  We investigate the observational signatures of a straightforward evolutionary
scenario for protoplanetary disks in which the disk mass of small (50 micron)
particles decreases homologously with time, but the disk structure and stellar
parameters do not change. Our goal is to identify optimal infrared spectral
indicators of the existence of disks, their structure, and mass evolution that
may be tested with the upcoming SIRTF mission. We present simulated spectral
energy distributions and colors over a wide range of masses. The SED is most
sensitive to disk mass in the far-IR and longer wavelengths, which is already
known from millimeter and radio observations. As the disk mass decreases, the
excess emission of the disk over the stellar photosphere diminishes more
rapidly at the longest rather than at short wavelengths. At near-infrared
wavelengths, the disk remains optically thick to stellar radiation over a wide
range of disk mass, resulting in a slower decline in the SED in this spectral
regime. Therefore, near-IR excesses (K-L) provide a robust means of detecting
disks in star clusters down to 1E-7 solar masses, while the far-IR excess
probes the disk mass. Reducing the disk mass results in a clear progression in
color-color diagrams with low mass disks displaying the bluest colors. We
interpret color-color diagrams for Taurus-Auriga sources in the context of
decreasing disk mass.


  Given any continuous self-map f of a Banach space E over K (where K is R or
C) and given any point p of E, we define a subset sigma(f,p) of K, called
spectrum of f at p, which coincides with the usual spectrum sigma(f) of f in
the linear case. More generally, we show that sigma(f,p) is always closed and,
when f is C^1, coincides with the spectrum sigma(f'(p)) of the Frechet
derivative of f at p. Some applications to bifurcation theory are given and
some peculiar examples of spectra are provided.


  We have investigated numerically the field-driven propagation of
perpendicularly magnetized ferromagnetic layers. It was then compared to the
historical one-dimensional domain wall (DW) propagation model widely used in
spintronics studies of magnetic nanostructures. In the particular regime of
layer thickness (h) of the order of the exchange length, anomalous velocity
peaks appear in the precessional regime, their shape and position shifting with
h. This has also been observed experimentally. Analyses of the simulations show
a distinct correlation between the curvature of the DW and the twist of the
magnetization vector within it, and the velocity peak. Associating a
phenomenological description of this twist with a four-coordinate DW
propagation model, we reproduce very well these kinks and show that they result
from the torque exerted by the stray field created by the domains on the
twisted magnetization. The position of the peaks is well predicted from the
DW's first flexural mode frequency, and depends strongly on the layer
thickness. Comparison of the proposed model to DW propagation data obtained on
dilute semiconductor ferromagnets GaMnAs and GaMnAsP sheds light on the origin
of the measured peaks.


  In radial basis function neural network (RBFNN) based real-time learning
tasks, forgetting mechanisms are widely used such that the neural network can
keep its sensitivity to new data. However, with forgetting mechanisms, some
useful knowledge will get lost simply because they are learned a long time ago,
which we refer to as the passive knowledge forgetting phenomenon. To address
this problem, this paper proposes a real-time training method named selective
memory recursive least squares (SMRLS) in which the classical forgetting
mechanisms are recast into a memory mechanism. Different from the forgetting
mechanism, which mainly evaluates the importance of samples according to the
time when samples are collected, the memory mechanism evaluates the importance
of samples through both temporal and spatial distribution of samples. With
SMRLS, the input space of the RBFNN is evenly divided into a finite number of
partitions and a synthesized objective function is developed using synthesized
samples from each partition. In addition to the current approximation error,
the neural network also updates its weights according to the recorded data from
the partition being visited. Compared with classical training methods including
the forgetting factor recursive least squares (FFRLS) and stochastic gradient
descent (SGD) methods, SMRLS achieves improved learning speed and
generalization capability, which are demonstrated by corresponding simulation
results.


  We perform classical molecular dynamics simulations to examine the intrinsic
energy dissipation in single-layer MoS$_{2}$ nanoresonators, where a point of
emphasis is to compare its dissipation characteristics with those of
single-layer graphene. Our key finding is that MoS$_{2}$ nanoresonators exhibit
significantly lower energy dissipation, and thus higher quality (Q)-factors by
at least a factor of four below room temperature, than graphene. Furthermore,
this high Q-factor endows MoS$_{2}$ nanoresonators with a higher figure of
merit, defined as frequency times Q-factor, despite a resonant frequency that
is $50%$ smaller than graphene for the same size. By utilizing arguments from
phonon-phonon scattering theory, we show that this reduced energy dissipation
is enabled by the large energy gap in the phonon dispersion of MoS$_{2}$, which
separates the acoustic phonon branches from the optical phonon branches,
leading to a preserving mechanism for the resonant oscillation of MoS$_{2}$
nanoresonators. We further investigate the effects of tensile mechanical strain
and nonlinear actuation on the Q-factors, where the tensile strain is found to
counteract the reductions in Q-factor that occur with higher actuation
amplitudes. Overall, our simulations illustrate the potential utility of
MoS$_{2}$ for high frequency sensing and actuation applications.


  Historical linguists have identified multiple forms of lexical semantic
change. We present a three-dimensional framework for integrating these forms
and a unified computational methodology for evaluating them concurrently. The
dimensions represent increases or decreases in semantic 1) sentiment, 2)
breadth, and 3) intensity. These dimensions can be complemented by the
evaluation of shifts in the frequency of the target words and the thematic
content of its collocates. This framework enables lexical semantic change to be
mapped economically and systematically and has applications in computational
social science. We present an illustrative analysis of semantic shifts in
mental health and mental illness in two corpora, demonstrating patterns of
semantic change that illuminate contemporary concerns about pathologization,
stigma, and concept creep.


  Including contributions of scale-dependent vacuum expectation values, we
derive new analytic formulas and obtain substantially different numerical
predictions for the running masses of quarks and charged-leptons at higher
scales in the SM, 2HDM and MSSM. These formulas exhibit significantly different
behaviours with respect to their dependence on gauge and Yukawa couplings than
those derived earlier. At one-loop level the masses of the first two
generations are found to be independent of Yukawa couplings of the third
generation in all the three effective theories in the small mixing limit.
Analytic formulas are also obtained for running $\tan\beta(\mu)$ in 2HDM and
MSSM. Other numerical analyses include study of the third generation masses at
high scales as functions of low-energy values of $\tan\beta$ and SUSY scale
$M_S=M_Z-10^4$ GeV.


