  A theoretical study of the intense-field multiphoton ionization of
hydrogenlike systems is performed by solving the time-dependent Dirac equation
within the dipole approximation. It is shown that the velocity-gauge results
agree to the ones in length gauge only if the negative-energy states are
included in the time propagation. On the other hand, for the considered laser
parameters, no significant difference is found in length gauge if the
negative-energy states are included or not. Within the adopted dipole
approximation the main relativistic effect is the shift of the ionization
potential. A simple scaling procedure is proposed to account for this effect.


  The relative isobaric yields of fragments produced in a series of heavy ion
induced multifragmentation reactions have been analyzed in the framework of a
Modified Fisher Model, primarily to determine the ratio of the symmetry energy
coefficient to the temperature, $a_a/T$, as a function of fragment mass A. The
extracted values increase from 5 to ~16 as A increases from 9 to 37. These
values have been compared to the results of calculations using the
Antisymmetrized Molecular Dynamics (AMD) model together with the statistical
decay code Gemini. The calculated ratios are in good agreement with those
extracted from the experiment. In contrast, the ratios determined from fitting
the primary fragment distributions from the AMD model calculation are ~ 4 and
show little variation with A. This observation indicates that the value of the
symmetry energy coefficient derived from final fragment observables may be
significantly different than the actual value at the time of fragment
formation. The experimentally observed pairing effect is also studied within
the same simulations. The Coulomb coefficient is also discussed.


  Volume-wise labeling in 3D medical images is a time-consuming task that
requires expertise. As a result, there is growing interest in using
semi-supervised learning (SSL) techniques to train models with limited labeled
data. However, the challenges and practical applications extend beyond SSL to
settings such as unsupervised domain adaptation (UDA) and semi-supervised
domain generalization (SemiDG). This work aims to develop a generic SSL
framework that can handle all three settings. We identify two main obstacles to
achieving this goal in the existing SSL framework: 1) the weakness of capturing
distribution-invariant features; and 2) the tendency for unlabeled data to be
overwhelmed by labeled data, leading to over-fitting to the labeled data during
training. To address these issues, we propose an Aggregating & Decoupling
framework. The aggregating part consists of a Diffusion encoder that constructs
a common knowledge set by extracting distribution-invariant features from
aggregated information from multiple distributions/domains. The decoupling part
consists of three decoders that decouple the training process with labeled and
unlabeled data, thus avoiding over-fitting to labeled data, specific domains
and classes. We evaluate our proposed framework on four benchmark datasets for
SSL, Class-imbalanced SSL, UDA and SemiDG. The results showcase notable
improvements compared to state-of-the-art methods across all four settings,
indicating the potential of our framework to tackle more challenging SSL
scenarios. Code and models are available at:
https://github.com/xmed-lab/GenericSSL.


  In this Letter, we show thermoelectric conversion efficiency is
\emph{exactly} determined by \emph{three} independent material parameters
$Z_{\rm gen}$, $\tau$, and $\beta$. Each parameter is a figure of merit hence
improving $\tau$ or $\beta$ is an additional way to increase the efficiency.
The $Z_{\rm gen}$ generalizes the traditional figure of merit \emph{zT}. Two
degrees of freedom $\tau $ and $\beta$ reflect the temperature gradients of the
material properties and are crucial to evaluate the heat current altered by
non-zero Thomson heat and asymmetric Joule heat escape. Physical insights on
high $\tau$ or $\beta$ materials explain why the single parameter approaches
can be inaccurate for efficiency prediction.


  While deep convolutional neural networks (CNN) have been successfully applied
for 2D image analysis, it is still challenging to apply them to 3D anisotropic
volumes, especially when the within-slice resolution is much higher than the
between-slice resolution and when the amount of 3D volumes is relatively small.
On one hand, direct learning of CNN with 3D convolution kernels suffers from
the lack of data and likely ends up with poor generalization; insufficient GPU
memory limits the model size or representational power. On the other hand,
applying 2D CNN with generalizable features to 2D slices ignores between-slice
information. Coupling 2D network with LSTM to further handle the between-slice
information is not optimal due to the difficulty in LSTM learning. To overcome
the above challenges, we propose a 3D Anisotropic Hybrid Network (AH-Net) that
transfers convolutional features learned from 2D images to 3D anisotropic
volumes. Such a transfer inherits the desired strong generalization capability
for within-slice information while naturally exploiting between-slice
information for more effective modelling. The focal loss is further utilized
for more effective end-to-end learning. We experiment with the proposed 3D
AH-Net on two different medical image analysis tasks, namely lesion detection
from a Digital Breast Tomosynthesis volume, and liver and liver tumor
segmentation from a Computed Tomography volume and obtain the state-of-the-art
results.


  We propose a new convolutional neural network (CNN) which performs coarse and
fine segmentation for end-to-end synthetic aperture radar (SAR) automatic
target recognition (ATR) system. In recent years, many CNNs for SAR ATR using
deep learning have been proposed, but most of them classify target classes from
fixed size target chips extracted from SAR imagery. On the other hand, we
proposed the CNN which outputs the score of the multiple target classes and a
background class for each pixel from the SAR imagery of arbitrary size and
multiple targets as fine segmentation. However, it was necessary for humans to
judge the CNN segmentation result. In this report, we propose a CNN called SAR
ATR with verification support (SAVERS), which performs region-wise (i.e.
coarse) segmentation and pixel-wise segmentation. SAVERS discriminates between
target and non-target, and classifies multiple target classes and non-target
class by coarse segmentation. This report describes the evaluation results of
SAVERS using the Moving and Stationary Target Acquisition and Recognition
(MSTAR) dataset.


  Clustering high-dimensional data often requires some form of dimensionality
reduction, where clustered variables are separated from "noise-looking"
variables. We cast this problem as finding a low-dimensional projection of the
data which is well-clustered. This yields a one-dimensional projection in the
simplest situation with two clusters, and extends naturally to a multi-label
scenario for more than two clusters. In this paper, (a) we first show that this
joint clustering and dimension reduction formulation is equivalent to
previously proposed discriminative clustering frameworks, thus leading to
convex relaxations of the problem, (b) we propose a novel sparse extension,
which is still cast as a convex relaxation and allows estimation in higher
dimensions, (c) we propose a natural extension for the multi-label scenario,
(d) we provide a new theoretical analysis of the performance of these
formulations with a simple probabilistic model, leading to scalings over the
form $d=O(\sqrt{n})$ for the affine invariant case and $d=O(n)$ for the sparse
case, where $n$ is the number of examples and $d$ the ambient dimension, and
finally, (e) we propose an efficient iterative algorithm with running-time
complexity proportional to $O(nd^2)$, improving on earlier algorithms which had
quadratic complexity in the number of examples.


  New sharp Strichartz estimates for the Maxwell system in two dimensions with
rough permittivity and non-trivial charges are proved. We use the FBI transform
to carry out the analysis in phase space. For this purpose, the Maxwell
equations are conjugated to a system of half-wave equations with rough
coefficients. For this system, Strichartz estimates are similarly derived as in
previous work by Tataru on scalar wave equations with rough coefficients. We
use the estimates to improve the local well-posedness theory for quasilinear
Maxwell equations in two dimensions.


  We considered the circulating current induced by the current magnification
and the persistent current induced by Aharonov-Casher flux. The persistent
currents have directional dependence on the direct current flow, but the
circulating currents have no directional dependence. Hence in the equilibrium,
only the persistent current can survives on the ring. For the charge current,
the persistent charge current cancelled between spin up and down states,
because of the time reversal symmetry of the Hamiltonian on the ring. So there
are only circulating charge currents on the ring for electrons with unpolarized
spin in the nonequilibrium. However, only the persistent spin currents
contributes to the spin currents for electrons with unpolarized spin.


  Magnetic Feshbach resonances are a key tool in the field of ultracold quantum
gases, but their full exploitation requires the generation of large, stable
magnetic fields up to 1000 G with fractional stabilities of better than
$10^{-4}$. Design considerations for electromagnets producing these fields,
such as optical access and fast dynamical response, mean that electric currents
in excess of 100 A are often needed to obtain the requisite field strengths. We
describe a simple digital proportional-integral-derivative current controller
constructed using a field-programmable gate array and off-the-shelf evaluation
boards which allows for gain scheduling, enabling optimal control of current
sources with non-linear actuators. Our controller can stabilize an electric
current of 337.5 A to the level of $7.5\times 10^{-7}$ in an averaging time of
10 minutes and with a control bandwidth of 2 kHz.


  This paper presents a high-quality multilingual dataset for the documentation
domain to advance research on localization of structured text. Unlike
widely-used datasets for translation of plain text, we collect XML-structured
parallel text segments from the online documentation for an enterprise software
platform. These Web pages have been professionally translated from English into
16 languages and maintained by domain experts, and around 100,000 text segments
are available for each language pair. We build and evaluate translation models
for seven target languages from English, with several different copy mechanisms
and an XML-constrained beam search. We also experiment with a non-English pair
to show that our dataset has the potential to explicitly enable $17 \times 16$
translation settings. Our experiments show that learning to translate with the
XML tags improves translation accuracy, and the beam search accurately
generates XML structures. We also discuss trade-offs of using the copy
mechanisms by focusing on translation of numerical words and named entities. We
further provide a detailed human analysis of gaps between the model output and
human translations for real-world applications, including suitability for
post-editing.


  A scenario of the inflaton evolution from cosmic inflation and matter
creation to dark matter/dark energy today is presented. To start with, a model
of the inflationary phase of the inflaton is introduced. The inflaton rolls
down a hilltop potential along with matter creation being dragged down by the
presence of matter. Presence of matter provides a mechanism to stop universe's
acceleration and hence the inflationary phase. The model predictions for the
standard metrics are fully consistent with the current CMB limits. The
potential could in principle be extended to complete a potential hill
subsequent to inflation. The evolution of the inflaton from the inflationary
phase to radiation/matter dominated eras and to current times can be inferred
qualitatively following the evolution of its equation of state parameter.
Existence of solutions to its dynamics, tracking matter as it evolves to
current times, provides a plausible reasoning for the relative order of
magnitudes of the cosmological parameters, in particular to the relative
abundance of dark matter today.


