric characterization seems to be beyond the capabilities of such
missions when using only emission spectroscopy during secondary eclipse or
target visits. Other methods such as transmission spectroscopy or orbital
photometry are probably needed in order to give additional constraints and
break degeneracies. (abridged)


  Aims : The hydrogen-deficient supergiants known as R Coronae Borealis (RCB)
stars might be the result of a double-degenerate merger of two white dwarfs
(WDs), or a final helium shell flash in a planetary nebula central star. In
this context, any information on the geometry of their circumstellar
environment and, in particular, the potential detection of elongated
structures, is of great importance. Methods : We obtained near-IR observations
of V854 Cen with the AMBER recombiner located at the Very Large Telescope
Interferometer (VLTI) array with the compact array (B$\leq$35m) in 2013 and the
long array (B$\leq$140m) in 2014. At each time, V854 Cen was at maximum light.
The $H$- and $K$-band continua were investigated by means of spectrally
dependant geometric models. These data were supplemented with mid-IR VISIR/VLT
images. Results : A dusty slightly elongated over density is discovered both in
the $H$- and $K$-band images. With the compact array, the central star is
unresolved ($\Theta\leq2.5$\,mas), but a flattened dusty environment of $8
\times 11$ mas is discovered whose flux increases from about $\sim$20% in the
$H$ band to reach about $\sim$50% at 2.3$\micron$, which indicates hot
(T$\sim$1500\,K) dust in the close vicinity of the star. The major axis is
oriented at a position angle (P.A.) of 126$\pm$29$\deg$. Adding the long-array
configuration dataset provides tighter constraints on the star diameter
($\Theta\leq1.0$ mas), a slight increase of the overdensity to $12 \times 15$
mas and a consistent P.A. of 133$\pm$49$\deg$. The closure phases, sensitive to
asymmetries, are null and compatible with a centro-symmetric, unperturbed
environment excluding point sources at the level of 3% of the total flux in
2013 and 2014. The VISIR images exhibit a flattened aspect ratio at the 15-20%
level at larger distances ($\sim$1$\arcsec$) with a position angle of
92$\pm$19$\deg$, marginally consistent with the interferometric observations.
Conclusions : This is the first time that a moderately elongated structure has
been observed around an RCB star. These observations confirm the numerous
suggestions for a bipolar structure proposed for this star in the literature,
which were mainly based on polarimetric and spectroscopic observations.


  Active regions (ARs) are the main sources of variety in solar dynamic events.
Automated detection and identification tools need to be developed for solar
features for a deeper understanding of the solar cycle. Of particular interest
here are the dynamical properties of the ARs, regardless of their internal
structure and sunspot distribution. We studied the oscillatory dynamics of two
ARs: NOAA 11327 and NOAA 11726 using two different methods of pattern
recognition. We developed a novel method of automated AR border detection and
compared it to an existing method for the proof-of-concept. The first method
uses least-squares fitting on the smallest ellipse enclosing the AR, while the
second method applies regression on the convex hull.} After processing the
data, we found that the axes and the inclination angle of the ellipse and the
convex hull oscillate in time. These oscillations are interpreted as the second
harmonic of the standing long-period kink oscillations (with the node at the
apex) of the magnetic flux tube connecting the two main sunspots of the ARs. In
both ARs we have estimated the distribution of the phase speed magnitude along
the magnetic tubes (along the two main spots) by interpreting the obtained
oscillation of the inclination angle as the standing second harmonic kink mode.
After comparing the obtained results for fast and slow kink modes, we conclude
that both of these modes are good candidates to explain the observed
oscillations of the AR inclination angles, as in the high plasma $\beta$ regime
the phase speeds of these modes are comparable and on the order of the
Alfv\'{e}n speed. Based on the properties of the observed oscillations, we
detected the appropriate depth of the sunspot patterns, which coincides with
estimations made by helioseismic methods. The latter analysis can be used as a
basis for developing a magneto-seismological tool for ARs.


  We study the geometric phase factors underlying the classical and the
corresponding quantum dynamics of a driven nonlinear oscillator exhibiting
chaotic dynamics. For the classical problem, we compute the geometric phase
factors associated with the phase space trajectories using Frenet-Serret
formulation. For the corresponding quantum problem, the geometric phase
associated with the time evolution of the wave function is computed. Our
studies suggest that the classical geometric phase may be related to the the
difference in the quantum geometric phases between two neighboring eigenstates.


  We introduce a model with conserved dynamics, where nearest neighbor pairs of
spins $\uparrow \downarrow (\downarrow \uparrow)$ can exchange to assume the
configuration $\downarrow \uparrow (\uparrow \downarrow)$, with rate $\beta
(\alpha)$, through energy decreasing moves only. We report exact solution for
the case when one of the rates, $\alpha$ or $\beta$, is zero. The
irreversibility of such dynamics results in strong dependence on the initial
conditions. Domain wall arguments suggest that for more general models with
steady states the dynamical critical exponent for the anisotropic spin exchange
is different from the isotropic value.


  Existing data-driven methods for garment animation, usually driven by linear
skinning, although effective on tight garments, do not handle loose-fitting
garments with complex deformations well. To address these limitations, we
develop a garment generative model based on deformation decomposition to
efficiently simulate loose garment deformation without directly using linear
skinning. Specifically, we learn a garment generative space with the proposed
generative model, where we decouple the latent representation into unposed
deformed garments and dynamic offsets during the decoding stage. With explicit
garment deformations decomposition, our generative model is able to generate
complex pose-driven deformations on canonical garment shapes. Furthermore, we
learn to transfer the body motions and previous state of the garment to the
latent space to regenerate dynamic results. In addition, we introduce a detail
enhancement module in an adversarial training setup to learn high-frequency
wrinkles. We demonstrate our method outperforms state-of-the-art data-driven
alternatives through extensive experiments and show qualitative and
quantitative analysis of results.


  We study an extension of Plotkin's call-by-value lambda-calculus via two
commutation rules (sigma-reductions). These commutation rules are sufficient to
remove harmful call-by-value normal forms from the calculus, so that it enjoys
elegant characterizations of many semantic properties. We prove that this
extended calculus is a conservative refinement of Plotkin's one. In particular,
the notions of solvability and potential valuability for this calculus coincide
with those for Plotkin's call-by-value lambda-calculus. The proof rests on a
standardization theorem proved by generalizing Takahashi's approach of parallel
reductions to our set of reduction rules. The standardization is weak (i.e.
redexes are not fully sequentialized) because of overlapping interferences
between reductions.


  Several Fe chalcogenide superconductors without hole pockets at the Fermi
level display high temperature superconductivity, in apparent contradiction to
naive spin fluctuation pairing arguments. Recently, scanning tunneling
microscopy measurements have measured the influence of impurities on some of
these materials, and claimed that non-magnetic impurities do not create in-gap
states, leading to the conclusion that the gap must be $s_{++}$, i.e.
conventional $s$ wave with no gap sign change. Here we critique this argument,
and give various ways sign-changing gaps can be consistent with the absence of
such bound states. In particular, we calculate the bound states for an $s_\pm$
system with a hole pocket below the Fermi level, and show that the nonmagnetic
impurity bound state energy generically tracks the gap edge $E_{min}$ in the
system, thereby rendering it unobservable. A failure to observe a bound state
in the case of a nonmagnetic impurity can therefore not be used as an argument
to exclude sign-changing pairing states.


  We construct embeddings G of the category of graphs into categories of
R-modules over a commutative ring R which are almost full in the sense that the
maps induced by the functoriality of G
  R[Hom_Graphs(X,Y)] --> Hom_R(GX,GY) are isomorphisms. The symbol R[S] above
denotes the free R-module with the basis S. This implies that, for any
cotorsion-free ring R, the categories of R-modules are not less complicated
than the category of graphs. A similar embedding of graphs into the category of
vector spaces with four distinguished subspaces (over any field, e.g. F_2={0,1}
is obtained).


  One of the most striking examples for the production of particles out of the
quantum vacuum due to external conditions is cosmological particle creation,
which is caused by the expansion or contraction of the Universe. Already in
1939, Schr\"odinger understood that the cosmic evolution could lead to a mixing
of positive and negative frequencies and that this "would mean production or
annihilation of matter, merely by the expansion". Later this phenomenon was
derived via more modern techniques of quantum field theory in curved
space-times by Parker (who apparently was not aware of Schr\"odinger's work)
and subsequently has been studied in numerous publications. Even though
cosmological particle creation typically occurs on extremely large length
scales, it is one of the very few examples for such fundamental effects where
we actually may have observational evidence: According to the inflationary
model of cosmology, the seeds for the anisotropies in the cosmic microwave
background (CMB) and basically all large scale structures stem from this
effect. In this Chapter, we shall provide a brief discussion of this phenomenon
and sketch a possibility for an experimental realization via an analogue in the
laboratory.


  Action spotting in soccer videos is the task of identifying the specific time
when a certain key action of the game occurs. Lately, it has received a large
amount of attention and powerful methods have been introduced. Action spotting
involves understanding the dynamics of the game, the complexity of events, and
the variation of video sequences. Most approaches have focused on the latter,
given that their models exploit the global visual features of the sequences. In
this work, we focus on the former by (a) identifying and representing the
players, referees, and goalkeepers as nodes in a graph, and by (b) modeling
their temporal interactions as sequences of graphs. For the player
identification, or player classification task, we obtain an accuracy of 97.72%
in our annotated benchmark. For the action spotting task, our method obtains an
overall performance of 57.83% average-mAP by combining it with other
audiovisual modalities. This performance surpasses similar graph-based methods
and has competitive results with heavy computing methods. Code and data are
available at https://github.com/IPCV/soccer_action_spotting.