  The results from the ESA Gaia astrometric mission and deep photometric
surveys have revolutionized our knowledge of the Milky Way. There are many
ongoing efforts to search these data for stellar substructure to find evidence
of individual accretion events that built up the Milky Way and its halo. One of
these newly identified features, called Nyx, was announced as an accreted
stellar stream traveling in the plane of the disk. Using a combination of
elemental abundances and stellar parameters from the GALAH and APOGEE surveys,
we find that the abundances of the highest likelihood Nyx members are entirely
consistent with membership of the thick disk, and inconsistent with a dwarf
galaxy origin. We conclude that the postulated Nyx stream is most probably a
high-velocity component of the Milky Way's thick disk. With the growing
availability of large data sets including kinematics, stellar parameters, and
detailed abundances, the probability of detecting chance associations
increases, and hence new searches for substructure require confirmation across
as many data dimensions as possible.


  In this paper, we propose a simple yet efficient strategy for improving the
multi-objective steepest descent method proposed by Fliege and Svaiter (Math
Methods Oper Res, 2000, 3: 479--494). The core idea behind this strategy
involves incorporating a positive modification parameter into the iterative
formulation of the multi-objective steepest descent algorithm in a
multiplicative manner. This modification parameter captures certain
second-order information associated with the objective functions. We provide
two distinct methods for calculating this modification parameter, leading to
the development of two improved multi-objective steepest descent algorithms
tailored for solving multi-objective optimization problems. Under reasonable
assumptions, we demonstrate the convergence of sequences generated by the first
algorithm toward a critical point. Moreover, for strongly convex
multi-objective optimization problems, we establish the linear convergence to
Pareto optimality of the sequence of generated points. The performance of the
new algorithms is empirically evaluated through a computational comparison on a
set of multi-objective test instances. The numerical results underscore that
the proposed algorithms consistently outperform the original multi-objective
steepest descent algorithm.


  The concerning rise of hateful content on online platforms has increased the
attention towards automatic hate speech detection, commonly formulated as a
supervised classification task. State-of-the-art deep learning-based approaches
usually require a substantial amount of labeled resources for training.
However, annotating hate speech resources is expensive, time-consuming, and
often harmful to the annotators. This creates a pressing need to transfer
knowledge from the existing labeled resources to low-resource hate speech
corpora with the goal of improving system performance. For this,
neighborhood-based frameworks have been shown to be effective. However, they
have limited flexibility. In our paper, we propose a novel training strategy
that allows flexible modeling of the relative proximity of neighbors retrieved
from a resource-rich corpus to learn the amount of transfer. In particular, we
incorporate neighborhood information with Optimal Transport, which permits
exploiting the geometry of the data embedding space. By aligning the joint
embedding and label distributions of neighbors, we demonstrate substantial
improvements over strong baselines, in low-resource scenarios, on different
publicly available hate speech corpora.


  The GLAST Large Area Telescope, scheduled for launch in 2006, is a next
generation space based gamma ray telescope which will improve in point source
sensitivity by a factor of 30 over that of EGRET below 10 GeV, and extend
beyond EGRET up to 300 GeV. Thus GLAST offers a unique opportunity to discover
WIMP dark matter through precision studies of gamma rays produced in pair
annihilations. The most dense region of dark matter in our galaxy is currently
thought to occur at the center; in particular, dark matter should concentrate
within 3 pc of the putative supermassive black hole located at the SgrA* radio
source. In fact, the 2nd and 3rd EGRET catalogs contain a significant point
source coincident with the Milky Way galactic center within a resolution of 12
arcminutes. The EGRET team has determined that the spectral and temporal
characteristics of this point source are consistent with dark matter WIMP
annihilations. More detailed analysis has determined that the magnitude and
spectrum of the EGRET source is consistent with relic WIMPs concentrated within
3 pc of the central supermassive black hole. Furthermore, the SgrA* radio
emission is consistent with the synchrotron radiation expected from electrons
and positrons produced in WIMP annihilations. If true, then GLAST should be
able to constrain the particle properties of the postulated WIMP with 1 month
of data.


  Recently, the effectiveness of text-to-speech (TTS) systems combined with
neural vocoders to generate high-fidelity speech has been shown. However,
collecting the required training data and building these advanced systems from
scratch are time and resource consuming. An economical approach is to develop a
neural vocoder to enhance the speech generated by existing or low-cost TTS
systems. Nonetheless, this approach usually suffers from two issues: 1)
temporal mismatches between TTS and natural waveforms and 2) acoustic
mismatches between training and testing data. To address these issues, we adopt
a cyclic voice conversion (VC) model to generate temporally matched pseudo-VC
data for training and acoustically matched enhanced data for testing the neural
vocoders. Because of the generality, this framework can be applied to arbitrary
TTS systems and neural vocoders. In this paper, we apply the proposed method
with a state-of-the-art WaveNet vocoder for two different basic TTS systems,
and both objective and subjective experimental results confirm the
effectiveness of the proposed framework.


  This dissertation investigates the flavor mixing effects in supersymmetric
models on electroweak precision observables, Higgs boson mass predictions,
B-physics observables, quark flavor violating Higgs decays, lepton flavor
violating charged lepton decays and lepton flavor violating Higgs decays. The
flavor mixing effects are studied in model independent way i.e. by putting
off-diagonal entries in the sfermion mass matrix by hand as well as in the
minimal flavor violating constrained MSSM, where mixing can originate from CKM
matrix in the case of squarks and from PMNS matrix in the case of sleptons. We
found that flavor mixing can have large impact to some observables, enabling us
to put new constraints on parameter space in supersymmetric models.