  Let G = (A U P, E) be a bipartite graph where A denotes a set of agents, P
denotes a set of posts and ranks on the edges denote preferences of the agents
over posts. A matching M in G is rank-maximal if it matches the maximum number
of applicants to their top-rank post, subject to this, the maximum number of
applicants to their second rank post and so on.
  In this paper, we develop a switching graph characterization of rank-maximal
matchings, which is a useful tool that encodes all rank-maximal matchings in an
instance. The characterization leads to simple and efficient algorithms for
several interesting problems. In particular, we give an efficient algorithm to
compute the set of rank-maximal pairs in an instance. We show that the problem
of counting the number of rank-maximal matchings is #P-Complete and also give
an FPRAS for the problem. Finally, we consider the problem of deciding whether
a rank-maximal matching is popular among all the rank-maximal matchings in a
given instance, and give an efficient algorithm for the problem.


  The quasi-optical modulation of linear polarization at millimeter and
sub-millimeter wavelengths can be achieved by using rotating half wave plates
(HWPs) in front of polarization sensitive detectors. Large operational
bandwidths are required when the same device is meant to work simultaneously
across different frequency bands. Previous realizations of half wave plates,
ranging from birefringent multi-plate to mesh-based devices, have achieved
bandwidths of the order of 100%. Here we present the design and the
experimental characterization of a reflective HWP able to work across
bandwidths of the order of 150%. The working principle of the novel device is
completely different from any previous realization and it is based on the
different phase-shift experienced by two orthogonal polarizations respectively
reflecting off an electric conductor and off an artificial magnetic conductor.


  In active galactic nuclei (AGN)-galaxy co-evolution models, AGN winds and
outflows are often invoked to explain why super-massive black holes and
galaxies stop growing efficiently at a certain phase of their lives. They are
commonly referred to as the leading actors of feedback processes. Evidence of
ultra-fast (v>0.05c) outflows in the innermost regions of AGN has been
collected in the past decade by sensitive X-ray observations for sizable
samples of AGN, mostly at low redshift. Here we present ultra-deep XMM-Newton
and Chandra spectral data of an obscured (Nh~2x10^{23} cm^-2), intrinsically
luminous (L2-10keV~4x10^{44} erg/s) quasar (named PID352) at z~1.6 (derived
from the X-ray spectral analysis) in the Chandra Deep Field-South. The source
is characterized by an iron emission and absorption line complex at observed
energies of E~2-3 keV. While the emission line is interpreted as being due to
neutral iron (consistent with the presence of cold absorption), the absorption
feature is due to highly ionized iron transitions (FeXXV, FeXXVI) with an
outflowing velocity of 0.14^{+0.02}_{-0.06}c, as derived from photoionization
models. The mass outflow rate - ~2 Msun/yr - is similar to the source accretion
rate, and the derived mechanical energy rate is ~9.5x10^{44} erg/s,
corresponding to 9% of the source bolometric luminosity. PID352 represents one
of the few cases where indications of X-ray outflowing gas have been observed
at high redshift thus far. This wind is powerful enough to provide feedback on
the host galaxy.


  Do the theorised different formation mechanisms of fast and slow rotators
produce an observable difference in their star formation histories? To study
this we identify quenching slow rotators in the MaNGA sample by selecting those
which lie below the star forming sequence and identify a sample of quenching
fast rotators which were matched in stellar mass. This results in a total
sample of 194 kinematically classified galaxies, which is agnostic to visual
morphology. We use u-r and NUV-u colours from SDSS and GALEX and an existing
inference package, STARPY, to conduct a first look at the onset time and
exponentially declining rate of quenching of these galaxies. An
Anderson-Darling test on the distribution of the inferred quenching rates
across the two kinematic populations reveals they are statistically
distinguishable ($3.2\sigma$). We find that fast rotators quench at a much
wider range of rates than slow rotators, consistent with a wide variety of
physical processes such as secular evolution, minor mergers, gas accretion and
environmentally driven mechanisms. Quenching is more likely to occur at rapid
rates ($\tau \lesssim 1~\rm{Gyr}$) for slow rotators, in agreement with
theories suggesting slow rotators are formed in dynamically fast processes,
such as major mergers. Interestingly, we also find that a subset of the fast
rotators quench at these same rapid rates as the bulk of the slow rotator
sample. We therefore discuss how the total gas mass of a merger, rather than
the merger mass ratio, may decide a galaxy's ultimate kinematic fate.


  The diagonal effect of orders is well documented in different markets, which
states that orders are more likely to be followed by orders of the same
aggressiveness and implies the presence of short-term correlations in order
flows. Based on the order flow data of 43 Chinese stocks, we investigate if
there are long-range correlations in the time series of order aggressiveness.
The detrending moving average analysis shows that there are crossovers in the
scaling behaviors of overall fluctuations and order aggressiveness exhibits
linear long-term correlations. We design an objective procedure to determine
the two Hurst indexes delimited by the crossover scale. We find no correlations
in the short term and strong correlations in the long term for all stocks
except for an outlier stock. The long-term correlation is found to depend on
several firm specific characteristics. We also find that there are nonlinear
long-term correlations in the order aggressiveness when we perform the
multifractal detrending moving average analysis.


  Our goal is to generate fonts with specific impressions, by training a
generative adversarial network with a font dataset with impression labels. The
main difficulty is that font impression is ambiguous and the absence of an
impression label does not always mean that the font does not have the
impression. This paper proposes a font generation model that is robust against
missing impression labels. The key ideas of the proposed method are (1)a
co-occurrence-based missing label estimator and (2)an impression label space
compressor. The first is to interpolate missing impression labels based on the
co-occurrence of labels in the dataset and use them for training the model as
completed label conditions. The second is an encoder-decoder module to compress
the high-dimensional impression space into low-dimensional. We proved that the
proposed model generates high-quality font images using multi-label data with
missing labels through qualitative and quantitative evaluations.


  Low earth orbit (LEO) satellite has been considered as a potential supplement
for the terrestrial Internet of Things (IoT). In this paper, we consider
grant-free non-orthogonal random access (GF-NORA) in orthogonal frequency
division multiplexing (OFDM) system to increase access capacity and reduce
access latency for LEO satellite-IoT. We focus on the joint device activity
detection (DAD) and channel estimation (CE) problem at the satellite access
point. The delay and the Doppler effect of the LEO satellite channel are
assumed to be partially compensated. We propose an OFDM-symbol repetition
technique to better distinguish the residual Doppler frequency shifts, and
present a grid-based parametric probability model to characterize channel
sparsity in the delay-Doppler-user domain, as well as to characterize the
relationship between the channel states and the device activity. Based on that,
we develop a robust Bayesian message passing algorithm named modified variance
state propagation (MVSP) for joint DAD and CE. Moreover, to tackle the mismatch
between the real channel and its on-grid representation, an
expectation-maximization (EM) framework is proposed to learn the grid
parameters. Simulation results demonstrate that our proposed algorithms
significantly outperform the existing approaches in both activity detection
probability and channel estimation accuracy.


  It is rare to succeed in getting mathematics into ordinary conversation
without meeting all kinds of reservations. In order to raise public awareness
of mathematics effectively, it is necessary to modify such attitudes. In this
paper, we point to some possible topics for general mathematical conversation.


  The dynamics of a gravitational wave propagating through a cosmic gauge field
are dramatically different than in vacuum. We show that a gravitational wave
acquires an effective mass, is birefringent, and its normal modes are a linear
combination of gravitational waves and gauge field excitations, leading to the
phenomenon of gravitational wave -- gauge field oscillations. These surprising
results provide insight into gravitational phenomena and may suggest new
approaches to a theory of quantum gravity.


  We study the quantum-mechanical transport on two-dimensional graphs by means
of continuous-time quantum walks and analyse the effect of different boundary
conditions (BCs). For periodic BCs in both directions, i.e., for tori, the
problem can be treated in a large measure analytically. Some of these results
carry over to graphs which obey open boundary conditions (OBCs), such as
cylinders or rectangles. Under OBCs the long time transition probabilities
(LPs) also display asymmetries for certain graphs, as a function of their
particular sizes. Interestingly, these effects do not show up in the marginal
distributions, obtained by summing the LPs along one direction.


  We develop the concept of operators in Hilbert spaces which are similar to
their adjoints via antiunitary operators, the latter being not necessarily
involutive. We discuss extension theory, refined polar and singular-value
decompositions, and antilinear eigenfunction expansions. The study is motivated
by physical symmetries in quantum mechanics with non-self-adjoint operators.


  Aerospace structures often experience high strain rate events such as
ballistic impact, crash, or crush. A material model has been developed that
enhances the capability to simulate the dynamic response of composite materials
under these loading conditions. The material model has been implemented into
the commercially available transient dynamic finite element code LS-DYNA as
MAT213. The model can simulate the nonlinear deformation, damage, and failure
that takes place in a composite under dynamic loading conditions. The specific
goal of this work is to characterize the MAT213 input for the representative
material. The specific composite material being examined consists of T700G
unidirectional carbon fibers and a low-melt PolyArylEtherKetone (LMPAEK)
thermoplastic resin system. It is formally referred to as Toray TC1225 LMPAEK
T700G. As the initial part of this work, this paper is focused on
characterizing the material parameters for the MAT213 deformation model based
on results obtained from multi-scale experimentation. The effort concentrated
on characterizing the in-plane material response suitable for use with thin
shell elements. For shell elements within MAT213, tabulated stress-strain
results from tension and compression tests in the longitudinal and transverse
directions and in-plane shear tests are required. Due to the difficulty of
measuring small strains in the transverse direction, a multi-scale testing
method was developed. Macro-scale testing is performed per the typical ASTM
methods while micro-scale testing uses a microscope along with smaller coupon
sizes to obtain the smaller strains in the transverse direction of each test.
For both testing methods, a VIC-2D camera and software for digital image
correlation analysis are used. Using the DIC combined with each test fixture,
reliable stress and strain data are collected.