  Many-body localization is a striking mechanism that prevents interacting
quantum systems from thermalizing. The absence of thermalization behaviour
manifests itself, for example, in a remanence of local particle number
configurations, a quantity that is robust over a parameter range. Local
particle numbers are directly accessible in programmable quantum simulators, in
systems of cold atoms even in two spatial dimensions. Yet, the classical
simulation aimed at building trust in quantum simulations is highly
challenging. In this work, we present a comprehensive tensor network simulation
of a many-body localized systems in two spatial dimensions using a variant of
an iPEPS algorithm. The required translational invariance can be restored by
implementing the disorder into an auxiliary spin system, providing an exact
disorder average under dynamics. We can quantitatively assess signatures of
many-body localization for the infinite system: Our methods are powerful enough
to provide crude dynamical estimates for the transition between localized and
ergodic phases. Interestingly, in this setting of finitely many disorder
values, which we also compare with simulations involving non-interacting
fermions and for which we discuss the emergent physics, localization emerges in
the interacting regime, for which we provide an intuitive argument, while
Anderson localization is absent.


  In this work, we propose the Informed Batch Belief Trees (IBBT) algorithm for
motion planning under motion and sensing uncertainties. The original stochastic
motion planning problem is divided into a deterministic motion planning problem
and a graph search problem. We solve the deterministic planning problem using
sampling-based methods such as PRM or RRG to construct a graph of nominal
trajectories. Then, an informed cost-to-go heuristic for the original problem
is computed based on the nominal trajectory graph. Finally, we grow a belief
tree by searching over the graph using the proposed heuristic. IBBT interleaves
between batch state sampling, nominal trajectory graph construction, heuristic
computing, and search over the graph to find belief space motion plans. IBBT is
an anytime, incremental algorithm. With an increasing number of batches of
samples added to the graph, the algorithm finds motion plans that converge to
the optimal one. IBBT is efficient by reusing results between sequential
iterations. The belief tree searching is an ordered search guided by an
informed heuristic. We test IBBT in different planning environments. Our
numerical investigation confirms that IBBT finds non-trivial motion plans and
is faster compared with previous similar methods.


  We present evidence for a Galactic North-South asymmetry in the number
density and bulk velocity of solar neighborhood stars. The number density
profile, which is derived from main-sequence stars in the Sloan Digital Sky
Survey, shows a (North - South)/(North + South) deficit at |z| ~ 400 pc and an
excess at |z| ~ 800 pc. The bulk velocity profile, which is derived from the
Sloan Extension for Galactic Understanding and Exploration, shows a gradual
trend across the Galactic midplane as well as smaller-scale features. We
speculate that the North-South asymmetry, which has the appearance of a
wavelike perturbation, is intrinsic to the disk. We explore the physics of this
phenomenon through an analysis of the linearized Boltzmann and Poisson
equations and through one-dimensional simulations. The perturbation may be
excited by the passage of a satellite galaxy or dark matter subhalo through the
Galactic disk, in which case we are witnessing a recent disk-heating event.


  Given a locally finite leafless tree $ T $, various algebraic groups over
local fields might appear as closed subgroups of $ \text{Aut} (T)$. We show
that the set of closed cocompact subgroups of $ \text{Aut} (T)$ that are
isomorphic to a quasi-split simple algebraic group is a closed subset of the
Chabauty space of $ \text{Aut} (T)$. This is done via a study of the integral
Bruhat$-$Tits model of $ \text{SL}_2 $ and $ \text{SU}_3^{L/K} $, that we carry
on over arbitrary local fields, without any restriction on the (residue)
characteristic. In particular, we show that in residue characteristic $ 2 $,
the Tits index of simple algebraic subgroups of $ \text{Aut} (T)$ is not always
preserved under Chabauty limits.


  The electronic and structural properties of excitons and trions in monolayer
transition metal dichalcogenides are investigated using both a multiband and a
single-band model. In the multiband model we construct the excitonic
Hamiltonian in the product base of the single-particle states at the conduction
and valence band edges. We decouple the corresponding energy eigenvalue
equation and solve the resulting differential equation self-consistently, using
the finite element method (FEM), to determine the energy eigenvalues and the
wave functions. As a comparison, we also consider the simple single-band model
which is often used in numerical studies. We solve the energy eigenvalue
equation using the FEM as well as with the stochastic variational method (SVM)
in which a variational wave function is expanded in a basis of a large number
of correlated Gaussians. We find good agreement between the results of both
methods, as well as with other theoretical works for excitons, and we also
compare with available experimental data. For trions the agreement between both
methods is not as good due to our neglect of angular correlations when using
the FEM. Finally, when comparing the two models, we see that the presence of
the valence bands in the mutiband model leads to differences with the
single-band model when (interband) interactions are strong.


  A large anomalous Hall effect (AHE) has recently been observed in the
intercalated transition metal dichalcogenide (TMDC) Co$_{1/3}$NbS$_{2}$ below a
known magnetic phase transition at $T_N$ = 29 K. The spins in this material are
widely believed to order in a highly symmetric collinear antiferromagnetic
configuration, causing extensive debate about how reports of an AHE can be
reconciled with such a state. In this article, we address this controversy by
presenting new neutron diffraction data on single crystals of
Co$_{1/3}$NbS$_{2}$ and an analysis that implies that moments in this material
order into a non-collinear configuration, but one that maintains the same
refelction symmetries as the collinear phase. We present new transport and
magneto-optic Kerr measurements which show that AHE signatures persist below
$T_N$ to temperatures as low as $T$ = 5 K and firmly associate them with the
long-range antiferromagnetic order. Finally, we show that these AHE signatures
can be quantitatively reproduced by density functional theory (DFT)
calculations based on the lattice and spin state determined with neutron
diffraction. These combined findings establishes the veracity of the 'crystal
Hall effect' picture, which shows how such effects can emerge from the shape of
magnetic orbitals in compounds containing chiral lattice symmetry regardless of
the symmetry of the ordered spin configuration. These results illuminate a new
path for the discovery of anomalous Hall materials and motivate a targeted
study of the transport properties of intercalated TMDCs and other compounds
containing antiferromagnetic order and chiral lattice symmetry.


  We study several aspects of the regular deformations of completely integrable
systems. Namely, we prove the existence of a Hamiltonian normal form for these
deformations and we show the necessary and sufficient conditions a perturbation
has to satisfy in order for the perturbed Hamiltonian to be a first order
deformation.


  Composition, atomic structure, and electronic properties of TM$_x$Mg$_y$O$_z$
clusters (TM = Cr, Ni, Fe, Co, $x+y \leq 3$) at realistic temperature $T$ and
partial oxygen pressure $p_{\textrm{O}_2}$ conditions are explored using the
{\em ab initio} atomistic thermodynamics approach. The low-energy isomers of
the different clusters are identified using a massively parallel cascade
genetic algorithm at the hybrid density-functional level of theory. On
analyzing a large set of data, we find that the fundamental gap E$_\textrm{g}$
of the thermodynamically stable clusters are strongly affected by the presence
of Mg-coordinated O$_2$ moieties. In contrast, the nature of the transition
metal does not play a significant role in determining E$_\textrm{g}$. Using
E$_\textrm{g}$ of a cluster as a descriptor of its redox properties, our
finding is against the conventional belief that the transition metal plays the
key role in determining the electronic and therefore chemical properties of the
clusters. High reactivity may be correlated more strongly with oxygen content
in the cluster than with any specific TM type.


  This paper provides an analysis of patent activity in the field of quantum
information processing. Data from the PatentScope database from the years
1993-2011 was used. In order to predict the future trends in the number of
filed patents time series models were used.


  Point cloud registration is a fundamental problem in 3D computer vision,
graphics and robotics. For the last few decades, existing registration
algorithms have struggled in situations with large transformations, noise, and
time constraints. In this paper, we introduce Deep Gaussian Mixture
Registration (DeepGMR), the first learning-based registration method that
explicitly leverages a probabilistic registration paradigm by formulating
registration as the minimization of KL-divergence between two probability
distributions modeled as mixtures of Gaussians. We design a neural network that
extracts pose-invariant correspondences between raw point clouds and Gaussian
Mixture Model (GMM) parameters and two differentiable compute blocks that
recover the optimal transformation from matched GMM parameters. This
construction allows the network learn an SE(3)-invariant feature space,
producing a global registration method that is real-time, generalizable, and
robust to noise. Across synthetic and real-world data, our proposed method
shows favorable performance when compared with state-of-the-art geometry-based
and learning-based registration methods.


  We characterize for the first time the performances of IBM quantum chips as
quantum batteries, specifically addressing the single-qubit Armonk processor.
By exploiting the Pulse access enabled to some of the IBM Quantum processors
via the Qiskit package, we investigate advantages and limitations of different
profiles for classical drives used to charge these miniaturized batteries,
establishing the optimal compromise between charging time and stored energy.
Moreover, we consider the role played by various possible initial conditions on
the functioning of the quantum batteries. As main result of our analysis, we
observe that unavoidable errors occurring in the initialization phase of the
qubit, which can be detrimental for quantum computing applications, only
marginally affects energy transfer and storage. This can lead
counter-intuitively to improvements of the performances. This is a strong
indication of the fact that IBM quantum devices are already in the proper range
of parameters to be considered as good and stable quantum batteries, comparable
to state of the art devices recently discussed in literature.


  We explore the role of parametrizations for nonperturbative QCD functions in
global analyses, with a specific application to extending a phenomenological
analysis of the parton distribution functions (PDFs) in the charged pion
realized in the xFitter fitting framework. The parametrization dependence of
PDFs in our pion fits substantially enlarges the uncertainties from the
experimental sources estimated in the previous analyses. We systematically
explore the parametrization dependence by employing a novel technique to
automate generation of polynomial parametrizations for PDFs that makes use of
B\'ezier curves. This technique is implemented in a C++ module Fant\^omas that
is included in the xFitter program. Our analysis reveals that the sea and gluon
distributions in the pion are not well disentangled, even when considering
measurements in leading-neutron deep inelastic scattering. For example, the
pion PDF solutions with a vanishing gluon and large quark sea are still
experimentally allowed, which elevates the importance of ongoing lattice and
nonperturbative QCD calculations, together with the planned pion scattering
experiments, for conclusive studies of the pion structure.