  Given a short exact sequence of groups with certain conditions, $1\to F\to
G\to H\to 1$, we prove that $G$ has solvable conjugacy problem if and only if
the corresponding action subgroup $A\leqslant Aut(F)$ is orbit decidable. From
this, we deduce that the conjugacy problem is solvable, among others, for all
groups of the form $\mathbb{Z}^2\rtimes F_m$, $F_2\rtimes F_m$, $F_n \rtimes
\mathbb{Z}$, and $\mathbb{Z}^n \rtimes_A F_m$ with virtually solvable action
group $A\leqslant GL_n(\mathbb{Z})$. Also, we give an easy way of constructing
groups of the form $\mathbb{Z}^4\rtimes F_n$ and $F_3\rtimes F_n$ with
unsolvable conjugacy problem. On the way, we solve the twisted conjugacy
problem for virtually surface and virtually polycyclic groups, and give an
example of a group with solvable conjugacy problem but unsolvable twisted
conjugacy problem. As an application, an alternative solution to the conjugacy
problem in $Aut(F_2)$ is given.


  Acyclic digraphs arise in many natural and artificial processes. Among the
broader set, dynamic citation networks represent a substantively important form
of acyclic digraphs. For example, the study of such networks includes the
spread of ideas through academic citations, the spread of innovation through
patent citations, and the development of precedent in common law systems. The
specific dynamics that produce such acyclic digraphs not only differentiate
them from other classes of graphs, but also provide guidance for the
development of meaningful distance measures. In this article, we develop and
apply our sink distance measure together with the single-linkage hierarchical
clustering algorithm to both a two-dimensional directed preferential attachment
model as well as empirical data drawn from the first quarter century of
decisions of the United States Supreme Court. Despite applying the simplest
combination of distance measures and clustering algorithms, analysis reveals
that more accurate and more interpretable clusterings are produced by this
scheme.


  The Neumann-Poincar\'{e} operator, a singular integral operator on the
boundary of a domain, naturally appears when one solves a conductivity
transmission problem via the boundary integral formulation. Recently, a series
expression of the Neumann-Poincar\'{e} operator was developed in two dimensions
based on geometric function theory. In this paper, we investigate geometric
properties of composite materials by using this series expansion. In
particular, we obtain explicit formulas for the polarization tensor and the
effective conductivity for an inclusion or a periodic array of inclusions of
arbitrary shape with extremal conductivity, in terms of the associated exterior
conformal mapping. Also, we observe by numerical computations that the spectrum
of the Neumann--Poincar\'{e} operator has a monotonic behavior with respect to
the shape deformation of the inclusion. Additionally, we derive inequality
relations of the coefficients of the Riemann mapping of an arbitrary Lipschitz
domain by using the properties of the polarization tensor corresponding to the
domain.


  The Heidelberg Dark Matter Search Experiment (HDMS) is a new ionization
Germanium experiment in a special design. Two concentric Ge crystals are housed
by one cryostat system, the outer detector acting as an effective shield
against multiple scattered photons for the inner crystal, which is the actual
dark matter target. We present first results after successfully running the
prototype detector for a period of about 15 months in the Gran Sasso
Underground Laboratory. We analyze the results in terms of limits on
WIMP-nucleon cross sections and present the status of the full scale
experiment, which will be installed in Gran Sasso in the course of this year.


  We investigate toy dynamical models of energy-level repulsion in quantum
eigenvalue sequences. We focus on parametric (with respect to a running
coupling or "complexity" parameter) stochastic processes that are capable of
relaxing towards a stationary regime (e. g. equilibrium, invariant asymptotic
measure). In view of ergodic property, that makes them appropriate for the
study of short-range fluctuations in any disordered, randomly-looking spectral
sequence (as exemplified e. g. by empirical nearest-neighbor spacings
histograms of various quantum systems). The pertinent Markov diffusion-type
processes (with values in the space of spacings) share a general form of
forward drifts $b(x) = {{N-1}\over {2x}} - x$, where $x>0$ stands for the
spacing value. Here $N = 2,3,5$ correspond to the familiar (generic)
random-matrix theory inspired cases, based on the exploitation of the Wigner
surmise (usually regarded as an approximate formula). N=4 corresponds to the
(non-generic) non-Hermitian Ginibre ensemble. The result appears to be exact in
the context of $2\times 2$ random matrices and indicates a potential validity
of other non-generic $N>5$ level repulsion laws.


  We investigate the role played by the vacuum of the primordial fluctuations
in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton
potential is a mass term and the unperturbed quantum geometry is governed by
the effective dynamics of Loop Quantum Cosmology. In this situation, the
phenomenologically interesting solutions have a preinflationary regime where
the kinetic energy of the inflaton dominates over the potential. For these kind
of solutions, we show that the primordial power spectra depend strongly on the
choice of vacuum. We study in detail the case of adiabatic states of low order
and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all
imposed at the bounce. The adiabatic spectra are typically suppressed at large
scales, and display rapid oscillations with an increase of power at
intermediate scales. In the non-oscillating vacuum, there is power suppression
for large scales, but the rapid oscillations are absent. We argue that the
oscillations are due to the imposition of initial adiabatic conditions in the
region of kinetic dominance, and that they would also be present in General
Relativity. Finally, we discuss the sensitivity of our results to changes of
the initial time and other data of the model.


  We compute the Hausdorff dimension of the set of singular vectors in function
fields and bound the Hausdorff dimension of the set of $\varepsilon$-Dirichlet
improvable vectors in this setting. This is a function field analogue of the
results of Cheung and Chevallier [Duke Math. J. 165 (2016), 2273--2329].


  In this note we discuss a toy model in which the value of the effective
cosmological constant is associated with a symmetry properties of the vacuum
background solution and defined by the model parameter associated with a scalar
field non-minimally coupled to gravity. Although the parameters in the model
seem to have unrealistic values to account for the present value of the
cosmological constant, the model demonstrates a possible alternative way it can
arise.


  A review and critique of the Isgur-Paton flux tube model of hadronic physics
is presented. This entails a detailed comparison with recent lattice gauge
theory results which exposes both the successes and shortcomings of the model.
Applications to hybrid masses, meson and hybrid meson decays, hadronic charge
radii, the spin-orbit force, baryonic hybrids, and hybrid photocouplings are
also discussed. Finally, I comment on the issue of adiabatic surface crossing
which appears in both the flux tube model and lattice studies.


  Recently, DiFrancesco and Zuber have characterized the RCFTs which have a
description in terms of a fusion potential in one variable, and proposed a
generalized potential to describe other theories. In this note we give a simple
criterion to determine when such a generalized description is possible. We also
determine which RCFTs can be described by a fusion potential in more than one
variable, finding that in fact all RCFTs can be described in such a way, as
conjectured by Gepner.