  We explore the multiparticle transition probabilities in Gaussian unitaries
effected by a two-mode Bogoliubov bosonic transformation on the mode
annihilation and creation operators. We show that the transition probabilities
can be characterized by remarkably simple, yet unsuspected recurrence equations
involving a linear combination of probabilities. The recurrence exhibits an
interferometric suppression term - a negative probability - which generalizes
the seminal Hong-Ou-Mandel effect to more than two indistinguishable photons
impinging on a beam splitter of rational transmittance. Unexpectedly,
interferences thus originate in this description from the cancellation of
probabilities instead of amplitudes. Our framework, which builds on the
generating function of the non-Gaussian matrix elements of Gaussian unitaries
in Fock basis, is illustrated here for the most common passive and active
linear coupling between two optical modes driven by a beam splitter or a
parametric amplifier. Hence, it also allows us to predict unsuspected
multiphoton interference effects in an optical amplifier of rational gain. In
particular, we confirm the newly found two-photon interferometric suppression
effect in an amplifier of gain 2 originating from timelike indistinguishability
(arXiv:2012.15165 [quant-ph]). Overall, going beyond standard two-mode optical
components, we expect our method will prove valuable for describing general
quantum circuits involving Bogoliubov bosonic transformations.


  Cluster dynamics and single-particle correlation are simultaneously treated
for the description of the ground state of ${}^{12} \mathrm{C} $. The recent
development of the antisymmetrized quasi cluster model (AQCM) makes it possible
to generate $jj$-coupling shell-model wave functions from $\alpha$ clusters
models. The cluster dynamics and the competition with the $jj$-coupling
shell-model structure can be estimated rather easily. In the present study, we
further include the effect of single-particle excitation; the mixing of the
two-particle-two-hole excited states is considered. The single-particle
excitation is not always taken into account in the standard cluster model
analyses, and the two-particle-two-hole states are found to strongly contribute
to the lowering of the ground state owing to the pairing-like correlations. By
extending AQCM, all of the basis states are prepared on the same footing, and
they are superposed based on the framework of the generator coordinate method
(GCM).


  The paper addresses an open problem raised in [Bartsch, Molle, Rizzi,
Verzini: Normalized solutions of mass supercritical Schr\"odinger equations
with potential, Comm. Part. Diff. Equ. 46 (2021), 1729-1756] on the existence
of normalized solutions to Schr\"odinger equations with potentials and
inhomogeneous nonlinearities. We consider the problem \[
  -\Delta u+V(x)u+\lambda u = |u|^{q-2}u+\beta |u|^{p-2}u, \quad
\|u\|^2_2=\int|u|^2dx = \alpha, \] both on $\mathbb{R}^N$ as well as on domains
$r\Omega$ where $\Omega\subset\mathbb{R}^N$ is an open bounded convex domain
and $r>0$ is large. The exponents satisfy $2<p<2+\frac4N<q<2^*=\frac{2N}{N-2}$,
so that the nonlinearity is a combination of a mass subcritical and a mass
supercritical term. Due to the presence of the potential a by now standard
approach based on the Pohozaev identity cannot be used. We develop a robust
method to study the existence of normalized solutions of nonlinear
Schr\"odinger equations with potential and find conditions on $V$ so that
normalized solutions exist. Our results are new even in the case $\beta=0$.


  A very general cosmological consideration suggests that, along with galactic
dark matter halos, much smaller dark matter structures may exist. These
structures are usually called 'clumps', and their mass extends to $10^{-6}
M_\odot$ or even lower. The clumps should give the main contribution into the
signal of dark matter annihilation, provided that they have survived until the
present time. Recent observations favor a cored profile for low-mass
astrophysical halos. We consider cored clumps and show that they are
significantly less firm than the standard NFW ones. In contrast to the standard
scenario, the cored clumps should have been completely destroyed inside $\sim
20$~{kpc} from the Milky Way center. The dwarf spheroidals should not contain
any dark matter clumps. On the other hand, even under the most pessimistic
assumption about the clump structure, the clumps should have survived in the
Milky Way at a distance exceeding $50$~{kpc} from the center, as well as in
low-density cosmic structures. There they significantly boost the dark matter
annihilation. We show that at least $~70\%$ of the clumps endured the
primordial structure formation should still exist untouched in the present-day
Universe.


  We prove that an integrated simple random walk, where random walk and
integrated random walk are conditioned to return to zero, has asymptotic
probability $n^{-1/2}$ to stay positive. This question is motivated by
so-called random polymer models and proves a conjecture by Caravenna and
Deuschel.


  This paper introduces a high-quality open-source speech synthesis dataset for
Kazakh, a low-resource language spoken by over 13 million people worldwide. The
dataset consists of about 93 hours of transcribed audio recordings spoken by
two professional speakers (female and male). It is the first publicly available
large-scale dataset developed to promote Kazakh text-to-speech (TTS)
applications in both academia and industry. In this paper, we share our
experience by describing the dataset development procedures and faced
challenges, and discuss important future directions. To demonstrate the
reliability of our dataset, we built baseline end-to-end TTS models and
evaluated them using the subjective mean opinion score (MOS) measure.
Evaluation results show that the best TTS models trained on our dataset achieve
MOS above 4 for both speakers, which makes them applicable for practical use.
The dataset, training recipe, and pretrained TTS models are freely available.


  We revisit the problem of the quarter-filled one-dimensional Kondo lattice
model, for which the existence of a dimerized phase and a non-zero charge gap
had been reported in Phys. Rev. Lett. \textbf{90}, 247204 (2003). Recently,
some objections were raised claiming that the system is neither dimerized nor
has a charge gap. In the interest of clarifying this important issue, we show
that these objections are based on results obtained under conditions in which
the dimer order is artificially suppressed. We use the incontrovertible
dimerized phase of the Majumdar-Ghosh point of the $J_{1}-J_{2}$ Heisenberg
model as a paradigm with which to illustrate this artificial suppression.
Finally, by means of extremely accurate DMRG calculations, we show that the
charge gap is indeed non-zero in the dimerized phase.


  Consider a finite connected graph possibly with multiple edges and loops. In
discrete geometric analysis, Kotani and Sunada constructed the crystal
associated to the graph as a standard realization of the maximal abelian
covering of the graph. As an application of what the author showed in an
earlier paper with Seshadri as a by-product of Geometric Invariant Theory, he
shows that the Voronoi tiling (also known as the Wigner-Seitz tiling) is hidden
in the crystal, that is, the crystal does not intrude the interiors of the
top-dimensional Voronoi cells. The result turns out to be closely related to
the tropical Abel-Jacobi map of the associated compact tropical curve.


  We review the current knowledge about nuclear star clusters (NSCs), the
spectacularly dense and massive assemblies of stars found at the centers of
most galaxies. Recent observational and theoretical work suggest that many NSC
properties, including their masses, densities, and stellar populations vary
with the properties of their host galaxies. Understanding the formation,
growth, and ultimate fate of NSCs therefore is crucial for a complete picture
of galaxy evolution. Throughout the review, we attempt to combine and distill
the available evidence into a coherent picture of NSC evolution. Combined, this
evidence points to a clear transition mass in galaxies of ~10^9 solar masses
where the characteristics of nuclear star clusters change. We argue that at
lower masses, NSCs are formed primarily from globular clusters that inspiral
into the center of the galaxy, while at higher masses, star formation within
the nucleus forms the bulk of the NSC. We also discuss the coexistence of NSCs
and central black holes, and how their growth may be linked. The extreme
densities of NSCs and their interaction with massive black holes lead to a wide
range of unique phenomena including tidal disruption and gravitational wave
events. Lastly, we review the evidence that many NSCs end up in the halos of
massive galaxies stripped of the stars that surrounded them, thus providing
valuable tracers of the galaxies' accretion histories.


  We recently proposed a novel approach to converging electronic energies
equivalent to high-level coupled-cluster (CC) computations by combining the
deterministic CC($P$;$Q$) formalism with the stochastic configuration
interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article
extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev.
Lett. 119, 223003 (2017)], which focused on recovering the energies obtained
with the CC method with singles, doubles, and triples (CCSDT) using the
information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches
truncated at triples and quadruples. It also reports our first semi-stochastic
CC($P$;$Q$) calculations aimed at converging the energies that correspond to
the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The
ability of the semi-stochastic CC($P$;$Q$) formalism to recover the CCSDT and
CCSDTQ energies, even when electronic quasi-degeneracies and triply and
quadruply excited clusters become substantial, is illustrated by a few
numerical examples, including the F-F bond breaking in ${\rm F}_{2}$, the
automerization of cyclobutadiene, and the double dissociation of the water
molecule.


  Interacting spin systems are of fundamental relevance in different areas of
physics, as well as in quantum information science, and biology. These spin
models represent the simplest, yet not fully understood, manifestation of
quantum many-body systems. An important outstanding problem is the efficient
numerical computation of dynamics in large spin systems. Here we propose a new
semiclassical method to study many-body spin dynamics in generic spin lattice
models. The method is based on a discrete Monte Carlo sampling in phase-space
in the framework of the so-called truncated Wigner approximation. Comparisons
with analytical and numerically exact calculations demonstrate the power of the
technique. They show that it correctly reproduces the dynamics of one- and
two-point correlations and spin squeezing at short times, thus capturing
entanglement. Our results open the possibility to study the quantum dynamics
accessible to recent experiments in regimes where other numerical methods are
inapplicable.


  In this paper, we review the representation theory of the infinite symmetric
group, and we extend the works of Kerov and Vershik by proving that the
irreducible characters of the infinite symmetric group always satisfy a central
limit theorem. Hence, for any point of the Thoma simplex, the corresponding
measures on the levels of the Young graph have a property of gaussian
concentration. By using the Robinson-Schensted-Knuth algorithm and the theory
of Pitman operators, we relate these results to the properties of certain
random permutations obtained by riffle shuffles, and to the behaviour of random
walks conditioned to stay in a Weyl chamber.


  Though the ultraviolet (UV) domain plays a vital role in the studies of
astronomical transient events, the UV time-domain sky remains largely
unexplored. We have designed a wide-field UV imager that can be flown on a
range of available platforms, such as high-altitude balloons, CubeSats, and
larger space missions. The major scientific goals are the variability of
astronomical sources, detection of transients such as supernovae, novae, tidal
disruption events, and characterizing AGN variability. The instrument has an 80
mm aperture with a circular field of view of 10.8 degrees, an angular
resolution of around 22 arcsec, and a 240-390 nm spectral observation window.
The detector for the instrument is a Microchannel Plate (MCP)-based image
intensifier with both photon counting and integration capabilities. An
FPGA-based detector readout mechanism and real-time data processing have been
implemented. The imager is designed in such a way that its lightweight and
compact nature are well fitted for the CubeSat dimensions. Here we present
various design and developmental aspects of this UV wide-field transient
explorer.