  In a geo-distributed database, data shards and their respective replicas are
deployed in distinct datacenters across multiple regions, enabling
regional-level disaster recovery and the ability to serve global users locally.
However, transaction processing in geo-distributed databases requires multiple
cross-region communications, especially during the commit phase, which can
significantly impact system performance.
  To optimize the performance of geo-distributed transactions, we propose
Decentralized Two-phase Commit (D2PC), a new transaction commit protocol aiming
to minimize the negative impact of cross-region communication. In D2PC, we
employ multiple co-coordinators that perform commit coordination in parallel.
Each co-coordinator is responsible for collecting 2PC votes and making a
PreCommit decision in its local region. This approach allows for the concurrent
invocation of multiple cross-region network round trips, and each region can
conclude its concurrency control locally before replication is complete, thus
significantly reducing the chances of blocking and enhancing system
concurrency. Moreover, we propose the bypass leader replication reply method,
leveraging decentralized co-coordinators to bypass the leader for message
transmission, thereby reducing the commit latency. Experimental results have
demonstrated that D2PC can reduce commit latency by 43% and improve throughput
by up to 2.43 times compared to the existing alternative geo-distributed
transaction processing methods.


  In this paper, we explore the interior dynamics of neutral and charged black
holes. Scalar collapses in flat, Schwarzschild, and Reissner-Nordstrom
geometries are simulated. We examine the dynamics in the vicinities of the
central singularity of a Schwarzschild black hole and of the inner horizon of a
Reissner-Nordstrom black hole. In simulating scalar collapses in Schwarzschild
and Reissner-Nordstrom geometries, Kruskal and Kruskal-like coordinates are
used, respectively, with the presence of a scalar field being taken into
account. It is found that, besides near the inner horizons of
Reissner-Nordstrom and Kerr black holes, mass inflation also takes place near
the central singularity in neutral scalar collapse. Approximate analytic
expressions for different types of mass inflation are partially obtained via a
close interplay between numerical and analytical approaches and an examination
of the connections between Schwarzschild black holes, Reissner-Nordstrom black
holes, neutral collapse, and charge scattering. We argue that the mass
inflations near the central singularity and the inner horizon are related to
the localness of the dynamics in strong gravity regions. This is in accord with
the Belinskii, Khalatnikov, and Lifshitz conjecture.


  Let ${\{K_m\}_{m\geq 4}}$ be the family of non-normal totally real cubic
number fields defined by the irreducible cubic polynomial
$f_m(x)=x^3-mx^2-(m+1)x-1$, where $m$ is an integer with $m\geq 4$. In this
paper, we will give a class number one criterion for $K_m$.


  Sintered samples of monoclinic zirconia (alpha-ZrO2) have been irradiated at
room temperature with 6.0-GeV Pb ions in the electronic slowing down regime.
X-ray diffraction (XRD) and micro-Raman spectroscopy measurements showed
unambiguously that a transition to the 'metastable' tetragonal phase
(beta-ZrO2) occurred at a fluence of 6.5x10^12 cm-2 for a large electronic
stopping power value (approx 32.5 MeV $\mu$m-1). At a lower fluence of
1.0x10^12 cm-2, no such phase transformation was detected. The
back-transformation from beta- to alpha-ZrO2 induced by isothermal or
isochronal thermal annealing was followed by XRD analysis. The
back-transformation started at an onset temperature around 500 K and was
completed by 973 K. Plots of the residual tetragonal phase fraction deduced
from XRD measurements versus annealing temperature or time are analyzed with
first- or second-order kinetic models. An activation energy close to 1 eV for
the back-transformation process is derived either from isothermal annealing
curves, using the so-called "cross-cut" method, or from the isochronal
annealing curve, using a second-order kinetic law. Correlation with the thermal
recovery of ion-induced paramagnetic centers monitored by EPR spectroscopy is
discussed. Effects of crystallite size evolution and oxygen migration upon
annealing are also addressed.


  We investigate the current-voltage characteristics of high-transparency
superconductor-insulator-normal metal (SIN) junctions with the specific tunnel
resistance below 30 kOhm per square micron. The junctions were fabricated from
different superconducting and normal conducting materials, including Nb, Al,
AuPd and Cu. The subgap leakage currents were found to be appreciably larger
than those given by the standard tunnelling model. We explain our results using
the model of two-electron tunnelling in the coherent diffusive transport
regime. We demonstrate that even in the high-transparency SIN-junctions, a
noticeable reduction of the subgap current can be achieved by splitting a
junction into several submicron sub-junctions. These structures can be used as
nonlinear low-noise shunts in Rapid-Single-Flux-Quantum (RSFQ) circuitry for
controlling Josephson qubits.


  Deep neural networks have proved to be a very effective way to perform
classification tasks. They excel when the input data is high dimensional, the
relationship between the input and the output is complicated, and the number of
labeled training examples is large. But it is hard to explain why a learned
network makes a particular classification decision on a particular test case.
This is due to their reliance on distributed hierarchical representations. If
we could take the knowledge acquired by the neural net and express the same
knowledge in a model that relies on hierarchical decisions instead, explaining
a particular decision would be much easier. We describe a way of using a
trained neural net to create a type of soft decision tree that generalizes
better than one learned directly from the training data.


  We propose to compute a sparse approximate inverse Cholesky factor $L$ of a
dense covariance matrix $\Theta$ by minimizing the Kullback-Leibler divergence
between the Gaussian distributions $\mathcal{N}(0, \Theta)$ and $\mathcal{N}(0,
L^{-\top} L^{-1})$, subject to a sparsity constraint. Surprisingly, this
problem has a closed-form solution that can be computed efficiently, recovering
the popular Vecchia approximation in spatial statistics. Based on recent
results on the approximate sparsity of inverse Cholesky factors of $\Theta$
obtained from pairwise evaluation of Green's functions of elliptic
boundary-value problems at points $\{x_{i}\}_{1 \leq i \leq N} \subset
\mathbb{R}^{d}$, we propose an elimination ordering and sparsity pattern that
allows us to compute $\epsilon$-approximate inverse Cholesky factors of such
$\Theta$ in computational complexity $\mathcal{O}(N \log(N/\epsilon)^d)$ in
space and $\mathcal{O}(N \log(N/\epsilon)^{2d})$ in time. To the best of our
knowledge, this is the best asymptotic complexity for this class of problems.
Furthermore, our method is embarrassingly parallel, automatically exploits
low-dimensional structure in the data, and can perform Gaussian-process
regression in linear (in $N$) space complexity. Motivated by the optimality
properties of our methods, we propose methods for applying it to the joint
covariance of training and prediction points in Gaussian-process regression,
greatly improving stability and computational cost. Finally, we show how to
apply our method to the important setting of Gaussian processes with additive
noise, sacrificing neither accuracy nor computational complexity.


  We propose a novel hybrid high-order method (HHO) to approximate singularly
perturbed fourth-order PDEs on domains with a possibly curved boundary. The two
key ideas in devising the method are the use of a Nitsche-type boundary penalty
technique to weakly enforce the boundary conditions and a scaling of the
weighting parameter in the stabilization operator that compares the singular
perturbation parameter to the square of the local mesh size. With these ideas
in hand, we derive stability and optimal error estimates over the whole range
of values for the singular perturbation parameter, including the zero value for
which a second-order elliptic problem is recovered. Numerical experiments
illustrate the theoretical analysis.


  We study the distribution of vacuum polarization charge induced by a Coulomb
impurity in massive graphene. By analytically computing the polarization
function, we show that the charge density is distributed in space in a
non-trivial fashion, and on a characteristic length-scale set by the effective
Compton wavelength. The density crosses over from a logarithmic behavior below
this scale, to a power law variation above it. Our results in the continuum
limit are confirmed by explicit diagonalization of the corresponding
tight-binding model on a finite-size lattice. Electron-electron interaction
effects are also discussed.


  We have begun a study of quantum ferroelectrics and paraelectrics. Simple 2D
short-range lattice model hamiltonians are constructed, keeping in mind the
phenomenology of real perovskite systems, like $SrTiO_{3}$ and $KTaO_{3}$.
Pertinent quantum tunneling phenomena, and the presence of an ice-like
constraint are demonstrated. The two simplest models, namely a plain quantum
four-state clock model, and a constrained one, are then studied in some detail.
We show the equivalence of the former, but not of the latter, to a quantum
Ising model. For the latter, we describe a very good analytical wavefunction
valid in the special case of zero coupling ($J = 0$). In order to study the
full quantum statistical mechanics of both models, a Path Integral Monte Carlo
calculation is set up, and implemented with a technique, which even in the
constrained case permits a good convergence for increasing time slice number
$m$. The method is applied first to the unconstrained model, which serves as a
check, and successively to the constrained quantum four-state clock model. It
is found that in both cases, a quantum phase transition still takes place at
finite coupling J, between a ferroelectric and a quantum paraelectric state,
even when the constraint hinders disordering of the ferroelectric state. This
model paraelectric state has a finite excitation gap, and no broken symmetry.
The possible role of additional ("oxygen hopping") kinetic terms in making
closer contact with the known phenomenology of $SrTiO_{3}$ is discussed.


  The approximability of a convex body is a number which measures the
difficulty to approximate that body by polytopes. We prove that twice the
approximability is equal to the volume entropy for a Hilbert geometry in
dimension two end three and that in higher dimension it is a lower bound of the
entropy.
  As a corollary we solve the entropy upper bound conjecture in dimension three
and give a new proof in dimension two from the one found in
Berck-Bernig-Vernicos (arXiv:0810.1123v2, published).