  We solve a conjecture raised by Bertoin (personal communication) on the
step-reinforced random walk, a non-Markovian process generalizing the elephant
random walk. We show that, under a 2+$\delta$-th moment condition, it undergoes
a phase transition in dimensions $d=1,2$ between recurrence and transience, and
that it is transient for all parameters in dimension $d\geq 3$.


  Phonon-assisted luminescence is a key property of defect centers in
semiconductors, and can be measured to perform the readout of the information
stored in a quantum bit, or to detect temperature variations. The investigation
of phonon-assisted luminescence usually employs phenomenological models, such
as that of Huang and Rhys, with restrictive assumptions that can fail to be
predictive. In this work, we predict luminescence and study exciton-phonon
couplings within a rigorous many-body perturbation theory framework, an
analysis that has never been performed for defect centers. In particular, we
study the optical emission of the negatively-charged boron vacancy in 2D
hexagonal boron nitride, which currently stands out among defect centers in 2D
materials thanks to its promise for applications in quantum information and
quantum sensing. We show that phonons are responsible for the observed
luminescence, which otherwise would be dark due to symmetry. We also show that
the symmetry breaking induced by the static Jahn-Teller effect is not able to
describe the presence of the experimentally observed peak at 1.5 eV.


  A connected reductive group G over a field k may be written as a quotient
H/S, where the k-group H is an extension of a quasitrivial torus by a simply
connected semisimple group, and S is a flasque k-torus, central in H (a flasque
torus is a torus whose cocharacter group is an H^1-trivial Galois lattice). The
flasque torus S is well-defined up to multiplication by a quasitrivial torus.
Such presentations G=H/S lead to a simplified approach of the Galois cohomology
of G and of related objects, such as the Brauer group of a smooth
compactification of G. When k is a number field, one also recovers known
formulas, in terms of S, for the quotient of the group of rational points by
R-equivalence, and for the abelian groups which measure the lack of weak
approximation and the failure of the Hasse principle for principal homogeneous
spaces.


  This paper examines the problem of adaptive influence maximization in social
networks. As adaptive decision making is a time-critical task, a realistic
feedback model has been considered, called myopic. In this direction, we
propose the myopic adaptive greedy policy that is guaranteed to provide a (1 -
1/e)-approximation of the optimal policy under a variant of the independent
cascade diffusion model. This strategy maximizes an alternative utility
function that has been proven to be adaptive monotone and adaptive submodular.
The proposed utility function considers the cumulative number of active nodes
through the time, instead of the total number of the active nodes at the end of
the diffusion. Our empirical analysis on real-world social networks reveals the
benefits of the proposed myopic strategy, validating our theoretical results.


  We study in detail the evolution of two massive stars at solar metallicity
(Z=0.014) taken from Romagnolo et al. (2024, Paper I); by running evolution
models for initial masses 60 and 200 Msun, using MESA and GENEC. For the mass
loss, we adopt the self-consistent m-CAK prescription for the optically thin
winds of OB-stars, a semi-empirical formula for H-rich thick wind of WNh stars,
and a hydrodynamically consistent formula for the H-poor thick wind of
classical Wolf-Rayet stars. We set initial rotation as 40% of the critical
angular velocity, overshooting =0.5, Tayler-Spruit for the angular momentum
transport, and Ledoux criterion for the convective layers. Both codes predict
different tracks across the HRD. For the 60 Msun case, Genec models predict a
more efficient rotational mixing and more chemically homogeneous evolution,
whereas MESA model predicts a large radial expansion post-MS reaching the LBV
phase. For the 200 Msun case, differences are less relevant because their
evolution is dominated by wind mass loss with a weaker dependence on internal
mixing, and only the treatment for superadiabacity creates an impact during the
He-burning stage. The switch of the mass loss based on the proximity to the
Eddington factor instead of the removal of outer layers, implies the existence
of WNh stars with a large mass fraction of hydrogen at the surface formed from
initial masses $\gtrsim60$ Msun. These stars are constrained in a Teff range of
the HR diagram which corresponds to the MS band, in agreement with the
observations of Galactic WNh stars. While our models employ a fixed $\Gamma_e$
threshold for the switch to thick winds, rather than a continuous thin-to-thick
wind model, the good reproduction of observations supports the robustness of
the wind model upgrades introduced in Paper I, allowing its application to
studies of late-stage stellar evolution before core collapse.


  As location-based applications become ubiquitous in emerging wireless
networks, Location Verification Systems (LVS) are of growing importance. In
this paper we propose, for the first time, a rigorous information-theoretic
framework for an LVS. The theoretical framework we develop illustrates how the
threshold used in the detection of a spoofed location can be optimized in terms
of the mutual information between the input and output data of the LVS. In
order to verify the legitimacy of our analytical framework we have carried out
detailed numerical simulations. Our simulations mimic the practical scenario
where a system deployed using our framework must make a binary Yes/No
"malicious decision" to each snapshot of the signal strength values obtained by
base stations. The comparison between simulation and analysis shows excellent
agreement. Our optimized LVS framework provides a defence against location
spoofing attacks in emerging wireless networks such as those envisioned for
Intelligent Transport Systems, where verification of location information is of
paramount importance.


  The interaction energies between two baryons at short distance in different
flavor channels are calculated from the constituent quark model (CQM) and are
compared with the recent lattice QCD (LQCD) results for baryon-baryon
potentials at short distance. We consider the six-quark system with two strange
quarks and focus on the quantum numbers,
(Flavor,Spin)=(1,0),(8,1),(10,1),($\overline{10}$,1) and (27,0). The
interaction energy is defined by subtracting out isolated baryon masses and
relative kinetic energy of two baryons from the total energy of a compact
six-quark state. We introduce interaction energy ratio between different
flavors as a useful measure to test the prediction of CQM. We find that the
ratios in CQM show good agreement with those in LQCD, which indicates that the
short range part of the baryon-baryon interaction can be understood
qualitatively in terms of the Pauli principle and spin-dependent color
interaction among constituent quarks.