  We study interfacial waves in a system of two horizontal layers of immiscible
inviscid fluids involved into horizontal vibrational motion. We analyze the
linear and nonlinear stability properties of the solitons in the system and
consider two-soliton collision scenarios. We describe the events of explosive
formation of sharp peaks on the interface, which may presumably lead to the
layer rapture, and find that beyond the vicinity of this peaks the system
dynamics can be represented as a kinetics of a soliton gas.


  We present a scheme to obtain anti-chiral edge states in an exciton-polariton
honeycomb lattice with strip geometry, where the modes corresponding to both
edges propagate in the same direction. Under resonant pumping the effect of a
polariton condensate with nonzero velocity in one linear polarization is
predicted to tilt the dispersion of polaritons in the other, which results in
an energy shift between two Dirac cones and the otherwise flat edge states
become tilted. Our simulations show that due to the spatial separation from the
bulk modes the edge modes are robust against disorder.


  We show that direct laser writing (DLW) in aqueous silver nitrate with a 1030
nm femtosecond (fs) laser results in deposition of a mixture of silver oxide
and silver, in contrast to the pure silver deposition previously reported with
780 nm fs DLW. However, adding photoinitiator prevents silver oxide formation
in a concentration-dependent manner. As a result, the resistivity of the
material can also be controlled by photoinitiator concentration with
resistivity being reduced from approximately 9e-3 $\Omega m$ to 3e-7 $\Omega
m$. Silver oxide peaks dominate the X-ray diffraction spectra when no
photoinitiator is present, while the peaks disappear with photoinitiator
concentrations above 0.05wt%. While femtosecond pulses are needed to initiate
deposition, a continues-wave laser when well overlapped with the previously
written material and supplying enough average power can lead to further
printing, suggesting thermal deposition can also occur where the photoinitiator
molecule also acts as a general reducing agent that prevents oxide formation.
We also compare the surface quality of printed lines for different
photoinitiator concentrations and laser printing conditions. A THz polarizer
and metamaterial are printed as a demonstration of silver oxide printing.


  We present results of a direct search for the decay KS --> e+e- with the KLOE
detector, obtained with a sample of e+e- --> phi --> KSKL events produced at
DAFNE, the Frascati phi-factory, for an integrated luminosity of 1.3fb-1. The
Standard Model prediction for this decay is BR(KS --> e+e-) = 1.6*10^-15. The
search has been performed tagging the KS decays by simultaneous detection of a
KL interaction in the calorimeter. Background rejection has been optimized by
using both kinematic cuts and particle identification. At the end of the
analysis chain we find BR(KS --> e+e-) < 2.1*10^-8 at 90% CL, which improves by
a factor of ~7 on the previous best result, obtained by CPLEAR experiment.


  We describe an efficient numerical method for simulating the dynamics of
interacting spin ensembles in the presence of dephasing and decay. The method
builds on the discrete truncated Wigner approximation for isolated systems,
which combines the mean-field dynamics of a spin ensemble with a Monte Carlo
sampling of discrete initial spin values to account for quantum correlations.
Here we show how this approach can be generalized for dissipative spin systems
by replacing the deterministic mean-field evolution by a stochastic process,
which describes the decay of coherences and populations while preserving the
length of each spin. We demonstrate the application of this technique for
simulating nonclassical spin-squeezing effects or the dynamics and steady
states of cavity QED models with hundred thousand interacting two-level systems
and without relying on any symmetries. This opens up the possibility to perform
accurate real-scale simulations of a diverse range of experiments in quantum
optics or with solid-state spin ensembles under realistic laboratory
conditions.


  The statistical state for the empirical Pareto's 80/20 rule has been found to
correspond to a normal or Gaussian distribution with a standard deviation that
is twice the mean. This finding represents large characteristic variations in
our society and nature. In this distribution, the rule can be also referred to
as, for example, the 25/5, 45/10, 60/15, or 90/25 rule. In addition, our result
suggests the existence of implicit negative contributors.


  Coherence is a crucial aspect of evaluating text readability and can be
assessed through two primary factors when evaluating an essay in a scoring
scenario. The first factor is logical coherence, characterized by the
appropriate use of discourse connectives and the establishment of logical
relationships between sentences. The second factor is the appropriateness of
punctuation, as inappropriate punctuation can lead to confused sentence
structure. To address these concerns, we propose a coherence scoring model
consisting of a regression model with two feature extractors: a local coherence
discriminative model and a punctuation correction model. We employ
gradient-boosting regression trees as the regression model and impose
monotonicity constraints on the input features. The results show that our
proposed model better generalizes unseen data. The model achieved third place
in track 1 of NLPCC 2023 shared task 7. Additionally, we briefly introduce our
solution for the remaining tracks, which achieves second place for track 2 and
first place for both track 3 and track 4.


  We prove the existence of infinite classes of cyclic G-decompositions of the
complete multipartite graph, G being a caterpillar, a hairy cycle or a cycle.
All the results are obtained by the construction of d-divisible
$\alpha$-labelings of G, introduced in [A. Pasotti, On d-graceful labelings, to
appear on Ars Combin.] as a generalization of classical $\alpha$-labelings,
whose existence implies that one of graph decompositions.


  A realistic material may possess defects, which often bring the material new
properties that have practical applications. The boundary defects of a
two-dimensional topologically ordered system are thought of as an alternative
way of realizing topological quantum computation. To facilitate the study of
such boundary defects, in this paper, we construct an exactly solvable
Hamiltonian model of topological orders with gapped boundary junctions, where
the boundary defects reside, by placing the Levin-Wen model on a disk, whose
gapped boundary is separated into multiple segments by junctions. We find that
the Hamiltonian of a gapped boundary junction is characterized by either a
morphism between or a common Frobenius subalgebra of the two Frobenius algebras
(in the input fusion category) characetrizing the two boundary segments joint
by the junction. We derive a formula of the ground state degeneracy and an
explicit ground-state basis of our model. We propose the notion of mobile and
immobile charges on the boundary and find that they are quantum observables and
label the ground-state basis. Our model is computation friendly.


  We present and analyze stochastic nonlinear differential equations generating
signals with the power-law distributions of the signal intensity, 1/f^b noise,
power-law autocorrelations and second order structural (height-height
correlation) functions. Analytical expressions for such characteristics are
derived and the comparison with numerical calculations is presented. The
numerical calculations reveal links between the proposed model and models where
signals consist of bursts characterized by the power-law distributions of burst
size, burst duration and the interburst time, as in a case of avalanches in
self-organized critical (SOC) models and the extreme event return times in
long-term memory processes. The presented approach may be useful for modeling
the long-range scaled processes exhibiting 1/f noise and power-law
distributions.


  We introduce a {\it non-regular} generalisation of the N\"{o}rlund mean, and
show its equivalence with a certain moving average. The Abelian and Tauberian
theorems establish relations with convergent sequences and certain power
series. A strong law of large numbers is also proved.


  Text classification is a natural language processing (NLP) task relevant to
many commercial applications, like e-commerce and customer service. Naturally,
classifying such excerpts accurately often represents a challenge, due to
intrinsic language aspects, like irony and nuance. To accomplish this task, one
must provide a robust numerical representation for documents, a process known
as embedding. Embedding represents a key NLP field nowadays, having faced a
significant advance in the last decade, especially after the introduction of
the word-to-vector concept and the popularization of Deep Learning models for
solving NLP tasks, including Convolutional Neural Networks (CNNs), Recurrent
Neural Networks (RNNs), and Transformer-based Language Models (TLMs). Despite
the impressive achievements in this field, the literature coverage regarding
generating embeddings for Brazilian Portuguese texts is scarce, especially when
considering commercial user reviews. Therefore, this work aims to provide a
comprehensive experimental study of embedding approaches targeting a binary
sentiment classification of user reviews in Brazilian Portuguese. This study
includes from classical (Bag-of-Words) to state-of-the-art (Transformer-based)
NLP models. The methods are evaluated with five open-source databases with
pre-defined data partitions made available in an open digital repository to
encourage reproducibility. The Fine-tuned TLMs achieved the best results for
all cases, being followed by the Feature-based TLM, LSTM, and CNN, with
alternate ranks, depending on the database under analysis.


  Dedicated to the centenary of the Ioffe Institute, the article contains the
shortest review of scientific achievements of the theorists of the institute
during this time. We concentrate mainly on research in the field of elementary
particle physics, astrophysics, nuclear theory and atoms. To obtain very
important scientific results became possible because outstanding theoreticians
worked at this Institute. The high level of research persisted in spite of
several mass moves of theorists - then to Kharkov, then to Moscow, then abroad.
The author can testify to the atmosphere that reigned in the FTI in person,
since he works at this institute since 1958. The article deals not only with
research activity, but also with the famous physics schools and their
outstanding cultural programs. We present also examples of extraordinary
successful activity of theorists far beyond the field of their narrow
specialization.


  This short document describes a traditional IR system that achieved MRR@100
equal to 0.298 on the MS MARCO Document Ranking leaderboard (on 2020-12-06).
Although inferior to most BERT-based models, it outperformed several neural
runs (as well as all non-neural ones), including two submissions that used a
large pretrained Transformer model for re-ranking. We provide software and data
to reproduce our results.


  This paper addresses the problem of time series forecasting for
non-stationary signals and multiple future steps prediction. To handle this
challenging task, we introduce DILATE (DIstortion Loss including shApe and
TimE), a new objective function for training deep neural networks. DILATE aims
at accurately predicting sudden changes, and explicitly incorporates two terms
supporting precise shape and temporal change detection. We introduce a
differentiable loss function suitable for training deep neural nets, and
provide a custom back-prop implementation for speeding up optimization. We also
introduce a variant of DILATE, which provides a smooth generalization of
temporally-constrained Dynamic Time Warping (DTW). Experiments carried out on
various non-stationary datasets reveal the very good behaviour of DILATE
compared to models trained with the standard Mean Squared Error (MSE) loss
function, and also to DTW and variants. DILATE is also agnostic to the choice
of the model, and we highlight its benefit for training fully connected
networks as well as specialized recurrent architectures, showing its capacity
to improve over state-of-the-art trajectory forecasting approaches.