  Graph neural networks are a popular variant of neural networks that work with
graph-structured data. In this work, we consider combining graph neural
networks with the energy-based view of Grathwohl et al. (2019) with the aim of
obtaining a more robust classifier. We successfully implement this framework by
proposing a novel method to ensure generation over features as well as the
adjacency matrix and evaluate our method against the standard graph
convolutional network (GCN) architecture (Kipf & Welling (2016)). Our approach
obtains comparable discriminative performance while improving robustness,
opening promising new directions for future research for energy-based graph
neural networks.


  We consider the nonlinear Cauchy problem for $ \Psi $- Hilfer fractional
differential equations and investigate the existence, interval of existence and
uniqueness of solution in the weighted space of functions. The continuous
dependence of solutions on initial conditions is proved via Weissinger fixed
point theorem. Picard's successive approximation method has been developed to
solve nonlinear Cauchy problem for differential equations with $ \Psi $- Hilfer
fractional derivative and an estimation have been obtained for the error bound.
Further, by Picard's successive approximation, we derive the representation
formula for the solution of linear Cauchy problem for $ \Psi $-Hilfer
fractional differential equation with constant coefficient and variable
coefficient in terms of Mittag-Leffler function and Generalized (Kilbas-Saigo)
Mittag-Leffler function.


  Let $f$ be an arbitrary integrable function on a finite measure space
$(X,\Sigma, \nu)$. We characterise the extreme points of the set $\Omega (f)$
of all measurable functions on $(X,\Sigma, \nu)$ majorised by $f$, providing a
complete answer to a problem raised by W.A.J. Luxemburg in 1967. Moreover, we
obtain a noncommutative version of this result.


  Succinct data structures give space-efficient representations of large
amounts of data without sacrificing performance. They rely one cleverly
designed data representations and algorithms. We present here the formalization
in Coq/SSReflect of two different tree-based succinct representations and their
accompanying algorithms. One is the Level-Order Unary Degree Sequence, which
encodes the structure of a tree in breadth-first order as a sequence of bits,
where access operations can be defined in terms of Rank and Select, which work
in constant time for static bit sequences. The other represents dynamic bit
sequences as binary balanced trees, where Rank and Select present a low
logarithmic overhead compared to their static versions, and with efficient
insertion and deletion. The two can be stacked to provide a dynamic
representation of dictionaries for instance. While both representations are
well-known, we believe this to be their first formalization and a needed step
towards provably-safe implementations of big data.


  Observations of large amount of massive galaxies with relatively old
populations found at high redshifts are challenging galaxy formation scenarios
within standard cosmology. Precise determinations of the average age of these
galaxies would be useful for the discussion of this problem. Here we carry out
a better constraint of the age of 200 V-shaped SED non-AGN galaxies at
redshifts $2<z<4$ of the catalog of FourStar Galaxy Evolution Survey,
identified by V-shape in their spectral energy distribution (SED) with a Lyman
and a Balmer break. SED fitting include a main stellar population in addition
to a residual younger population and extinction. The galaxies are younger at
higher redshift on average. However, for the galaxies with $z>2.5$, we do not
see a significant evolution of their average age, with all average ages of
galaxies mostly remaining between 1 and 2 Gyr. Our research find that most
massive galaxies ($\sim 10^{10} M_\odot$ ) are older (typically $>\sim 1$ Gyr
old) and formed earlier than less massive galaxies in our sample.


  Barrow proposed that the area law of the horizon entropy might receive a
"fractal correction" $S\propto A^{1+\Delta/2}$ due to quantum gravitational
effects, with $0\leqslant \Delta \leqslant 1$ measures the deviation from the
standard area law. While such a modification has been widely studied in the
literature, its corresponding theory of gravity has not been discussed. We
follow Jacobson's approach to derive the modified gravity theory (interpreted
as an effective theory), and find that in the stationary case the resulting
theory only differs from general relativity by a re-scaled cosmological
constant. Consequently in asymptotically flat stationary spacetimes the theory
is identical to general relativity. The theory is not applicable when there is
no horizon; the multi-horizon case is complicated. We emphasize on the
importance of identifying the correct thermodynamic mass in a theory with
modified thermodynamics to avoid inconsistencies. We also comment on the
Hawking evaporation rate beyond the effective theory. In addition, we show that
the Bekenstein bound is satisfied if the thermodynamic mass is used as the
energy, up to a constant prefactor. We briefly comment on the Tsallis entropy
case as well. Interestingly, for the latter, the requirement that Bekenstein
bound holds imposes a lower bound on the non-extensive parameter: $\delta >
1/2$, which unfortunately rules out the previously suggested possibility that
the expansion of the universe can accelerate with normal matter field alone.


  We use a method of Goulden and Jackson to bound freq_1(K), the limiting
frequency of 1 in the Kolakoski word K. We prove that |freq_1(K) - 1/2| <=
17/762, assuming the limit exists, and establish the semi-rigorous bound
|freq_1(K) - 1/2| <= 1/46.


  We present a theoretical analysis of the evaporative cooling of a
magnetically guided atomic beam by means of discrete radio-frequency antennas.
First we derive the changes in flux and temperature, as well as in collision
rate and phase-space density, for a single evaporation step. Next we show how
the occurrence of collisions during the propagation between two successive
antennas can be probed. Finally, we discuss the optimization of the evaporation
ramp with several antennas to reach quantum degeneracy. We estimate the number
of antennas required to increase the phase-space density by several orders of
magnitude. We find that at least 30 antennas are needed to gain a factor $10^8$
in phase-space density.


  We consider partially hyperbolic attractors for non-singular endomorphisms
admitting an invariant stable bundle and a positively invariant cone field with
non-uniform cone expansion at a positive Lebesgue measure set of points. We
prove volume lemmas for both Lebesgue measure on the topological basin of the
attractor and the SRB measure supported on the attractor.As a consequence under
a mild assumption we prove exponential large deviation bounds for the
convergence of Birkhoff averages associated to continuous observables with
respect to the SRB measure.


  We report on the experimental findings of a thin-slit grid diffraction of a
coherent light beam with sinusoidal amplitude. We create the sinusoidal
amplitude by placing a thin-slit grid at the center of the dark fringes of an
interference pattern resulting from laser light passing through a dual pinhole.
The experimental results show good agreement with diffraction calculations of a
thin-slit grid placed at the center of the dark fringes produced by two
coherent beams that intersect at small angle. The results are applied to
wire-grid diffraction in the Afshar experiment.


  End-to-end production of object tracklets from high resolution video in
real-time and with high accuracy remains a challenging problem due to the cost
of object detection on each frame. In this work we present Localization-based
Tracking (LBT), an extension to any tracker that follows the tracking by
detection or joint detection and tracking paradigms. Localization-based
Tracking focuses only on regions likely to contain objects to boost detection
speed and avoid matching errors. We evaluate LBT as an extension to two example
trackers (KIOU and SORT) on the UA-DETRAC and MOT20 datasets. LBT-extended
trackers outperform all other reported algorithms in terms of PR-MOTA, PR-MOTP,
and mostly tracked objects on the UA-DETRAC benchmark, establishing a new
state-of-the art. relative to tracking by detection with KIOU, LBT-extended
KIOU achieves a 25% higher frame-rate and is 1.1% more accurate in terms of
PR-MOTA on the UA-DETRAC dataset. LBT-extended SORT achieves a 62% speedup and
a 3.2% increase in PR-MOTA on the UA-DETRAC dataset. On MOT20, LBT-extended
KIOU has a 50% higher frame-rate than tracking by detection and is 0.4% more
accurate in terms of MOTA. As of submission time, our LBT-extended KIOU tracker
places 10th overall on the MOT20 benchmark.


  Homological mirror symmetry predicts that there is a relation between
autoequivalence groups of derived categories of coherent sheaves on Calabi-Yau
varieties, and the symplectic mapping class groups of symplectic manifolds. In
this paper, as an analogue of Dehn twists for mapping class groups of closed
oriented real surfaces, we study spherical twists for derived categories of
algebraic varieties. We introduce the intersection number and relate it to
group-theoretic properties of spherical twists. As an application, we compute
the center of autoequivalence groups of derived categories of K3 surfaces.


  The algebra of diffeomorphisms derived from general coordinate
transformations on commuting coordinates is represented by differential
operators on noncommutative spaces. The algebra remains unchanged, the
comultiplication however is deformed, that way we have found a deformed
bialgebra of diffeomorphisms. Scalar, vector and tensor fields are defined with
appropriate transformation laws under the deformed algebra and a differential
calculus is developed. For pedagogical reasons the formalism is developed for
the $\theta$-deformed space as it is the best known example of deformed spaces.


  The use of fundus images for the early screening of eye diseases is of great
clinical importance. Due to its powerful performance, deep learning is becoming
more and more popular in related applications, such as lesion segmentation,
biomarkers segmentation, disease diagnosis and image synthesis. Therefore, it
is very necessary to summarize the recent developments in deep learning for
fundus images with a review paper. In this review, we introduce 143 application
papers with a carefully designed hierarchy. Moreover, 33 publicly available
datasets are presented. Summaries and analyses are provided for each task.
Finally, limitations common to all tasks are revealed and possible solutions
are given. We will also release and regularly update the state-of-the-art
results and newly-released datasets at https://github.com/nkicsl/Fundus Review
to adapt to the rapid development of this field.


  The structure of $\Delta\Delta$ dibaryon is studied in the extended chiral
SU(3) quark model in which vector meson exchanges are included. The effect from
the vector meson fields is very similar to that from the one-gluon exchange
(OGE) interaction. Both in the chiral SU(3) quark model and in the extended
chiral SU(3) quark model, the resultant mass of the $\Delta\Delta$ dibaryon is
lower than the threshold of the $\Delta\Delta$ channel but higher than that of
the $\Delta N\pi$ channel.


  We consider a three-dimensional Riemannian manifold equipped with two
circulant structures - a metric g and a structure q, which is an isometry with
respect to g and the third power of q is minus identity. We discuss some
curvature properties of this manifold, we give an example of such a manifold
and find a condition for q to be parallel with respect to the Riemannian
connection of g.