  We develop a unified theoretical framework for the efficient description of
multiphoton states generated and propagating in loop-based optical networks
which contain nonlinear elements. These active optical components are modeled
as nonlinear media, resembling a two-mode squeezer. First, such nonlinear
components can be seeded to manipulate quantum states of light, as such
enabling photon addition protocols. And, second, they can function as an
amplifying medium for quantum light. To prove the practical importance of our
approach, the impact of multiple round trips is analyzed for states propagating
in experimentally relevant loop configurations of networks, such as
time-multiplexed driven quantum walks and iterative photon-number state
generation protocols. Our method not only enables us to model such complex
systems but also allows us to propose alternative setups that overcome previous
limitations. To characterize the systems under study, we provide exact
expressions for fidelities with target states, success probabilities of
heralding-type measurements, and correlations between optical modes, including
many realistic imperfections. Moreover, we provide an easily implementable
numerical approach by devising a vector-type representation of photonic states,
measurement operators, and passive and active processes.


  This is a special collection of problems that were given to select applicants
during oral entrance exams to the math department of Moscow State University.
These problems were designed to prevent Jews and other undesirables from
getting a passing grade. Among problems that were used by the department to
blackball unwanted candidate students, these problems are distinguished by
having a simple solution that is difficult to find. Using problems with a
simple solution protected the administration from extra complaints and appeals.
This collection therefore has mathematical as well as historical value.


  We introduce topological gauge fields as nontrivial field configurations
enforced by topological currents. These fields crucially determine the form of
statistical gauge fields that couple to matter and transmute their statistics.
We discuss the physical mechanism underlying the composite particle picture and
argue that it is a duality of gauge forms that naturally relates to the notion
of bosonisation in arbitrary dimensions. This is based on obtaining a
generalised version of flux attachment, which yields a density-dependent gauge
potential. We recover well-known results, resolve old controversies, and
suggest a microscopic mechanism for the emergence of such a gauge field. We
also outline potential directions for experimental realisations in ultracold
atom platforms.


  We show that back-action noise in interferometric measurements such as
gravitational-waves detectors can be completely suppressed by a local control
of mirrors motion. An optomechanical sensor with an optimized measurement
strategy is used to monitor mirror displacements. A feedback loop then
eliminates radiation-pressure effects without adding noise. This very efficient
technique leads to an increased sensitivity for the interferometric
measurement, which becomes only limited by phase noise. Back-action
cancellation is furthermore insensitive to losses in the interferometer.


  Galaxy groups are quite underluminous in X-rays compared to clusters, so the
intracluster medium has to be considerably underdense in the former. We
consider this to be due to substantial energy fed back into the ICM when the
baryons in the member galaxies condense into stars ending up in SNe, or accrete
on to central supermassive black holes energizing AGNs. We compute the outflow
and the blowout effects driven by the AGNs and the resulting, steep
luminosity-temperature correlation L_X-T. We compare this with the SN
contribution and with the X-ray data; the latter require the AGN energy to be
coupled to the surrounding ICM at fractional levels around 5 10^{-2}. We link
the L_X-T behavior with the parallel effects of the AGN feedback on the gas in
the host galaxy; we find that these yield a correlation steep up to
M_{\bullet}\propto \sigma^5 between the galactic velocity dispersions and the
central BH masses.


  We report the detection of a faint old stellar system at
$(\alpha,\delta)=(194.29^\circ,~34.32^\circ)$ (SDSS J1257+3419), based on the
spatial distribution of bright red-giant branch stars in the Sloan Digital Sky
Survey Data Release 4. SDSS J1257+3419 has a half-light radius of $38\pm 12$ pc
and an absolute integrated $V$-magnitude of $M_V=-4.8^{+1.4}_{-1.0}$ mag at a
heliocentric distance of $150\pm 15$ kpc. A comparison between SDSS J1257+3419
and known Galactic halo objects suggests that SDSS J1257+3419 is either (a) a
faint and small dwarf galaxy or (b) a faint and widely extended globular
cluster. In the former case, SDSS J1257+3419 could represent an entity of a
postulated subhalo of the Milky Way. Further photometric and dynamical study of
this stellar system is vital to discriminate these possibilities.


  In this paper we give an alternative construction of a certain class of
Deformed Double Current Algebras. These algebras are deformations of $U({\rm
End}(\Bbbk^r)[x,y])$ and they were initially defined and studied by N.Guay in
his papers. Here we construct them as algebras of endomorphisms in Deligne
category. We do this by taking an ultraproduct of spherical subalgebras of the
extended Cherednik algebras of finite rank.


  We investigate correlations among complementary observables. In particular,
we show how to take advantage of mutually unbiased bases (MUBs) for the
efficient detection of entanglement in arbitrarily high-dimensional,
multipartite and continuous variable quantum systems. The introduced
entanglement criteria are relatively easy to implement experimentally since
they require only a few local measurement settings. In addition, we establish a
link between the separability problem and the maximum number of mutually
unbiased bases -- opening a new avenue in this long-standing open problem.


  Let $\mathbb{M}:=(M(X),p)$ be a direct summand of the motive associated with
a geometrically split, geometrically variety over a field $F$ satisfying the
nilpotence principle. We show that under some conditions on an extension $E/F$,
if $\mathbb{M}$ is a direct summand of another motive $M$ over an extension
$E$, then $\mathbb{M}$ is a direct summand of $M$ over $F$.


  Cohen and Godin constructed positive boundary topological quantum field
theory (TQFT) structure on the homology of free loop spaces of oriented closed
smooth manifolds by associating a certain operations called string operations
to orientable surfaces with parametrized boundaries. We show that all TQFT
string operations associated to surfaces of genus at least one vanish
identically. This is a simple consequence of properties of the loop coproduct
which will be discussed in detail. One interesting property is that the loop
coproduct is nontrivial only on the degree $d$ homology group of the connected
component of $LM$ consisting of contractible loops, where $d=\dim M$, with
values in the degree 0 homology group of constant loops. Thus the loop
coproduct behaves in a dramatically simpler way than the loop product.


  The method of moving frames in Lie sphere geometry has produced significant
results in the classification of Dupin hypersurfaces in spheres. What is the
secret of its effectiveness? The answer emerges in the classification of
nonumbilic isoparametric surfaces in the space form geometries. Using the
method of moving frames, the proof of this classification is an elementary
exercise. The same proof classifies the cyclides of Dupin in M\"obius geometry
and finally in Lie sphere geometry, where all nonumbilic Dupin immersions are
Lie sphere congruent to each other.