  We present analytical next-to-leading order results for the correlator of
baryonic currents at the three loop level with one finite mass quark. We obtain
the massless and the HQET limit of the correlator from the general formula as
particular cases. We also give explicit expressions for the moments of the
spectral density.


  Photo-generated charge in thick, back-illuminated, fully-depleted CCDs is
transported by electric fields from the silicon substrate to the collecting
well at the front gate of the CCDs. However, electric fields transverse to the
surface of the CCD -with diverse origins such as doping gradients, guard rings
around the imaging area of the sensor, and physical stresses on the silicon
lattice- displace this charge, effectively modifying the pixel area and
producing noticeable signals in astrometric and photometric measurements. We
use data from the science verification period of the Dark Energy Survey (DES)
to characterize these effects in the Dark Energy Camera (DECam) CCDs. The
transverse fields mainly manifest as concentric rings ("tree rings") and bright
stripes near the boundaries of the detectors ("edge distortions") with relative
amplitudes of about 1% and 10% in the flat-field images, respectively. Their
nature as pixel size variations is confirmed by comparing their photometric and
astrometric signatures. Using flat-field images from DECam, we derive templates
in the five DES photometric bands (grizY) for the tree rings and the edge
distortions as a function of their position in each DECam detector. These
templates can be directly incorporated into the derivation of photometric and
astrometric solutions, helping to meet the DES photometric and astrometric
requirements.


  The presence of a confining boundary can modify the local structure of a
liquid markedly. In addition, small samples of finite size are known to exhibit
systematic deviations of thermodynamic quantities relative to their bulk
values. Here, we consider the static structure factor of a liquid sample in
slab geometry with open boundaries at the surfaces, which can be thought of as
virtually cutting out the sample from a macroscopically large, homogeneous
fluid. This situation is a relevant limit for the interpretation of
grazing-incidence diffraction experiments at liquid interfaces and films. We
derive an exact, closed expression for the slab structure factor, with the bulk
structure factor as the only input. This shows that such free boundary
conditions cause significant differences between the two structure factors, in
particular at small wavenumbers. An asymptotic analysis of this result yields
the scaling exponent and an accurate, useful approximation of these finite-size
corrections. Furthermore, the open boundaries permit the interpretation of the
slab as an open system, supporting particle exchange with a reservoir. We
relate the slab structure factor to the particle number fluctuations and
discuss conditions under which the subvolume of the slab represents a grand
canonical ensemble with chemical potential $\mu$ and temperature $T$. Thus, the
open slab serves as a test-bed for the small-system thermodynamics in a $\mu T$
reservoir. We provide a microscopically justified and exact result for the size
dependence of the isothermal compressibility. Our findings are corroborated by
simulation data for Lennard-Jones liquids at two representative temperatures.


  This paper studies the continuous time mean-variance portfolio selection
problem with one kind of non-linear wealth dynamics. To deal the expectation
constraint, an auxiliary stochastic control problem is firstly solved by two
new generalized stochastic Riccati equations from which a candidate portfolio
in feedback form is constructed, and the corresponding wealth process will
never cross the vertex of the parabola. In order to verify the optimality of
the candidate portfolio, the convex duality (requires the monotonicity of the
cost function) is established to give another more direct expression of the
terminal wealth level. The variance-optimal martingale measure and the link
between the non-linear financial market and the classical linear market are
also provided. Finally, we obtain the efficient frontier in closed form. From
our results, people are more likely to invest their money in riskless asset
compared with the classical linear market.


  An analytic static monopole solution is found in global AdS$_4$, in the limit
of small backreaction. This solution is mapped in Poincar\'e patch to a falling
monopole configuration, which is dual to a local quench triggered by the
injection of a condensate. Choosing boundary conditions which are dual to a
time-independent Hamiltonian, we find the same functional form of the
energy-momentum tensor as the one of a quench dual to a falling black hole. On
the contrary, the details of the spread of entanglement entropy are very
different from the falling black hole case where the quench induces always a
higher entropy compared to the vacuum, i.e. $\Delta S >0$. In the propagation
of entanglement entropy for the monopole quench, there is instead a competition
between a negative contribution to $\Delta S$ due to the scalar condensate and
a positive one carried by the freely propagating quasiparticles generated by
the energy injection.


  We consider interior H\"{o}lder regularity of the spatial gradient of
viscosity solutions to the normalized $p(x,t)$-Laplace equation $$
u_t=\left(\delta_{ij}+(p(x,t)-2)\frac{u_i u_j}{|Du|^2}\right)u_{ij} $$ with
some suitable assumptions on $p(x,t)$, which arises naturally from a two-player
zero-sum stochastic differential game with probabilities depending on space and
time.


  We present high-resolution images of the strongly bipolar planetary nebula
NGC 6537, obtained with Hubble Space Telescope and with the infrared adaptive
optics system on the Very Large Telescope. The central star is detected for the
first time. Using the multi-band photometry and constraints from the dynamical
age of the nebula, we derive a temperature in the range 1.5-2.5 10^5 K, a
luminosity~10^3 L_sun and a core mass M_c~0.7-0.9 M_sun. The progenitor mass is
probably in the range M_i = 3-7 M_sun. The extinction map shows a largely
symmetric, and compact dust structure, which is most likely a shell, located at
the neck of the bipolar flow, only 4 arcsec from the star. The dust shell
traces a short-lived phase of very high mass loss at the end of the AGB. The
dynamical age of the shell and bipolar lobes are very similar but the
morphologies are very different. The data suggests that the mass loss during
the ejection of the compact shell was largely spherically symmetric, and the
pronounced bipolarity formed afterwards. The dynamical ages of the bipolar
lobes and dust shell are similar, which is consistent with suggestions that
bipolar structures form in a run-away event at the very last stages of the AGB
mass loss. The inner edge of the dust shell is ionized, and PAH emission is
seen just outside the ionized gas. We associate the PAH emission with the
photo-dissociation region of the molecular shell.


  The statistical characterization of the sum of random variables (RVs) are
useful for investigating the performance of wireless communication systems. We
derive exact closed-form expressions for the probability density function (PDF)
and cumulative distribution function (CDF) of a sum of independent but not
identically distributed (i.n.i.d.) Fisher-Snedecor $\mathcal{F}$ RVs. Both PDF
and CDF are given in terms of the multivariate Fox's $H$-function. Besides, a
simple and accurate approximation to the sum of i.n.i.d. Fisher-Snedecor
$\mathcal{F}$ variates is presented using the moment matching method. The
obtained PDF and CDF are used to evaluate the performance of wireless
communication applications including the outage probability, the effective
capacity and the channel capacities under four different adaptive transmission
strategies. Moreover, the corresponding approximate expressions are obtained to
provide useful insights for the design and deployment of wireless communication
systems. In addition, we derive simple asymptotic expressions for the proposed
mathematical analysis in the high signal-to-noise ratio regime. Finally, the
numerical results demonstrate the accuracy of the derived expressions.


  We propose a novel transformer model, capable of segmenting medical images of
varying modalities. Challenges posed by the fine grained nature of medical
image analysis mean that the adaptation of the transformer for their analysis
is still at nascent stages. The overwhelming success of the UNet lay in its
ability to appreciate the fine-grained nature of the segmentation task, an
ability which existing transformer based models do not currently posses. To
address this shortcoming, we propose The Fully Convolutional Transformer (FCT),
which builds on the proven ability of Convolutional Neural Networks to learn
effective image representations, and combines them with the ability of
Transformers to effectively capture long-term dependencies in its inputs. The
FCT is the first fully convolutional Transformer model in medical imaging
literature. It processes its input in two stages, where first, it learns to
extract long range semantic dependencies from the input image, and then learns
to capture hierarchical global attributes from the features. FCT is compact,
accurate and robust. Our results show that it outperforms all existing
transformer architectures by large margins across multiple medical image
segmentation datasets of varying data modalities without the need for any
pre-training. FCT outperforms its immediate competitor on the ACDC dataset by
1.3%, on the Synapse dataset by 4.4%, on the Spleen dataset by 1.2% and on ISIC
2017 dataset by 1.1% on the dice metric, with up to five times fewer
parameters. Our code, environments and models will be available via GitHub.


  We discuss possible parallel textures of the Yukawa coupling matrices in the
generaltwo-Higgs-doublet model (2HDM). In those textures the flavor changing
neutral currentsare naturally suppressed. Motivated by a phenomenologically
successful texturewith four texture zeros in the standard model, we propose a
predictive ansatz for the Yukawa coupling matrices with the same texture in the
general 2HDM. Compared with the six texture-zero based ansatz proposed by Cheng
and Sher, it is in a better agreement with the data of quark mixings and CP
violation. The four texture-zero based ansatz predicts a different hierarchy in
the Yukawa coupling matrix elements. As a consequence, in the lepton sector,
the related Yukawa couplings are less constrained by the experimental upper
bound of $\mu\to e\gamma$, which allows significantly larger predictions for
other processes. The contributions from neutral scalar interactions to the
lepton number violation decay modes $\ell\to \ell_{1}\ell_{2}\ell_{3}$ are
calculated in both ansatz. It is shown that the predictions from the four
texture-zero based ansatz could be two order of magnitude greater than that
from the six texture-zero based one. The branching ratio of $\mu\to 3e$ and
$\tau\to 3\mu$ can reach $7.5 \times 10^{-17}$ and $1.3\tiems 10^{-10}$
respectively. The predicted ratio of $Br(\mu\to 3e)/Br(\tau\to 3e)$ is also
larger and almost parameter independent. Those differences make the two ansatz
to be easily distinguished by the future experiments.


  The characterization of the polarimetric properties of the planet Earth is
important for the interpretation of expected observations and the planning of
future instruments. We present a multi-wavelengths and multi-phase set of
benchmark values for the polarization signal of the integrated light from the
planet Earth derived from new polarimetric observations of the earthshine
back-scattered from the Moon's dark side. Using a new, specially designed wide
field polarimeter we measured the fractional polarization of the earthshine in
the B, V, R and I filters for Earth phase angles alpha between 30{\deg} and
110{\deg}. The phase dependence of the earthshine polarization is fitted by a
function p x sin(alpha)^2. To determine the polarization of the planet Earth we
correct our earthshine measurements by a polarization efficiency function for
the lunar surface derived from measurements of lunar samples from the
literature. The polarization of the earthshine decreases towards longer
wavelengths and is about a factor 1.3 lower for the higher albedo highlands.
For mare regions the measured maximum polarization is about 13 % at quadrature
in the B band. The resulting fractional polarizations for Earth are 24.6 % for
the B band, 19.1 % for the V band, 13.5 % for the R band, and 8.3 % for the I
band. Together with literature values for the spectral reflectivity of Earth we
obtain a contrast between the polarized flux of the Earth and the (total) flux
of the Sun with an uncertainty of less than 20 % and we find that the best
phase to detect an Earth twin is around an Earth phase alpha=65{\deg}. The
polarimetric models of Earth-like planets from Stam (2008) are in qualitative
agreement with our results but there are also significant differences which
might guide more detailed computations.