  The ability to place objects in the environment is an important skill for a
personal robot. An object should not only be placed stably, but should also be
placed in its preferred location/orientation. For instance, a plate is
preferred to be inserted vertically into the slot of a dish-rack as compared to
be placed horizontally in it. Unstructured environments such as homes have a
large variety of object types as well as of placing areas. Therefore our
algorithms should be able to handle placing new object types and new placing
areas. These reasons make placing a challenging manipulation task. In this
work, we propose a supervised learning algorithm for finding good placements
given the point-clouds of the object and the placing area. It learns to combine
the features that capture support, stability and preferred placements using a
shared sparsity structure in the parameters. Even when neither the object nor
the placing area is seen previously in the training set, our algorithm predicts
good placements. In extensive experiments, our method enables the robot to
stably place several new objects in several new placing areas with 98%
success-rate; and it placed the objects in their preferred placements in 92% of
the cases.


  We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons
and fermions with delta-interaction and arbitrary internal degrees of freedom
to the case of hard wall boundary conditions. We give an analysis of the ground
state properties of fermionic systems with two internal degrees of freedom,
including expansions of the ground state energy in the weak and strong coupling
limits in the repulsive and attractive regimes.


  We have obtained observations of the ultraviolet spectrum of AM CVn, an
ultra-short-period helium cataclysmic variable, using the Space Telescope
Imaging Spectrograph (STIS) aboard the Hubble Space Telescope (HST). We
obtained data in time-tag mode during two consecutive orbits of HST, covering
1600-3150 and 1140-1710 Angstrom, respectively. The mean spectrum is
approximately flat in f-nu. The absorption profiles of the strong lines of N V,
Si IV, C IV, He II, and N IV are blue-shifted and in some cases asymmetric,
evidencing a wind that is partly occulted by the accretion disk. There is weak
red-shifted emission from N V and He II. The profiles of these lines vary
mildly with time. The light curve shows a decline of ~20% over the span of the
observations. There is also flickering and a 27 s (or 54 s) "dwarf nova
oscillation", revealed in a power-spectrum analysis. The amplitude of this
oscillation is larger at shorter wavelengths. We assemble and illustrate the
spectral energy distribution (s.e.d.) of AM CVn from the ultraviolet to the
near-infrared. Modeling the accretion phenomenon in this binary system can in
principle lead to a robust estimate of the mass accretion rate on to the
central white dwarf, which is of great interest in characterizing the
evolutionary history of the binary system. Inferences about the mass accretion
rate depend strongly on the local radiative properties of the disk, as we
illustrate. Uncertainty in the distance of AM CVn and other parameters of the
binary system presently limit the ability to confidently infer the mass
accretion rate.


  We propose a variant of hybrid inflation which is applicable in a wide class
of supersymmetric grand unified models. The observed temperature perturbations
of cosmic background radiation can be reproduced with natural values of the
parameters of the theory and a grand unification scale which is consistent with
the unification of the minimal supersymmetric standard model gauge couplings as
measured at LEP. The termination of inflation is smooth and does not produce
any topological defects. Finally, we present a specific supersymmetric model
where our smooth hybrid inflationary scenario is realized.


  Motivated by the characterization theorem about the Jensen convexity of
quasiarithmetic means obtained by the authors in 2021, our main goal is to
establish a characterization of the Jensen convexity of quasideviation as well
as of Bajraktarevi\'c means without any additional and unnatural regularity
assumptions.


  In this work we explore the effect of binarity in the decretion disc of Be
stars, in order to explain their variability. To this aim, we performed
smoothed particle hydrodynamics (SPH) simulations on Be binary systems,
following the matter ejected isotropically from the equator of the Be star
towards the base of an isothermal decretion disc. We let the system evolve for
time long enough to be considered at steady state, and focus on the effect of
viscosity for coplanar prograde binary orbits. The disc structure is found to
be locked to the orbital phase, exhibiting also a dependence on the azimuthal
angle.
  Additionally, we present the first results from detailed non-local
thermodynamic equilibrium (non-LTE) radiative transfer calculations of the disc
structure computed with the SPH code. This is achieved by the use of the
three-dimensional (3D) Monte Carlo code HDUST, which can produce predictions
with respect to a series of observables.


  A review is given of the theoretical expectations of the self couplings of
gauge bosons and of the present experimental information on the couplings. The
possibilities for future measurements are also discussed.


  We develop the stub model for the Dirac Quantum Dot, an electron confining
device on a grapheme surface. Analytical results for the average conductance
and the correlation functions are obtained and found in agreement with those
found previously using semiclassical calculation. Comparison with available
data are presented. The results reported here demonstrate the applicability of
Random Matrix Theory in the case of Dirac electrons confined in a stadium.


  I propose a new paired-wavefunction with a parameter that continuously
interpolates from the 1D Jastrow-product to the Majumdar-Ghosh
dimer-wavefunction appropriate for the frustrated Heisenberg $S = 1/2$
antiferromagnet. This spin paired-state constructed in $S_z$ basis is an
alternative to the well-known resonating-valence-bond basis state for
describing the $S = 0$ ground-state with no apparent long-range spin order.
Some numerical evidences are presented.


  We show through simulation that quantum interference in non-sequential double
ionization can be used to control the recollision with subsequent ionization
(RESI) mechanism. This includes the shape, localization and symmetry of RESI
electron-momentum distributions, which may be shifted from a correlated to an
anti-correlated distribution or vice versa, far below the direct ionization
threshold intensity. As a testing ground, we reproduce recent experimental
results by employing specific coherent superpositions of excitation channels.
We examine two types of interference, from electron indistinguishability and
intra-cycle events, and from different excitation channels.


  We study Mott phases and superfluid-insulator (SI) transitions of ultracold
bosonic atoms in a two-dimensional square optical lattice at commensurate
filling and in the presence of a synthetic periodic vector potential
characterized by a strength $p$ and a period $l=qa$, where $q$ is an integer
and $a$ is the lattice spacing. We show that the Schr\"odinger equation for the
non-interacting bosons in the presence of such a periodic vector potential can
be reduced to an one-dimensional Harper-like equation which yields $q$ energy
bands. The lowest of these bands have either single or double minima whose
position within the magnetic Brillouin zone can be tuned by varying $p$ for a
given $q$. Using these energies and a strong-coupling expansion technique, we
compute the phase diagram of these bosons in the presence of a deep optical
lattice. We chart out the $p$ and $q$ dependence of the momentum distribution
of the bosons in the Mott phases near the SI transitions and demonstrate that
the bosons exhibit several re-entrant field-induced SI transitions for any
fixed period $q$. We also predict that the superfluid density of the resultant
superfluid state near such a SI transition has a periodicity $q$ ($q/2$) in
real space for odd (even) $q$ and suggest experiments to test our theory.


  Large-scale graphs are ubiquitous in real-world scenarios and can be trained
by Graph Neural Networks (GNNs) to generate representation for downstream
tasks. Given the abundant information and complex topology of a large-scale
graph, we argue that redundancy exists in such graphs and will degrade the
training efficiency. Unfortunately, the model scalability severely restricts
the efficiency of training large-scale graphs via vanilla GNNs. Despite recent
advances in sampling-based training methods, sampling-based GNNs generally
overlook the redundancy issue. It still takes intolerable time to train these
models on large-scale graphs. Thereby, we propose to drop redundancy and
improve efficiency of training large-scale graphs with GNNs, by rethinking the
inherent characteristics in a graph.
  In this paper, we pioneer to propose a once-for-all method, termed DropReef,
to drop the redundancy in large-scale graphs. Specifically, we first conduct
preliminary experiments to explore potential redundancy in large-scale graphs.
Next, we present a metric to quantify the neighbor heterophily of all nodes in
a graph. Based on both experimental and theoretical analysis, we reveal the
redundancy in a large-scale graph, i.e., nodes with high neighbor heterophily
and a great number of neighbors. Then, we propose DropReef to detect and drop
the redundancy in large-scale graphs once and for all, helping reduce the
training time while ensuring no sacrifice in the model accuracy. To demonstrate
the effectiveness of DropReef, we apply it to recent state-of-the-art
sampling-based GNNs for training large-scale graphs, owing to the high
precision of such models. With DropReef leveraged, the training efficiency of
models can be greatly promoted. DropReef is highly compatible and is offline
performed, benefiting the state-of-the-art sampling-based GNNs in the present
and future to a significant extent.


  Latent block models are used for probabilistic biclustering, which is shown
to be an effective method for analyzing various relational data sets. However,
there has been no statistical test method for determining the row and column
cluster numbers of latent block models. Recent studies have constructed
statistical-test-based methods for stochastic block models, which assume that
the observed matrix is a square symmetric matrix and that the cluster
assignments are the same for rows and columns. In this study, we developed a
new goodness-of-fit test for latent block models to test whether an observed
data matrix fits a given set of row and column cluster numbers, or it consists
of more clusters in at least one direction of the row and the column. To
construct the test method, we used a result from the random matrix theory for a
sample covariance matrix. We experimentally demonstrated the effectiveness of
the proposed method by showing the asymptotic behavior of the test statistic
and measuring the test accuracy.


  Efficiently controlling the trapping process, especially the trapping
efficiency, is central in the study of trap problem in complex systems, since
it is a fundamental mechanism for diverse other dynamic processes. Thus, it is
of theoretical and practical significance to study the control technique for
trapping problem. In this paper, we study the trapping problem in a family of
proposed directed fractals with a deep trap at a central node. The directed
fractals are a generalization of previous undirected fractals by introducing
the directed edge weights dominated by a parameter. We characterize all the
eigenvalues and their degeneracies for an associated matrix governing the
trapping process. The eigenvalues are provided through an exact recursive
relation deduced from the self-similar structure of the fractals. We also
obtain the expressions for the smallest eigenvalue and the mean first-passage
time (MFPT) as a measure of trapping efficiency, which is the expected time for
the walker to first visit the trap. The MFPT is evaluated according to the
proved fact that it is approximately equal to reciprocal of the smallest
eigenvalue. We show that the MFPT is controlled by the weight parameter, by
modifying which, the MFPT can scale superlinealy, linearly, or sublinearly with
the system size. Thus, this work paves a way to delicately controlling the
trapping process in the fractals.