  Using the soft-pion theorem and the assumption on the final-state
interactions, we include the contribution of $DK$ continuum into the QCD sum
rules for $D_{sJ}(2317)$ meson. We find that this contribution can
significantly lower the mass and the decay constant of $D_s(0^+)$ state. For
the value of the current quark mass $m_c(m_c)=1.286 {\rm GeV}$, we obtain the
mass of $D_s(0^+)$ $M=2.33 \pm 0.02 {\rm GeV}$ in the interval $s_0=7.5-8.0
{\rm GeV}^2$, being in agreement with the experimental data, and the vector
current decay constant of $D_s(0^+)$ $f_0=0.128 \pm 0.013 {\rm GeV}$, much
lower than those obtained in previous literature.


  C. Bishop has constructed an example of an entire function f in
Eremenko-Lyubich class with at least two grand orbits of oscillating wandering
domains. In this paper we show that his example has exactly two such orbits,
that is, f has no unexpected wandering domains. We apply this result to the
classical problem of relating the Julia sets of composite functions with the
Julia set of its members. More precisely, we show the existence of two entire
maps f and g in Eremenko-Lyubich class such that the Fatou set of f compose
with g has a wandering domain, while all Fatou components of f or g are
preperiodic. This complements a result of A. Singh and results of W. Bergweiler
and A. Hinkkanen related to this problem.


  We propose a unified physical framework for transport in variably saturated
porous media. This approach allows fluid flow and solute migration to be
treated as ensemble averages of fluid and solute particles, respectively. We
consider the cases of homogeneous and heterogeneous porous materials. Within a
fractal mobile-immobile (MIM) continuous time random walk framework, the
heterogeneity will be characterized by algebraically decaying particle
retention-times. We derive the corresponding (nonlinear) continuum limit
partial differential equations and we compare their solutions to Monte Carlo
simulation results. The proposed methodology is fairly general and can be used
to track fluid and solutes particles trajectories, for a variety of initial and
boundary conditions.


  By introducing a nonlinearly transforming goldstino field
non-super\-sym\-metric matter can be coupled to supergravity. This implies the
possibility of coupling a standard model with one Higgs to supergravity.


  We deduce Katz's theorems for $(A,B)$-exponential sums over finite fields
using $\ell$-adic cohomology and a theorem of Denef-Loeser, removing the
hypothesis that $A+B$ is relatively prime to the characteristic $p$. In some
degenerate cases, the Betti number estimate is improved using toric
decomposition and Adolphson-Sperber's bound for the degree of $L$-functions.
Applying the facial decomposition theorem in \cite{W1}, we prove that the
universal family of $(A,B)$-polynomials is generically ordinary for its
$L$-function when $p$ is in certain arithmetic progression.


  We present three examples of Green biset functors for which their simple
modules can be parametrized. These are particular cases of a conjecture by
Serge Bouc classifying the simple modules over a Green biset functor A, that
generalizes the classification of simple biset functors. We also prove this
conjecture under certain hypothesis for A.


  With the proliferation of online social networking services and mobile smart
devices equipped with mobile communications module and position sensor module,
massive amount of multimedia data has been collected, stored and shared. This
trend has put forward higher request on massive multimedia data retrieval. In
this paper, we investigate a novel spatial query named region of visual
interests query (RoVIQ), which aims to search users containing geographical
information and visual words. Three baseline methods are presented to introduce
how to exploit existing techniques to address this problem. Then we propose the
definition of this query and related notions at the first time. To improve the
performance of query, we propose a novel spatial indexing structure called
quadtree based inverted visual index which is a combination of quadtree,
inverted index and visual words. Based on it, we design a efficient search
algorithm named region of visual interests search to support RoVIQ.
Experimental evaluations on real geo-image datasets demonstrate that our
solution outperforms state-of-the-art method.


  We present a theoretical investigation of the anomalous ferroelectricity of
mixed-stack charge transfer molecular crystals, based on the Peierls-Hubbard
model, and first principles calculations for its parameterization. This
approach is first validated by reproducing the temperature-induced transition
and the electronic polarization of TTF-CA, and then applied to a novel series
of hydrogen-bonded crystals, for which room temperature ferroelectricity has
recently been claimed. Our analysis shows that the hydrogen-bonded systems
present a very low degree of charge transfer and hence support a very small
polarization. A critical re-examination of experimental data supports our
findings, shedding doubts on the ferroelectricity of these systems. More
generally, our modelling allows the rationalization of general features of the
ferroelectric transition in charge transfer crystals, and suggests design
principles for materials optimization.


  This paper demonstrates the method of estimation of critical temperature Tc
value of high-temperature superconductors from the dispersive part of AC
susceptibility measurement using a pair of neural networks.


  We are interested in the uniqueness of solutions to Maxwell's equations when
the magnetic permeability $\mu$ and the permittivity $\varepsilon$ are
symmetric positive definite matrix-valued functions in $\mathbb{R}^{3}$. We
show that a unique continuation result for globally $W^{1,\infty}$ coefficients
in a smooth, bounded domain, allows one to prove that the solution is unique in
the case of coefficients which are piecewise $W^{1,\infty}$ with respect to a
suitable countable collection of sub-domains with $C^{0}$ boundaries. Such
suitable collections include any bounded finite collection. The proof relies on
a general argument, not specific to Maxwell's equations. This result is then
extended to the case when within these sub-domains the permeability and
permittivity are only $L^\infty$ in sets of small measure.


  A unified approach to prove the converses for the quantum channel capacity
theorems is presented. These converses include the strong converse theorems for
classical or quantum information transfer with error exponents and novel
explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz
strong converse for the classical channel capacity theorems. We provide a new
proof for the error exponents for the classical information transfer. A long
standing problem in quantum information theory has been to find out the strong
converse for the channel capacity theorem when quantum information is sent
across the channel. We give the quantum error exponent thereby giving a
one-shot exponential upper bound on the fidelity. We then apply our results to
show that the strong converse holds for the quantum information transfer across
an erasure channel for maximally entangled channel inputs.