  In this paper we define an action of the Weyl group on the quiver varieties
$M_{m,\grl}(d,v)$ with generic $(m,\grl)$. To do it we describe a set of
generators of the projective ring of a quiver variety. We also prove
connectness for the smooth quiver variety $M(d,v)$ and normality for $M_0(d,v)$
in the case of a quiver of finite type and $d-v$ a regular weight.


  The predictions of the Bohmian and the decoherent (or consistent) histories
formulations of the quantum mechanics of a closed system are compared for
histories -- sequences of alternatives at a series of times. For certain kinds
of histories, Bohmian mechanics and decoherent histories may both be formulated
in the same mathematical framework within which they can be compared. In that
framework, Bohmian mechanics and decoherent histories represent a given history
by different operators. Their predictions for the probabilities of histories
therefore generally differ. However, in an idealized model of measurement, the
predictions of Bohmian mechanics and decoherent histories coincide for the
probabilities of records of measurement outcomes. The formulations are thus
difficult to distinguish experimentally. They may differ in their accounts of
the past history of the universe in quantum cosmology.


  We analyze the results of an experimental setup that consist of two
statistically independent laser beams that cross, interfere and end at
detectors. At the beam intersection we place a thin wire at the center of a
dark interference fringe and analyze the complementarity inequality. We find
that the complementarity inequality is fulfilled provided we include a
scattering interaction. We find that this interaction is implicit in the
formalism of quantum theory; however, this interaction is active only when the
conservation laws are satisfied.


  Layered 5d transition metal oxides (TMOs) have attracted significant interest
in recent years because of the rich physical properties induced by the
interplay between spin-orbit coupling, bandwidth and on-site Coulomb repulsion.
In Sr2IrO4, this interplay opens a gap near the Fermi energy and stabilizes a
Jeff=1/2 spin-orbital entangled insulating state at low temperatures. Whether
this metal-insulating transition (MIT) is Mott-type (electronic-correlation
driven) or Slater-type (magnetic-order driven) has been under intense debate.
We address this issue via spatially resolved imaging and spectroscopic studies
of the Sr2IrO4 surface using scanning tunneling microscopy/spectroscopy
(STM/S). The STS results clearly illustrate the opening of the (~150-250 meV)
insulating gap at low temperatures, in qualitative agreement with our
density-functional theory (DFT) calculations. More importantly, the measured
temperature dependence of the gap width coupled with our DFT+dynamical mean
field theory (DMFT) results strongly support the Slater-type MIT scenario in
Sr2IrO4. The STS data further reveal a pseudogap structure above the Neel
temperature, presumably related to the presence of antiferromagnetic
fluctuations.


  We experimentally demonstrate that a long distance actively stabilized
Mach-Zehnder fibre optical interferometer can be used to reliably implement the
GV95 quantum cryptography protocol employing orthogonal states. A
proof-of-principle experiment using an interferometer composed of 1 km of
spooled optical fibres connecting Alice and Bob is performed. The active
stabilisation against phase drifts is done with a classical channel
wavelength-multiplexed with the quantum channel and a high stable visibility
implying a QBER of 2.2 % is shown.


  CP violation in the neutral kaon system is known to be dominated by the
mixing of K0 and anti-K0. Direct CP violation in the 2 pion decays of neutral
kaons has been a controversial subject over the last decade. A strong
experimental effort has been devoted to the precise measurement of the direct
CP violation parameter re(epsilon'/epsilon). After 10 years of detector
development, data collection and analysis, the NA48 experiment at CERN and the
KTeV experiment at Fermilab have now established direct CP violation as a fact.
Both KTeV and NA48 use the same experimental principle, measuring the double
ratio of long lived and short lived neutral kaons to two charged and two
neutral pions. However, their experimental and analysis techniques differ in
important ways, and I will extensively discuss the two approaches. I will also
present the latest results on epsilon'/epsilon from both experiments, which
were announced just a few months ago.


  Many systems that can be described in terms of diffusion-limited `chemical'
reactions display non-equilibrium continuous transitions separating active from
inactive, absorbing states, where stochastic fluctuations cease entirely. Their
critical properties can be analyzed via a path-integral representation of the
corresponding classical master equation, and the dynamical renormalization
group. An overview over the ensuing universality classes in single-species
processes is given, and generalizations to reactions with multiple particle
species are discussed as well. The generic case is represented by the processes
A <-> A + A, and A -> 0, which map onto Reggeon field theory with the critical
exponents of directed percolation (DP). For branching and annihilating random
walks (BARW) A -> (m+1) A and A + A -> 0, the mean-field rate equation predicts
an active state only. Yet BARW with odd m display a DP transition for d <= 2.
For even offspring number m, the particle number parity is conserved locally.
Below d_c' = 4/3, this leads to the emergence of an inactive phase that is
characterized by the power laws of the pair annihilation process. The critical
exponents at the transition are those of the `parity-conserving' (PC)
universality class. For local processes without memory, competing pair or
triplet annihilation and fission reactions k A -> (k - l) A, k A -> (k+m)A with
k=2,3 appear to yield the only other universality classes not described by
mean-field theory. In these reactions, site occupation number restrictions play
a crucial role.


  We consider the most general CP-conserving renormalizable effective scalar
potential involving two doublets plus one singlet Higgs and satisfying the
electroweak gauge symmetry. After deriving the electroweak-symmetry breaking
conditions, we focus on special cases, characterized by specific symmetry
properties and/or relations to supersymmetry-inspired extensions of the
Standard Model (e.g. n/NMSSM, UMSSM). We then investigate the question of the
reconstruction of the potential parameters from the Higgs masses and mixing
angles and show that in some specific cases, such as the one of an underlying
NMSSM, an accuracy at the order of leading-logarithms is achievable with
minimal effort. We finally study a few phenomenological consequences for this
latter model. More specifically, we consider how our parameter reconstruction
modifies the outcome of two publicly available codes : micrOMEGAs and
NMSSMTools. We observed noteworthy effects in regions of parameter space where
Higgs-to-Higgs decays are relevant, impacting the collider searches for light
Higgs states and the prediction of the Dark-Matter relic density.


  Let $\pi$ be a cuspidal automorphic representation of
$PGL_2(\mathbb{A}_\mathbb{Q})$ of arithmetic conductor $C$ and archimedean
parameter $T$, and let $\phi$ be an $L^2$-normalized automorphic form in the
space of $\pi$. The sup-norm problem asks for bounds on $\| \phi \|_\infty$ in
terms of $C$ and $T$. The quantum unique ergodicity (QUE) problem concerns the
limiting behavior of the $L^2$-mass $|\phi|^2 (g) \, d g$ of $\phi$. All
previous work on these problems in the conductor-aspect has focused on the case
that $\phi$ is a newform.
  In this work, we study these problems for a class of automorphic forms that
are not newforms. Precisely, we assume that for each prime divisor $p$ of $C$,
the local component $\pi_p$ is supercuspidal (and satisfies some additional
technical hypotheses), and consider automorphic forms $\phi$ for which the
local components $\phi_p \in \pi_p$ are "minimal" vectors. Such vectors may be
understood as non-archimedean analogues of lowest weight vectors in holomorphic
discrete series representations of $PGL_2(\mathbb{R})$.
  For automorphic forms as above, we prove a sup-norm bound that is sharper
than what is known in the newform case. In particular, if $\pi_\infty$ is a
holomorphic discrete series of lowest weight $k$, we obtain the optimal bound
$C^{1/8 -\epsilon} k^{1/4 - \epsilon} \ll_{\epsilon} |\phi|_\infty
\ll_{\epsilon} C^{1/8 + \epsilon} k^{1/4+\epsilon}$. We prove also that these
forms give analytic test vectors for the QUE period, thereby demonstrating the
equivalence between the strong QUE and the subconvexity problems for this class
of vectors. This finding contrasts the known failure of this equivalence for
newforms of powerful level.


  (Abridged) We present the results from a detailed analysis of the 0.6 - 10
keV spectra of 23 ASCA observations of 18 objects. We find that in most cases
the underlying continuum can be well-represented by a powerlaw with a photon
index Gamma approx 2. However we find strong evidence for photoionized gas in
the line-of-sight to 13/18 objects. We present detailed modelling of this gas
based upon the ION photoionization code. We find the X-ray ionization parameter
for the ionized material is strongly peaked at Ux approx 0.1. The column
densities of ionized material are typically in the range N_{H,z} approx
10^{21}--10^{23} cm^{-2}, although highly ionized column densities up to
10^{24} cm^{-2} cannot be excluded in some cases. We also investigate the
importance of the emission-spectrum from the ionized gas, finding that it
significantly improves the fit to many sources with an intensity consistent
with material subtending a large solid angle at the central source. A deficit
of counts is observed at approx 1 keV in the sources exhibiting the strongest
absorption features. We suggest this is likely to be the signature of a second
zone of (more highly) ionized gas, which might have been seen previously in the
deep Fe K-shell edges observed in some Ginga observations. We find evidence
that the ionized material in NGC 3227 and MCG-6-30-15 contains embedded dust,
whilst there is no such evidence in the other sources


  We formulate a set of linear equations that describe the behaviour of small
eccentricities in a protoplanetary system consisting of a gaseous disc and a
planet. Eccentricity propagates through the disc by means of pressure and
self-gravity, and is exchanged with the planet via secular interactions.
Excitation and damping of eccentricity can occur through Lindblad and
corotation resonances, as well as viscosity. We compute normal modes of the
coupled disc-planet system in the case of short-period giant planets orbiting
inside an inner cavity, possibly carved by the stellar magnetosphere.
Three-dimensional effects allow for a mode to be trapped in the inner parts of
the disc. This mode can easily grow within the disc's lifetime. An eccentric
mode dominated by the planet can also grow, although less rapidly. We compute
the structure and growth rates of these modes and their dependence on the
assumed properties of the disc.