  In this paper we investigate the limit performance of Floating Gossip, a new,
fully distributed Gossip Learning scheme which relies on Floating Content to
implement location-based probabilistic evolution of machine learning models in
an infrastructure-less manner. We consider dynamic scenarios where continuous
learning is necessary, and we adopt a mean field approach to investigate the
limit performance of Floating Gossip in terms of amount of data that users can
incorporate into their models, as a function of the main system parameters.
Different from existing approaches in which either communication or computing
aspects of Gossip Learning are analyzed and optimized, our approach accounts
for the compound impact of both aspects. We validate our results through
detailed simulations, proving good accuracy. Our model shows that Floating
Gossip can be very effective in implementing continuous training and update of
machine learning models in a cooperative manner, based on opportunistic
exchanges among moving users.


  A two-component fermion model with conventional two-body interactions was
recently shown to have anyonic excitations. We here propose a scheme to
physically implement this model by transforming each chain of two two-component
fermions to the two capacitively coupled chains of superconducting devices. In
particular, we elaborate how to achieve the wanted operations to create and
manipulate the topological quantum states, providing an experimentally feasible
scenario to access the topological memory and to build the anyonic
interferometry.


  The effect of a spherical monodromy defect on the entanglement entropy and
central charge $C_T$ of a free conformal scalar field propagating on an
odd-dimensional sphere is investigated. As on even spheres the central charge
becomes negative for a range of the flux parameter, $\delta$, with possible
implications for reflection positivity. The work is mostly numerical but closed
forms are found for the $Z_2$ monodromy ($\delta=1/2$) yielding an explicit
$d\to\infty$ limit, $C_T\to -6/\pi$


  This article investigates why the genus two, supermoduli space of curves will
split in contrast to, potentially, almost all other supermoduli spaces. We use
that the dimension of the odd, versal deformation space of a genus two, super
Riemann surface is two dimensional. As a consequence, the odd versal
deformations can be generated by Schiffer variations at the associated points
of a Szego kernel. This idea is present in D'Hoker and Phong's two loop,
superstring amplitude calculation. We show how this idea, combined with Donagi
and Witten's characterization of supermoduli obstructions, will result in a
splitting of supermoduli space in genus two.


  Creating artistic 3D scenes can be time-consuming and requires specialized
knowledge. To address this, recent works such as ARF, use a radiance
field-based approach with style constraints to generate 3D scenes that resemble
a style image provided by the user. However, these methods lack fine-grained
control over the resulting scenes. In this paper, we introduce Controllable
Artistic Radiance Fields (CoARF), a novel algorithm for controllable 3D scene
stylization. CoARF enables style transfer for specified objects, compositional
3D style transfer and semantic-aware style transfer. We achieve controllability
using segmentation masks with different label-dependent loss functions. We also
propose a semantic-aware nearest neighbor matching algorithm to improve the
style transfer quality. Our extensive experiments demonstrate that CoARF
provides user-specified controllability of style transfer and superior style
transfer quality with more precise feature matching.


  The Bernshtein-Kushnirenko-Khovanskii theorem provides a generic root count
for system of Laurent polynomials in terms of the mixed volume of their Newton
polytopes (i.e., the BKK bound). A recent and far-reaching generalization of
this theorem is the study of birationally invariant intersection index by Kaveh
and Khovanskii. This short note establishes a simple geometric condition on the
equality between the BKK bound and the intersection index for a system of
vector spaces of Laurent polynomials. Applying this, we show that the
intersection index for the algebraic Kuramoto equations equals their BKK bound.


  Grand canonical Monte Carlo simulations have been performed to determine the
adsorption behavior of Ar and Kr atoms on the exterior surface of a rope
(bundle) consisting of many carbon nanotubes. The computed adsorption isotherms
reveal phase transitions associated with the successive creation of quasi-one
dimensional lines of atoms near and parallel to the intersection of two
adjacent nanotubes.


  In this paper, we first propose a cohomological derivation of the celebrated
Euler's Pentagonal Number Theorem. Then we prove an identity that corresponds
to a bosonic extension of the theorem. The proof corresponds to a cohomological
re-derivation of Euler's another celebrated identity.


  The Pauli-Villars regularization is appropriate to discuss the UV sensitivity
of low-energy observables because it mimics how the contributions of new
particles at high energies cancel large quantum corrections from the light
particles in the effective field theory. We discuss the UV sensitivity of the
Casimir energy density and pressure in an extra-dimensional model in this
regularization scheme, and clarify the condition on the regulator fields to
preserve the Lorentz symmetry of the vacuum state. Some of the conditions are
automatically satisfied in spontaneously-broken supersymmetric models, but
supersymmetry is not enough to ensure the Lorentz symmetry. We show that the
necessary regulators can be introduced as bulk fields. We also evaluate the
Casimir energy density with such regulators, and its deviation from the result
obtained in the analytic regularization.


  Deep learning has gained great popularity due to its widespread success on
many inference problems. We consider the application of deep learning to the
sparse linear inverse problem, where one seeks to recover a sparse signal from
a few noisy linear measurements. In this paper, we propose two novel
neural-network architectures that decouple prediction errors across layers in
the same way that the approximate message passing (AMP) algorithms decouple
them across iterations: through Onsager correction. First, we propose a
"learned AMP" network that significantly improves upon Gregor and LeCun's
"learned ISTA." Second, inspired by the recently proposed "vector AMP" (VAMP)
algorithm, we propose a "learned VAMP" network that offers increased robustness
to deviations in the measurement matrix from i.i.d. Gaussian. In both cases, we
jointly learn the linear transforms and scalar nonlinearities of the network.
Interestingly, with i.i.d. signals, the linear transforms and scalar
nonlinearities prescribed by the VAMP algorithm coincide with the values
learned through back-propagation, leading to an intuitive interpretation of
learned VAMP. Finally, we apply our methods to two problems from 5G wireless
communications: compressive random access and massive-MIMO channel estimation.


  We present the first interferometric molecular line and dust emission maps
for the Galactic Center (GC) cloud G0.253+0.016, observed using the Combined
Array for Research in Millimeter--wave Astronomy (CARMA) and the Submillimeter
Array (SMA). This cloud is very dense, and concentrates a mass exceeding the
Orion Molecular Cloud Complex (2x10^5 M_sun) into a radius of only 3pc, but it
is essentially starless. G0.253+0.016 therefore violates "star formation laws"
presently used to explain trends in galactic and extragalactic star formation
by a factor ~45. Our observations show a lack of dense cores of significant
mass and density, thus explaining the low star formation activity. Instead,
cores with low densities and line widths 1km/s---probably the narrowest lines
reported for the GC region to date---are found. Evolution over several 10^5 yr
is needed before more massive cores, and possibly an Arches--like stellar
cluster, could form. Given the disruptive dynamics of the GC region, and the
potentially unbound nature of G0.253+0.016, it is not clear that this evolution
will happen.


  Researchers commonly perform sentiment analysis on large collections of short
texts like tweets, Reddit posts or newspaper headlines that are all focused on
a specific topic, theme or event. Usually, general-purpose sentiment analysis
methods are used. These perform well on average but miss the variation in
meaning that happens across different contexts, for example, the word "active"
has a very different intention and valence in the phrase "active lifestyle"
versus "active volcano". This work presents a new approach, CIDER (Context
Informed Dictionary and sEmantic Reasoner), which performs context-sensitive
linguistic analysis, where the valence of sentiment-laden terms is inferred
from the whole corpus before being used to score the individual texts. In this
paper, we detail the CIDER algorithm and demonstrate that it outperforms
state-of-the-art generalist unsupervised sentiment analysis techniques on a
large collection of tweets about the weather. CIDER is also applicable to
alternative (non-sentiment) linguistic scales. A case study on gender in the UK
is presented, with the identification of highly gendered and sentiment-laden
days. We have made our implementation of CIDER available as a Python package:
https://pypi.org/project/ciderpolarity/.


  The optical properties of a thin-shell wormhole (TSW) with a Hayward profile
is investigated. Adopting the ray-tracing method, we demonstrate that the TSW's
contralateral spacetime is capable of reflecting a significant portion of light
back to the observer spacetime. We analyze the effective potential, light
deflection, and azimuthal angle of the TSW and find that these quantities are
affected by the mass ratio of the black holes (BHs). Specifically, if the mass
of the contralateral spacetime BH is greater than that of the original
spacetime BH, and the impact parameter satisfies the condition $Hb_{\rm
c2}<b_{1}<b_{\rm c1}$, the trajectory of the photon exhibits round-trip
characteristics. Assuming the presence of a thin accretion disk surrounding the
observing spacetime BH, our results indicate that the image formed by the TSW
exhibits additional photon rings and a lensing band compared to an image
produced by a BH alone.


  We study the nonlinear Schr\"odinger equation posed on product spaces
$\mathbf R^n\times \mathcal M^k$, for $n\geq 1$ and $k\geq1$, with $\mathcal
M^k$ any $k$-dimensional compact Riemaniann manifold. The main results concern
global well-posedness and scattering for small data solutions in non-isotropic
Sobolev fractional spaces. In the particular case of $k=2$, $H^1$-scattering is
also obtained.


  The evaporation of black holes into apparently thermal radiation poses a
serious conundrum for theoretical physics: at face value, it appears that in
the presence of a black hole quantum evolution is non-unitary and destroys
information. This information loss paradox has its seed in the presence of a
horizon causally separating the interior and asymptotic regions in a black hole
spacetime. A quantitative resolution of the paradox could take several forms:
(a) a precise argument that the underlying quantum theory is unitary, and that
information loss must be an artifact of approximations in the derivation of
black hole evaporation, (b) an explicit construction showing how information
can be recovered by the asymptotic observer, (c) a demonstration that the
causal disconnection of the black hole interior from infinity is an artifact of
the semiclassical approximation. This review summarizes progress on all these
fronts.