  We examine numerical rounding errors of some deterministic solvers for
systems of ordinary differential equations (ODEs). We show that the
accumulation of rounding errors results in a solution that is inherently random
and we obtain the theoretical distribution of the trajectory as a function of
time, the step size and the numerical precision of the computer. We consider,
in particular, systems which amplify the effect of the rounding errors so that
over long time periods the solutions exhibit divergent behaviour. By performing
multiple repetitions with different values of the time step size, we observe
numerically the random distributions predicted theoretically. We mainly focus
on the explicit Euler and RK4 methods but also briefly consider more complex
algorithms such as the implicit solvers VODE and RADAU5.


  In most notions of locality in error correcting codes -- notably locally
recoverable codes (LRCs) and locally decodable codes (LDCs) -- a decoder seeks
to learn a single symbol of a message while looking at only a few symbols of
the corresponding codeword. However, suppose that one wants to recover r > 1
symbols of the message. The two extremes are repeating the single-query
algorithm r times (this is the intuition behind LRCs with availability,
primitive multiset batch codes, and PIR codes) or simply running a global
decoding algorithm to recover the whole thing. In this paper, we investigate
what can happen in between these two extremes: at what value of r does
repetition stop being a good idea? In order to begin to study this question we
introduce robust batch codes, which seek to find r symbols of the message using
m queries to the codeword, in the presence of erasures. We focus on the case
where r = m, which can be seen as a generalization of the MDS property.
Surprisingly, we show that for this notion of locality, repetition is optimal
even up to very large values of $r = \Omega(k)$.


  In the present paper we investigate the performance of explicit splitting
schemes and related techniques applied to a rigid body model subject to a
stochastic torque and random perturbations in the inertia tensor. Results are
discussed and compared with traditional solvers for such model.


  We study the relationship of soliton solutions for electron system with those
of the sigma model on the noncommutative space, working directly in the
operator formalism. We find that some soliton solutions of the sigma model are
also the solitons of the electron system and are classified by the same
topological numbers.


  We consider an anisotropic first-order ODE aggregation model and its
approximation by a second-order relaxation system. The relaxation model
contains a small parameter $\varepsilon$, which can be interpreted as inertia
or response time. We examine rigorously the limit $\varepsilon \to 0$ of
solutions to the relaxation system. Of major interest is how discontinuous (in
velocities) solutions to the first-order model are captured in the zero-inertia
limit. We find that near such discontinuities, solutions to the second-order
model perform fast transitions within a time layer of size
$\mathcal{O}(\varepsilon^{2/3})$. We validate this scale with numerical
simulations.


  In this letter, we analyze a terrestrial wireless communication network
assisted by an aerial intelligent reflecting surface (IRS). We consider a
packet scheduling problem at the ground base station (BS) aimed at improving
the information freshness by selecting packets based on their AoI. To further
improve the communication quality, the trajectory of the unmanned aerial
vehicle (UAV) which carries the IRS is optimized with joint active and passive
beamforming design. To solve the formulated non-convex problem, we propose an
iterative alternating optimization problem based on a successive convex
approximation (SCA) algorithm. The simulation results shows significant
performance improvement in terms of weighted sum AoI, and the SCA solution
converges quickly with low computational complexity.


  In this work, we introduce an optimal transport framework for inferring power
distributions over both spatial location and temporal frequency. Recently, it
has been shown that optimal transport is a powerful tool for estimating spatial
spectra that change smoothly over time. In this work, we consider the tracking
of the spatio-temporal spectrum corresponding to a small number of moving
broad-band signal sources. Typically, such tracking problems are addressed by
treating the spatio-temporal power distribution in a frequency-by-frequency
manner, allowing to use well-understood models for narrow-band signals. This
however leads to decreased target resolution due to inefficient use of the
available information. We propose an extension of the optimal transport
framework that exploits information from several frequencies simultaneously by
estimating a spatio-temporal distribution penalized by a group-sparsity
regularizer. This approach finds a spatial spectrum that changes smoothly over
time, and at each time instance has a small support that is similar across
frequencies. To the best of the authors knowledge, this is the first
formulation combining optimal transport and sparsity for solving inverse
problems. As is shown on simulated and real data, our method can successfully
track targets in scenarios where information from separate frequency bands
alone is insufficient.


  Telescopes measuring cosmic microwave background (CMB) polarization on large
angular scales require exquisite control of systematic errors to ensure the
fidelity of the cosmological results. In particular, far-sidelobe contamination
from wide angle scattering is a potentially prominent source of systematic
error for large aperture microwave telescopes. Here we describe and demonstrate
a ray-tracing-based modeling technique to predict far sidelobes for a Three
Mirror Anistigmat (TMA) telescope designed to observe the CMB from the South
Pole. Those sidelobes are produced by light scattered in the receiver optics
subsequently interacting with the walls of the surrounding telescope enclosure.
After comparing simulated sidelobe maps and angular power spectra for different
enclosure wall treatments, we propose a highly scattering surface that would
provide more than an order of magnitude reduction in the degree-scale
far-sidelobe contrast compared to a typical reflective surface. We conclude by
discussing the fabrication of a prototype scattering wall panel and presenting
measurements of its angular scattering profile.


  We apply a convolutional neural network (CNN) to classify and detect quasars
in the Sloan Digital Sky Survey Stripe 82 and also to predict the photometric
redshifts of quasars. The network takes the variability of objects into account
by converting light curves into images. The width of the images, noted w,
corresponds to the five magnitudes ugriz and the height of the images, noted h,
represents the date of the observation. The CNN provides good results since its
precision is 0.988 for a recall of 0.90, compared to a precision of 0.985 for
the same recall with a random forest classifier. Moreover 175 new quasar
candidates are found with the CNN considering a fixed recall of 0.97. The
combination of probabilities given by the CNN and the random forest makes good
performance even better with a precision of 0.99 for a recall of 0.90.
  For the redshift predictions, the CNN presents excellent results which are
higher than those obtained with a feature extraction step and different
classifiers (a K-nearest-neighbors, a support vector machine, a random forest
and a gaussian process classifier). Indeed, the accuracy of the CNN within
|\Delta z|<0.1 can reach 78.09%, within |\Delta z|<0.2 reaches 86.15%, within
|\Delta z|<0.3 reaches 91.2% and the value of rms is 0.359. The performance of
the KNN decreases for the three |\Delta z| regions, since within the accuracy
of |\Delta z|<0.1, |\Delta z|<0.2 and |\Delta z|<0.3 is 73.72%, 82.46% and
90.09% respectively, and the value of rms amounts to 0.395. So the CNN
successfully reduces the dispersion and the catastrophic redshifts of quasars.
This new method is very promising for the future of big databases like the
Large Synoptic Survey Telescope.