  Of 104 AGN known to exhibit H$_2$O maser emission, X-ray data that enable
estimation of column densities, or lower limits, are available for 42.
Contributing to this, we report analysis of new and archival X-ray data for 8
galaxies and collation of values for three more. Maser emission is indicative
of large columns of cold gas, and in five of the eight new cases, maser spectra
point toward origins in accretion disks viewed close-to edge-on (a.k.a.
"disk-maser" systems). In these, we detect hard continuum and Fe K$\alpha$
emission with equivalent widths on the order of 1 keV, which is consistent with
Compton reflection, fluorescence by cold material, and obscuring columns $\ga
10^{24}$ cm$^{-2}$. Reviewing the full sample of 42, 95% exhibit N$_{\rm H}
>10^{23}$ cm$^{-2}$ and 60% exhibit N$_{\rm H} >10^{24}$ cm$^{-2}$. Half of
these are now recognized to be disk masers (up from 13); in this sub-sample,
which is likely to be more homogeneous vis-\'a-vis the origin of maser
emission, 76% exhibit N$_{\rm H} >10^{24}$ cm$^{-2}$. The probability of a
common parent distribution of columns for disk-masers and other AGN masers is
<3%. Because ground-based surveys of AGN to detect new disk masers are
relatively unbiased with respect to X-ray brightness and comparatively
inexpensive, they may also be efficient guides for the sensitive pointed X-ray
observations required to identify Compton-thick objects outside of shallow
surveys.


  Precise time-dependent measurements of the Z = 2 component in the cosmic
radiation provide crucial information about the propagation of charged
particles through the heliosphere. The PAMELA experiment, with its long flight
duration (15th June 2006 - 23rd January 2016) and the low energy threshold (80
MeV/n) is an ideal detector for cosmic ray solar modulation studies. In this
paper, the helium nuclei spectra measured by the PAMELA instrument from July
2006 to December 2009 over a Carrington rotation time basis are presented. A
state-of-the-art three-dimensional model for cosmic-ray propagation inside the
heliosphere was used to interpret the time-dependent measured fluxes.
Proton-to-helium flux ratio time profiles at various rigidities are also
presented in order to study any features which could result from the different
masses and local interstellar spectra shapes.


  The task of translating between programming languages differs from the
challenge of translating natural languages in that programming languages are
designed with a far more rigid set of structural and grammatical rules.
Previous work has used a tree-to-tree encoder/decoder model to take advantage
of the inherent tree structure of programs during translation. Neural decoders,
however, by default do not exploit known grammar rules of the target language.
In this paper, we describe a tree decoder that leverages knowledge of a
language's grammar rules to exclusively generate syntactically correct
programs. We find that this grammar-based tree-to-tree model outperforms the
state of the art tree-to-tree model in translating between two programming
languages on a previously used synthetic task.


  We investigate the light-cone effect on the Shapiro time delay. The extra
time delay caused by Jupiter on the 8th of September 2002 can be measured by
advanced VLBI (very long baseline interferometry). Our expression for the delay
is in complete agreement with that of Kopeikin (2001), in which he argued that
the excess time delay was due to the propagation of gravity. The present
letter, however, shows that the excess comes from nothing but the propagation
of light, namely the light-cone effect. To make a robust confirmation of
general relativity by the coming Jupiter event, it is important to take account
of the light-cone effect on the Shapiro time delay.


  Rapoport's rule claims that latitudinal ranges of plant and animal species
are generally smaller at low than at high latitudes. However, doubts as to the
generality of the rule have been expressed, because studies providing evidence
against the rule are more numerous than those in support of it. In groups for
which support has been provided, the trend of increasing latitudinal ranges
with latitude is restricted to or at least most distinct at high latitudes,
suggesting that the effect may be a local phenomenon, for example the result of
glaciations. Here we test the rule using two models, a simple one-dimensional
one with a fixed number of animals expanding in a northern or southerly
direction only, and the evolutionary/ecological Chowdhury model using birth,
ageing, death, mutation, speciation, prey-predator relations and food levels.
Simulations with both models gave results contradicting Rapoport's rule. In the
first, latitudinal ranges were roughly independent of latitude, in the second,
latitudinal ranges were greatest at low latitudes, as also shown empirically
for some well studied groups of animals.


  Bollob\'as and Nikiforov conjectured that for any graph $G \neq K_n$ with $m$
edges \[ \lambda_1^2+\lambda_2^2\le \bigg( 1-\frac{1}{\omega(G)}\bigg)2m\]
where $\lambda_1$ and $\lambda_2$ denote the two largest eigenvalues of the
adjacency matrix $A(G)$, and $\omega$ denotes the clique number of $G$. This
conjecture was recently verified for triangle-free graphs by Lin, Ning and Wu
and for regular graphs by Zhang. Elphick, Wocjan and Linz proposed a
generalization of this conjecture. In this note, we verify this generalized
conjecture for the family of graphs on $m$ edges, which contain at most
$O(m^{1.5-\varepsilon})$ triangles for some $\varepsilon > 0$. In particular,
we show that the conjecture is true for planar graphs, book-free graphs and
cycle-free graphs.


  We study the effect of disorder on the London penetration depth in iron-based
superconductors. The theory is based on a two-band model with
quasi-two-dimensional Fermi surfaces, which allows for the coexistence region
in the phase diagram between magnetic and superconducting states in the
presence of intraband and interband scattering. Within the quasiclassical
approximation we derive and solve Eilenberger's equations, which include a weak
external magnetic field, and provide analytical expressions for the penetration
depth in the various limiting cases. A complete numerical analysis of the
doping and temperature dependence of the London penetration depth reveals the
crucial effect of disorder scattering, which is especially pronounced in the
coexistence phase. The experimental implications of our results are discussed.


  It is generally held that >100 TeV emission from astrophysical objects
unambiguously demonstrates the presence of PeV protons or nuclei, due to the
unavoidable Klein-Nishina suppression of inverse Compton emission from
electrons. However, in the presence of inverse Compton dominated cooling, hard
high-energy electron spectra are possible. We show that the environmental
requirements for such spectra can naturally be met in spiral arms, and in
particular in regions of enhanced star formation activity, the natural
locations for the most promising electron accelerators: powerful young pulsars.
Our scenario suggests a population of hard ultra-high energy sources is likely
to be revealed in future searches, and may also provide a natural explanation
for the 100 TeV sources recently reported by HAWC.


  The STEREO mission has been providing stereoscopic view of filament eruptions
in EUV. The clearest view during a filament eruption is seen in He II 304 A
observations. One of the main problems visualizing filament dynamics in He II
304 A is the strong background contrast due to surface features. We present a
technique that removes background features and leaves behind only the
filamentary structure, as seen by STEREO-A and B. The technique uses a pair of
STEREO He II 304 A images observed simultaneously. The STEREO-B image is
geometrically transformed to STEREO-A view so that the background images appear
similar. Filaments being elevated structures, i.e., not lying on the same
spherical surface as background features, do not appear similar in the
transformed view. Thus, subtracting the two images cancels the background but
leaves behind the filament structure. We apply this technique to study the
dynamics of the filament eruption event of 22 May 2008, which was observed by
STEREO and followed by several ground-based observatories participating in the
Joint Observing Programme (JOP 178).


  In this thesis, we study Laplacian eigenfunctions on metric graphs, also
known as quantum graphs. We restrict the discussion to standard quantum graphs.
These are finite connected metric graphs with functions that satisfy Neumann
vertex conditions.
  The first goal of this thesis is the study of the nodal count problem. That
is the number of points on which the $n$th eigenfunction vanishes. We provide a
probabilistic setting using which we are able to define the nodal
count\textquoteright s statistics. We show that the nodal count statistics
admit a topological symmetry by which the first Betti number of the graph can
be obtained. We revise a conjecture that predicts a universal Gaussian behavior
of the nodal count statistics for large graphs and we prove it for a certain
family of graphs.
  The second goal is to formulate and study the Neumann count, which is the
number of local extrema of the $n$th eigenfunction. This counting problem is
motivated by the Neumann partitions of planar domains, a novel concept in
spectral geometry. We provide uniform bounds on the Neumann count and
investigate its statistics. We show that the Neumann count provides
complimentary geometrical information to that obtained from the nodal count. We
show that for a certain family of growing tree graphs the Neumann count
statistics approaches a Gaussian distribution.
  The third goal is a genericity result, which justifies the generality of the
Neumann count discussion. To this day it was known that generically,
eigenfunctions do not vanish on vertices. We generalize this result to
derivatives at vertices as well. That is, generically, the derivatives of an
eigenfunction on interior vertices do not vanish.


  We study with ARPES the renormalization and quasiparticle lifetimes of the
$d_{xy}$ and $d_{xz}$/$d_{yz}$ orbitals in two iron pnictides, LiFeAs and
Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ (Co8). We find that both quantities depend
on orbital character rather than on the position on the Fermi Surface (for
example hole or electron pocket). In LiFeAs, the renormalizations are larger
for $d_{xy}$, while they are similar on both types of orbitals in Co8. The most
salient feature, which proved robust against all the ARPES caveats we could
think of, is that the lifetimes for $d_{xy}$ exhibit a markedly different
behavior than those for $d_{xz}$/$d_{yz}$. They have smaller values near $E_F$
and exhibit larger $\omega$ and temperature dependences. While the behavior of
$d_{xy}$ is compatible with a Fermi liquid description, it is not the case for
$d_{xz}$/$d_{yz}$. This situation should have important consequences for the
physics of iron pnictides, which have not been considered up to now. More
generally, it raises interesting questions on how a Fermi liquid regime can be
established in a multiband system with small effective bandwidths.


  We attempt to a physical interpretation of some known static vacuum solutions
of Einstein's equations, namely, the A and B metrics of Ehlers and Kundt. All
of them have axial symmetry, so they can be transformed to the Weyl form. In
Weyl coordinates $\ln\sqrt{-g_{44}}$ obeys a Laplace equation, and from this a
source, called The Newtonian image source can be identified. We use the image
sources to interpret the metrics. The procedure is sucessful in some cases. In
others it fails because the Weyl transform does not have reasonable properties
at infinity.