  SARComm is a novel wireless communication system that enables passive
satellite backscatter connectivity using existing spaceborne synthetic aperture
radar (SAR) signals. We demonstrate that SAR signals from the European Space
Agency's Sentinel-1 satellite, used to image Earth's terrain, can be leveraged
to enable low-power ground-to-satellite communication. This paper presents the
first cooperative, on-the-ground target that modulates SAR backscatter to send
information bits and analyzes how to extract them from publicly available
Sentinel-1 datasets. To demonstrate the system, we evaluate the effectiveness
of modulating the radar cross section of corner reflectors both mechanically
and electronically to encode data bits, develop a deployment algorithm to
optimize corner reflector placement, and present a SAR processing pipeline to
enable communication.


  In this paper, we are interested in the $L^p$-estimates of the Boltzmann
equation in the case that the distribution function stays around a travelling
local Maxwellian. For this, we divide both sides of the Boltzmann equation by
the velocity distribution function with a fractional exponent and reformulate
the Boltzmann equation into a regularized one. This amounts to endowing
additional integrability on the collision kernel, which in turn enables us to
apply simple H\"{o}lder type inequalities. Our results cover the whole range of
Lebesgue exponents: $0<p\leq \infty$.


  We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t)
killed at the moving boundary of the cone {(t,x):0<x<t}. This article
determines the parabolic Martin boundary and all harmonic functions associated
with this process. To that end, the asymptotics of Green's functions are
determined along all directions. We also find the exit probabilities at the
edges, the probability of remaining in the cone forever and the laws of the
exit point and exit time. From this, we derive an explicit formula for the
transition kernel of the process. These results arise from two different
methods initially introduced to study random walks. An analytical approach,
developed in the 1970s by Malyshev and based on the steepest descent method on
a Riemann surface, is used to determine the asymptotics of the Green's
functions. A recursive compensation approach, inspired by the method developed
in the 1990s by Adan, Wessels and Zijm, is used to determine the harmonic
functions.


  Na I D absorbing systems toward Type Ia supernovae (SNe Ia) have been
intensively studied over the last decade with the aim of finding circumstellar
material (CSM), which is an indirect probe of the progenitor system. However,
it is difficult to deconvolve CSM components from non-variable, and often
dominant, components created by interstellar material (ISM). We present a
series of high-resolution spectra of SN Ia 2014J from before maximum brightness
to ~250 days after maximum brightness. The late-time spectrum provides unique
information for determining the origin of the Na I D absorption systems. The
deep late-time observation allows us to probe the environment around the SN at
a large scale, extending to ~40 pc. We find that a spectrum of diffuse light in
the vicinity, but not directly in the line-of-sight, of the SN has absorbing
systems nearly identical to those obtained for the "pure" SN line-of-sight.
Therefore, basically all Na I D systems seen toward SN 2014J must originate
from foreground material that extends to at least ~40 pc in projection and none
at the CSM scale. A fluctuation in the column densities at a scale of ~20 pc is
also identified. After subtracting the diffuse, "background" spectrum, the
late-time SN Na I D profile along the SN line-of-sight is consistent with the
profile in the near-maximum brightness spectra. The lack of variability on a ~1
year timescale is consistent with the ISM interpretation for the gas.


  This review discusses a paradigm that has become of increasing importance in
the theory of quantum phase transitions; namely, the coupling of the
order-parameter fluctuations to other soft modes, and the resulting
impossibility of constructing a simple Landau-Ginzburg-Wilson theory in terms
of the order parameter only. The soft modes in question are manifestations of
generic scale invariance, i.e., the appearance of long-range order in whole
regions in the phase diagram. The concept of generic scale invariance, and its
influence on critical behavior, is explained using various examples, both
classical and quantum mechanical. The peculiarities of quantum phase
transitions are discussed, with emphasis on the fact that they are more
susceptible to the effects of generic scale invariance than their classical
counterparts. Explicit examples include: the quantum ferromagnetic transition
in metals, with or without quenched disorder; the metal-superconductor
transition at zero temperature; and the quantum antiferromagnetic transition.
Analogies with classical phase transitions in liquid crystals and classical
fluids are pointed out, and a unifying conceptual framework is developed for
all transitions that are influenced by generic scale invariance.


  Systems biology is an emerging interdisciplinary area of research that
focuses on study of complex interactions in a biological system, such as gene
regulatory networks. The discovery of gene regulatory networks leads to a wide
range of applications, such as pathways related to a disease that can unveil in
what way the disease acts and provide novel tentative drug targets. In
addition, the development of biological models from discovered networks or
pathways can help to predict the responses to disease and can be much useful
for the novel drug development and treatments. The inference of regulatory
networks from biological data is still in its infancy stage. This paper
proposes a recurrent neural network (RNN) based gene regulatory network (GRN)
model hybridized with generalized extended Kalman filter for weight update in
backpropagation through time training algorithm. The RNN is a complex neural
network that gives a better settlement between the biological closeness and
mathematical flexibility to model GRN. The RNN is able to capture complex,
non-linear and dynamic relationship among variables. Gene expression data are
inherently noisy and Kalman filter performs well for estimation even in noisy
data. Hence, non-linear version of Kalman filter, i.e., generalized extended
Kalman filter has been applied for weight update during network training. The
developed model has been applied on DNA SOS repair network, IRMA network, and
two synthetic networks from DREAM Challenge. We compared our results with other
state-of-the-art techniques that show superiority of our model. Further, 5%
Gaussian noise has been added in the dataset and result of the proposed model
shows negligible effect of noise on the results.


  Recently, many streaming algorithms have utilized generalizations of the fact
that the expected maximum distance of any $4$-wise independent random walk on a
line over $n$ steps is $O(\sqrt{n})$. In this paper, we show that $4$-wise
independence is required for all of these algorithms, by constructing a
$3$-wise independent random walk with expected maximum distance
$\Omega(\sqrt{n} \lg n)$ from the origin. We prove that this bound is tight for
the first and second moment, and also extract a surprising matrix inequality
from these results.
  Next, we consider a generalization where the steps $X_i$ are $k$-wise
independent random variables with bounded $p$th moments. For general $k, p$, we
determine the (asymptotically) maximum possible $p$th moment of the supremum of
$X_1 + \dots + X_i$ over $1 \le i \le n$. We highlight the case $k = 4, p = 2$:
here, we prove that the second moment of the furthest distance traveled is
$O(\sum X_i^2)$. For this case, we only need the $X_i$'s to have bounded second
moments and do not even need the $X_i$'s to be identically distributed. This
implies an asymptotically stronger statement than Kolmogorov's maximal
inequality that requires only $4$-wise independent random variables, and
generalizes a recent result of B{\l}asiok.


  The majority of massive stars reside in binary systems, which are expected to
experience mass transfer during their evolution. However, so far the conditions
under which mass transfer leads to a common envelope, and thus possibly to a
merging of both stars, are not well understood. Main uncertainties arise from
the possible swelling of the mass gainer, and from angular momentum loss from
the binary system, during non-conservative mass transfer. We have computed a
dense grid of detailed models of stars accreting mass at constant rates, to
determine their radius increase due to their thermal disequilibrium. While we
find that models with faster than thermal timescale accretion generally expand,
this expansion remains quite limited in the intermediate mass regime even for
accretion rates which exceed the thermal timescale accretion rate by a factor
of 100. Our models of massive accretion stars expand to extreme radii under
those conditions. When the accretion rate exceed the Eddington accretion rate,
our models expand dynamically. We have derived analytical fits to the radius
evolution of our models and a prescription for the borderline between stable
mass transfer and mergers for arbitrary accretion efficiencies. We then apply
our results to grids of binary models adopting various constant mass transfer
efficiencies and angular momentum budgets. We find that the former parameter
has the stronger effect on the outcome of the Roche lobe overflow. Our results
are consistent with detailed binary evolution models, and often lead to a
smaller initial parameter space for stable mass transfer than other recipes in
the literature. We use this method to investigate the origin of the Wolf-Rayet
stars with O star companions in the Small Magellanic Cloud, and find that the
efficiency of the mass transfer process which lead to the formation of the
Wolf-Rayet star was likely below 50%.


  Interest in smart cities is rapidly rising due to the global rise in
urbanization and the wide-scale instrumentation of modern cities. Due to the
considerable infrastructural cost of setting up smart cities and smart
communities, researchers are exploring the use of existing vehicles on the
roads as "message ferries" for the transport data for smart community
applications to avoid the cost of installing new communication infrastructure.
In this paper, we propose an opportunistic data ferry selection algorithm that
strives to select vehicles that can minimize the overall delay for data
delivery from a source to a given destination. Our proposed opportunistic
algorithm utilizes an ensemble of online hiring algorithms, which are run
together in passive mode, to select the online hiring algorithm that has
performed the best in recent history. The proposed ensemble based algorithm is
evaluated empirically using real-world traces from taxies plying routes in
Shanghai, China, and its performance is compared against a baseline of four
state-of-the-art online hiring algorithms. A number of experiments are
conducted and our results indicate that the proposed algorithm can reduce the
overall delay compared to the baseline by an impressive 13% to 258%.


  We investigate a possibility to measure parameters of the Littlest Higgs
model with T-parity at the ILC with sqrt(s) = 500 GeV. The model predicts new
gauge bosons (AH, ZH, and WH), among which the heavy photon (AH) is a candidate
for dark matter. Through Monte Carlo simulations of the process of e+ e- -> AH
ZH, we show that the masses can be determined with accuracies of 16.2% for m_AH
and 4.3% for m_ZH. In additionally, the vacuum expectation value can be
determined with accuracies of 4.3%.