  We study the effect of a probe string to black hole complexity according to
the CA (Complexity equals Action) conjecture. Our system contains a particle
moving on the boundary of black hole spacetime. In the dual description this
corresponds to the insertion of a fundamental string on the bulk spacetime. The
total action consists of the Einstein-Hilbert term and the Nambu-Goto term. The
effect of this string is expressed by the Nambu-Goto term. Focusing on the
Nambu-Goto term, we analyse the time development of this system. Our results
show some interesting properties of complexity. This gives a useful hint for
defining complexity in quantum field theories.


  We report here our spectropolarimetric observations obtained using the
Espadons/CFHT high resolution spectrograph of two M dwarf stars which standard
models suggest are fully convective: EV Lac (M3.5) and HH And (M5.5). The
difference in their rotational velocity makes them good targets to study the
dependence of the magnetic field topology in M dwarfs on rotation. Our results
reveal some aspects of the field topology in EV Lac and HH And. We measured
mean longitudinal magnetic field strengths (Bz) in EV Lac ranging from 18+-3 G
to -40+-3 G. The Bz variations are seen to occur in a timescale of less than 50
minutes, significantly shorter than the rotation period, and are not due to a
flaring event. We discuss some formation scenarios of the Zeeman signatures
found in EV Lac. For HH And we could not detect circular polarization and thus
we place an upper limit to Bz of 5 G.


  Jets are multi-partonic systems that develop before interactions with the
quark-gluon plasma set in and lead to energy loss and modifications of their
substructure. Jet modification depends on the degree to which the medium can
resolve the internal jet structure that is dictated by the physics of coherence
governed by a critical angle $\theta_c$. Using resummed quenching weights that
incorporate the IOE framework for medium-induced radiation and embedding the
system into a realistic heavy-ion environment we compute the dependence of jet
suppression on the cone angle $R$ of the jet, both at RHIC and the LHC. At RHIC
kinematics we see a very mild cone angle dependence for the range of $R$
studied, similar to what was found at the LHC. We also present results for the
jet azimuthal anisotropy $v_2$ as a function of $R$. We observe that as
centrality is decreased, $v_2$ for moderate $R$ jets sequentially collapse
towards the result for small $R = 0.1$. The reason of this sequential grouping
is the evolution of $\theta_c$ with centrality due to its strong dependence on
the in-medium traversed length. For jets with $R > \theta_c$, traversing
shorter lengths within the medium will make a larger difference than for jets
with $R < \theta_c$, since the size of the resolved phase-space over which
quenching weights are resummed will be reduced. For this reason, $v_2(R)$ is
quite sensitive to the typical value of $\theta_c$ at a given centrality.


  We discuss the structure of integral etale motivic cohomology groups of
smooth and projective schemes over algebraically closed fields, finite fields,
local fields, and arithmetic schemes.


  We consider a function U satisfying a degenerate elliptic equation on
(0,+\infty)\times R^N with mixed Dirichlet-Neumann boundary conditions. The
Neumann condition is prescribed on a bounded domain \Omega\subset R^N of class
C^{1;1}, whereas the Dirichlet data is on the exterior of \Omega. We prove
Holder regularity estimates of U/d^s, where d is a distance function defined
as d(z) := dist(z;R^N\setminus\Omega), for z\in (0,+\infty)\times R^N. The
degenerate elliptic equation arises from the Caffarelli-Silvestre extension of
the Dirichlet problem for the fractional Laplacian. Our proof relies on
compactness and blow-up analysis arguments.


  Small satellite networks (SSNs), which are constructed by large number of
small satellites in low earth orbits (LEO), are considered as promising ways to
provide ubiquitous Internet access. To handle stochastic Internet traffic,
on-board routing is necessary in SSNs. However, large-scale, high dynamic SSN
topologies and limited resources make on-board routing in SSNs face great
challenges. To address this issue, we turn to graph neural network (GNN), a
deep learning network inherently designed for graph data, motivated by the fact
that SSNs can be naturally modeled as graphs. By exploiting GNN's topology
extraction capabilities, we propose a GNN-based learning routing approach (GLR)
to achieve near-optimal on-board routing with low complexity. We design
high-order and low-order feature extractor and cross process to deal with high
dynamic topologies of SSNs, even those topologies that have never been seen in
training. Simulation results demonstrate that GLR results in a significant
reduction in routing computation cost while achieves near-optimal routing
performance in SSNs with different scales compared with typical existing
satellite routing algorithms.


  Locating objects referred to in natural language poses a significant
challenge for autonomous agents. Existing CLIP-based open-vocabulary methods
successfully perform 3D object retrieval with simple (bare) queries but cannot
cope with ambiguous descriptions that demand an understanding of object
relations. To tackle this problem, we propose a modular approach called BBQ
(Beyond Bare Queries), which constructs 3D scene spatial graph representation
with metric edges and utilizes a large language model as a human-to-agent
interface through our deductive scene reasoning algorithm. BBQ employs robust
DINO-powered associations to form 3D objects, an advanced raycasting algorithm
to project them to 2D, and a vision-language model to describe them as graph
nodes. On Replica and ScanNet datasets, we show that the designed method
accurately constructs 3D object-centric maps. We have demonstrated that their
quality takes a leading place for open-vocabulary 3D semantic segmentation
against other zero-shot methods. Also, we show that leveraging spatial
relations is especially effective for scenes containing multiple entities of
the same semantic class. On Sr3D and Nr3D benchmarks, our deductive approach
demonstrates a significant improvement, enabling retrieving objects by complex
queries compared to other state-of-the-art methods. Considering our design
solutions, we achieved a processing speed approximately x3 times faster than
the closest analog. This promising performance enables our approach for usage
in applied intelligent robotics projects. We make the code publicly available
at linukc.github.io/bbq/.


  We consider the problem of testing the dimension of uncharacterised classical
and quantum systems in a prepare-and-measure setup. Here we assume the
preparation and measurement devices to be independent, thereby making the
problem non-convex. We present a simple method for generating nonlinear
dimension witnesses for systems of arbitrary dimension. The simplest of our
witnesses is highly robust to technical imperfections, and can certify the use
of qubits in the presence of arbitrary noise and arbitrarily low detection
efficiency. Finally, we show that this witness can be used to certify the
presence of randomness, suggesting applications in quantum information
processing.


  We present a new dust extension to the Monte Carlo radiative transfer code
crash, which enables it to simulate the propagation of ionizing radiation
through mixtures of gas and dust. The new code is applied to study the impact
of dust absorption on idealized galactic H II regions and on small scale
reionization. We find that H II regions are reduced in size by the presence of
dust, while their inner temperature and ionization structure remain largely
unaffected. In the small scale reionization simulation, dust hardens ionization
fronts and delays the overlap of ionized bubbles. This effect is found to
depend only weakly on the assumed abundance of dust in underdense regions.


  A search is presented for hidden-sector bosons, $\chi$, produced in the decay
${B^0\!\to K^*(892)^0\chi}$, with $K^*(892)^0\!\to K^{+}\pi^{-}$ and
$\chi\!\to\mu^+\mu^-$. The search is performed using $pp$-collision data
corresponding to 3.0 fb$^{-1}$ collected with the LHCb detector. No significant
signal is observed in the accessible mass range $214 \leq m({\chi}) \leq 4350$
MeV, and upper limits are placed on the branching fraction product
$\mathcal{B}(B^0\!\to K^*(892)^0\chi)\times\mathcal{B}(\chi\!\to\mu^+\mu^-)$ as
a function of the mass and lifetime of the $\chi$ boson. These limits are of
the order of $10^{-9}$ for $\chi$ lifetimes less than 100 ps over most of the
$m(\chi)$ range, and place the most stringent constraints to date on many
theories that predict the existence of additional low-mass bosons.


  We show that there is an almost complex structure on a differential calculus
on finite points coming from a bidirected finite graph without multiple edges
or loops. We concentrate on a polygon as a concrete case. In particular, a
`holomorphic structure on the exterior bundle' built from the polygon is
studied. Also a positive Hochschild 2-cocycle on the vertex set of the polygon,
albeit a trivial one, is shown to arise naturally from the almost complex
structure.


  Numerical simulations are used to determine the influence of the non-local
and local interactions on the intermittency corrections in the scaling
properties of 3D turbulence. We show that neglect of local interactions leads
to an enhanced small-scale energy spectrum and to a significantly larger number
of very intense vortices (tornadoes) and stronger intermittency. On the other
hand, neglect of the non-local interactions results in even stronger
small-scale spectrum but significantly weaker intermittency. Based on these
observations, a new model of turbulence is proposed, in which non-local
(RDT-like) interactions couple large and small scale via a multiplicative
process with additive noise and the local interactions are modeled by a
turbulent viscosity. This model is used to derive a simple toy version of the
Langevin equations for small-scale velocity increments. A Gaussian
approximation for the large scale fields yields the Fokker-Planck equation for
the probability distribution function of the velocity increments.
  Steady state solutions of this equation allows to qualitatively explain the
anomalous corrections and the skewness generation along scale.


  We prove that, assuming $\mathrm{ZF}$, and restricted to any pointed set,
Chaitin's $\Omega_U:x\mapsto
\Omega_U^x=\sum_{U^x(\sigma)\downarrow}2^{-|\sigma|}$ is not injective for any
universal prefix-free Turing machine $U$, and that $\Omega_U^x$ fails to be
degree invariant in a very strong sense, answering several recent questions in
descriptive set theory. Moreover, we show that under $\mathrm{ZF}+\mathrm{AD}$,
every function $f$ mapping $x$ to $x$-random must be uncountable-to-one over an
upper cone of Turing degrees.


  In recent Kwasniewski's papers inspired by O. V. Viskov it was shown that the
$\psi$-calculus in parts appears to be almost automatic, natural extension of
classical operator calculus of Rota - Mullin or equivalently - of umbral
calculus of Roman and Rota. At the same time this calculus is an example of the
algebraization of the analysis - here restricted to the algebra of polynomials.
The first part of the article is the review of the recent author's
contribution. The main definitions and theorems of Finite Fibonomial
  Operator Calculus which is a special case of $\psi$-extented Rota's finite
operator calculus are presented there. In the second part the characterization
of Fibonacci Cobweb poset P as DAG and oDAG is given. The dim 2 poset such that
its Hasse diagram coincide with digraf of P is constructed.