  Quantum calculus based on the right invertible divided difference operator
$D_{\sigma}^{\tau}$ is proposed here in context of algebraic analysis
\cite{DPR}. The linear operator $D_{\sigma}^{\tau}$, specified with the help of
two fixed maps $\sigma\;, \tau\colon M\rightarrow M$, generalizes the quantum
derivative operator used in $h$- or $q$-calculus \cite{kac}. In the domain of
$D_{\sigma}^{\tau}$ there are special elements defined as
$D_{\sigma}^{\tau}$-polynomials and the corresponding Taylor formula is proved.


  Stellar binaries are the most important energy reservoir of star clusters.
Via three-body encounters, binaries can reverse the core collapse and prevent a
star cluster from reaching equipartition. Moreover, binaries are essential for
the formation of stellar exotica, such as blue straggler stars,
intermediate-mass black holes and massive ($\gtrsim{}30$ M$_\odot$) black hole
binaries.


  Let $p\in(1,\infty)$, $q\in[1,\infty)$, $s\in\mathbb{R}$ and $\tau\in[0,
1-\frac{1}{\max\{p,q\}}]$. In this paper, the authors establish the
$\varphi$-transform characterizations of Besov-Hausdorff spaces $B{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ and Triebel-Lizorkin-Hausdorff spaces $F{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ ($q>1$); as applications, the authors then
establish their embedding properties (which on $B{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ is also sharp), smooth atomic and molecular
decomposition characterizations for suitable $\tau$. Moreover, using their
atomic and molecular decomposition characterizations, the authors investigate
the trace properties and the boundedness of pseudo-differential operators with
homogeneous symbols in $B{\dot H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ and $F{\dot
H}_{p,q}^{s,\tau}(\mathbb{R}^n)$ ($q>1$), which generalize the corresponding
classical results on homogeneous Besov and Triebel-Lizorkin spaces when
$p\in(1,\infty)$ and $q\in[1,\infty)$ by taking $\tau=0$.


  Uranus and Neptune are commonly considered ice giants, and it is often
assumed that, in addition to a solar mix of hydrogen and helium, they contain
roughly twice as much water as rock. This classical picture has led to
successful models of their internal structure and has been understood to be
compatible with the composition of the solar nebula during their formation
(Reynolds and Summers 1965; Podolak and Cameron 1974; Podolak and Reynolds
1984; Podolak et al. 1995; Nettelmann et al. 2013). However, the dominance of
water has been recently questioned (Teanby et al. 2020; Helled and Fortney
2020; Podolak et al. 2022). Planetesimals in the outer solar system are
composed mainly of refractory materials, leading to an inconsistency between
the icy composition of Uranus and Neptune and the ice-poor planetesimals they
accreted during formation (Podolak et al. 2022). Here we elaborate on this
problem, and propose a new potential solution. We show that chemical reactions
between planetesimals dominated by organic-rich refractory materials and the
hydrogen in gaseous atmospheres of protoplanets can form large amounts of
methane 'ice'. Uranus and Neptune could thus be compatible with having accreted
refractory-dominated planetesimals, while still remaining icy. Using random
statistical computer models for a wide parameter space, we show that the
resulting methane-rich internal composition could be a natural solution, giving
a good match to the size, mass and moment of inertia of Uranus and Neptune,
whereas rock-rich models appear to only work if a rocky interior is heavily
mixed with hydrogen. Our model predicts a lower than solar hydrogen to helium
ratio, which can be tested. We conclude that Uranus, Neptune and similar
exoplanets could be methane-rich, and discuss why Jupiter and Saturn cannot.


  Metasurfaces are promising tools towards novel designs for flat optics
applications. As such their quality and tolerance to fabrication imperfections
need to be evaluated with specific tools. However, most such tools rely on the
geometrical optics approximation and are not straightforwardly applicable to
metasurfaces. In this Letter, we introduce and evaluate, for metasurfaces,
parameters such as the intercept factor and the slope error usually defined for
solar concentrators in the realm of ray-optics. After proposing definitions
valid in physical optics, we put forward an approach to calculate them. As
examples, we design three different concentrators based on three specific unit
cells and assess them numerically. The concept allows for the comparison of the
efficiency of the metasurfaces, their sensitivities to fabrication
imperfections and will be critical for practical systems.


  A notable role in understanding of microscopic electronic properties of high
temperature superconductors (HTSC) belongs to angle resolved photoemission
spectroscopy (ARPES). This technique supplies a direct window into reciprocal
space of solids: the momentum-energy space where quasiparticles (the electrons
dressed in clouds of interactions) dwell. Any interaction in the electronic
system, e.g. superconducting pairing, leads to modification of the
quasi-particle spectrum--to redistribution of the spectral weight over the
momentum-energy space probed by ARPES. A continued development of the technique
had an effect that the picture seen through the ARPES window became clearer and
sharper until the complexity of the electronic band structure of the cuprates
had been resolved. Now, in an optimal for superconductivity doping range, the
cuprates much resemble a normal metal with well predicted electronic structure,
though with rather strong electron-electron interaction. This principal
disentanglement of the complex physics from complex structure reduced the
mystery of HTSC to a tangible problem of interaction responsible for
quasi-particle formation. Here we present a short overview of resent ARPES
results, which, we believe, denote a way to resolve the HTSC puzzle.


  Primordial non-Gaussianities (PNG) leave unique signatures in the bispectrum
of the large-scale structure. With upcoming galaxy surveys set to improve PNG
constraints by at least one order of magnitude, it is important to account for
any potential contamination. In our work we show how to include wide-angle
effects into the 3-dimensional observed galaxy bispectrum. We compute the
leading wide-angle corrections to the monopole, finding that they could mimic
local PNG with an amplitude of $f_{\rm NL} = \mathcal{O}\left( 0.1 \right)$. We
also compute the dipole induced by wide-angle effects, whose amplitude is a
few-percent of the flat-sky monopole. We estimate that wide-angle effects in
the monopole can be safely neglected for survey volumes of the order of
$8~\mathrm{Gpc}^3 h^{-3}$, while the dipole can start being detected from
surveys probing volumes larger than $50~\mathrm{Gpc}^3 h^{-3}$. Our formalism
can be readily adapted to realistic survey geometries and to include
relativistic effects, which may become relevant at high redshifts.


  Today's heavy machine learning tasks are fueled by large datasets. Computing
is performed with power hungry processors whose performance is ultimately
limited by the data transfer to and from memory. Optics is one of the powerful
means of communicating and processing information and there is intense current
interest in optical information processing for realizing high-speed
computations. Here we present and experimentally demonstrate an optical
computing framework based on spatiotemporal effects in multimode fibers for a
range of learning tasks from classifying COVID-19 X-ray lung images and speech
recognition to predicting age from face images. The presented framework
overcomes the energy scaling problem of existing systems without compromising
speed. We leveraged simultaneous, linear, and nonlinear interaction of spatial
modes as a computation engine. We numerically and experimentally showed the
ability of the method to execute several different tasks with accuracy
comparable to a digital implementation.


  We construct birational maps that satisfy the parametric set-theoretical
Yang-Baxter equation and its entwining generalisation. For this purpose, we
employ Darboux transformations related to integrable Nonlinear Schr\"odinger
type equations and study the refactorisation problems of the product of their
associated Darboux matrices. Additionally, we study various algebraic
properties of the derived maps, such as invariants and associated symplectic or
Poisson structures, and we prove their complete integrability in the Liouville
sense.


  With the Auger Engineering Radio Array (AERA) located at the Pierre Auger
Observatory, radio emission of extensive air showers is observed. To exploit
the physics potential of AERA, electric-field amplitude measurements with the
radio detector stations need to be well-calibrated on an absolute level. A
convenient tool for far-field calibration campaigns is a flying drone. Here we
make use of an octocopter to place a calibrated source at freely chosen
positions above the radio detector array. Special emphasis is put on the
reconstruction of the octocopter position and its accuracy during the flights.
The antenna response pattern of the radio detector stations was measured in a
recent calibration campaign. Results of these measurements are presented and
compared to simulations. It is found that measurements and simulations are in
good agreement.


  In this paper we prove a generalization of Montel's theorem for a class of
first order elliptic equations with measurable coefficients involving
Hodge-Dirac operators. We then apply this result to sequences of solutions of
second order uniformly elliptic equations with measurable coefficients on
divergence form and show that this results in a precompactness result for such
sequences.


  Past approaches to translate a phrase in a language L1 to a language L2 using
a dictionary-based approach require grammar rules to restructure initial
translations. This paper introduces a novel method without using any grammar
rules to translate a given phrase in L1, which does not exist in the
dictionary, to L2. We require at least one L1-L2 bilingual dictionary and
n-gram data in L2. The average manual evaluation score of our translations is
4.29/5.00, which implies very high quality.


  We begin with a review of a well known class of networks, Classical Bayesian
(CB) nets (also called causal probabilistic nets by some). Given a situation
which includes randomness, CB nets are used to calculate the probabilities of
various hypotheses about the situation, conditioned on the available evidence.
We introduce a new class of networks, which we call Quantum Bayesian (QB) nets,
that generalize CB nets to the quantum mechanical regime. We explain how to use
QB nets to calculate quantum mechanical conditional probabilities (in case of
either sharp or fuzzy observations), and discuss the connection of QB nets to
Feynman Path integrals. We give examples of QB nets that involve a single
spin-half particle passing through a configuration of two or three
Stern-Gerlach magnets. For the examples given, we present the numerical values
of various conditional probabilities, as calculated by a general computer
program especially written for this purpose.


  We investigate the effects of magnetic impurities in a superconducting state
with $s_\pm$ pairing symmetry. Within a two-band model, we find that the
intra-band magnetic scattering serves as a pair breaker while the inter-band
magnetic scattering preserves pairing and hardly affects transition temperature
in the Born limit. We also show that the same physics can persist beyond the
weak scattering region. Our results coincide with recent experimental
measurements in iron-based superconductors and thus provides an indirect
evidence of the possible $s_\pm$ pairing symmetry in these materials.