  Emulators for low-energy nuclear physics can provide fast & accurate
predictions of bound-state and scattering observables for applications that
require repeated calculations with different parameters, such as Bayesian
uncertainty quantification. In this paper, we extend a scattering emulator
based on the Kohn variational principle (KVP) to momentum space (including
coupled channels) with arbitrary boundary conditions, which enable the
mitigation of spurious singularities known as Kohn anomalies. We test it on a
modern chiral nucleon-nucleon (NN) interaction, including emulation of the
coupled channels. We provide comparisons between a Lippmann-Schwinger equation
emulator and our KVP momentum-space emulator for a representative set of
neutron-proton (np) scattering observables, and also introduce a
quasi-spline-based approach for the KVP-based emulator. Our findings show that
while there are some trade-offs between accuracy and speed, all three emulators
perform well. Self-contained Jupyter notebooks that generate the results and
figures in this paper are publicly available.


  Video amodal segmentation is a particularly challenging task in computer
vision, which requires to deduce the full shape of an object from the visible
parts of it. Recently, some studies have achieved promising performance by
using motion flow to integrate information across frames under a
self-supervised setting. However, motion flow has a clear limitation by the two
factors of moving cameras and object deformation. This paper presents a
rethinking to previous works. We particularly leverage the supervised signals
with object-centric representation in \textit{real-world scenarios}. The
underlying idea is the supervision signal of the specific object and the
features from different views can mutually benefit the deduction of the full
mask in any specific frame. We thus propose an Efficient object-centric
Representation amodal Segmentation (EoRaS). Specially, beyond solely relying on
supervision signals, we design a translation module to project image features
into the Bird's-Eye View (BEV), which introduces 3D information to improve
current feature quality. Furthermore, we propose a multi-view fusion layer
based temporal module which is equipped with a set of object slots and
interacts with features from different views by attention mechanism to fulfill
sufficient object representation completion. As a result, the full mask of the
object can be decoded from image features updated by object slots. Extensive
experiments on both real-world and synthetic benchmarks demonstrate the
superiority of our proposed method, achieving state-of-the-art performance. Our
code will be released at \url{https://github.com/kfan21/EoRaS}.


  This paper studies the inference about linear functionals of high-dimensional
low-rank matrices. While most existing inference methods would require
consistent estimation of the true rank, our procedure is robust to rank
misspecification, making it a promising approach in applications where rank
estimation can be unreliable. We estimate the low-rank spaces using
pre-specified weighting matrices, known as diversified projections. A novel
statistical insight is that, unlike the usual statistical wisdom that
overfitting mainly introduces additional variances, the over-estimated low-rank
space also gives rise to a non-negligible bias due to an implicit ridge-type
regularization. We develop a new inference procedure and show that the central
limit theorem holds as long as the pre-specified rank is no smaller than the
true rank. Empirically, we apply our method to the U.S. federal grants
allocation data and test the existence of pork-barrel politics.


  For a compact simply connected simple Lie group $G$ with an involution
$\alpha$, we compute the $G\rtimes \Z/2$-equivariant K-theory of $G$ where $G$
acts by conjugation and $\Z/2$ acts either by $\alpha$ or by $g\mapsto
\alpha(g)^{-1}$. We also give a representation-theoretic interpretation of
those groups, as well as of $K_G(G)$.


  A chiral unitary approach for antikaon-nucleon scattering in on-shell
factorization is studied. We find multiple sets of parameters for which the
model describes all existing hadronic data similarly well. We confirm the
two-pole structure of the $\Lambda (1405)$. The narrow $\Lambda(1405)$ pole
appears at comparable positions in the complex energy plane, whereas the
location of the broad pole suffers from a large uncertainty. In the second
step, we use a simple model for photoproduction of $K^+\pi\Sigma$ off the
proton and confront it with the experimental data from the CLAS collaboration.
It is found that only a few of the hadronic solutions allow for a consistent
description of the CLAS data within the assumed reaction mechanism.


  Control of the crystalline orientation of nitrogen-vacancy (NV) defects in
diamond is here demonstrated by tuning the temperature of chemical vapor
deposition (CVD) growth on a (113)-oriented diamond substrate. We show that
preferential alignment of NV defects along the [111] axis is significantly
improved when the CVD growth temperature is decreased. This effect is then
combined with temperature-dependent incorporation of NV defects during the CVD
growth to obtain preferential alignment over dense ensembles of NV defects
spatially localized in thin diamond layers. These results demonstrate that
growth temperature can be exploited as an additional degree of freedom to
engineer optimized diamond samples for quantum sensing applications.


  We derive a semi-analytical pricing formula for European VIX call options
under the Heston-Hawkes stochastic volatility model introduced in
arXiv:2210.15343. This arbitrage-free model incorporates the volatility
clustering feature by adding an independent compound Hawkes process to the
Heston volatility. Using the Markov property of the exponential Hawkes an
explicit expression of $\text{VIX}^2$ is derived as a linear combination of the
variance and the Hawkes intensity. We apply qualitative ODE theory to study the
existence of some generalized Riccati ODEs. Thereafter, we compute the joint
characteristic function of the variance and the Hawkes intensity exploiting the
exponential affine structure of the model. Finally, the pricing formula is
obtained by applying standard Fourier techniques.


  This thesis studies range-based WSN localization problem in 3D environments
that induce coplanarity. In most real-world applications, even though the
environment is 3D, the grounded sensor nodes are usually deployed on 2D planar
surfaces. Examples of these surfaces include structures seen in both indoor
(e.g. floors, doors, walls, tables etc.) and outdoor (e.g. mountains, valleys,
hills etc.) environments. In such environments, sensor nodes typically appear
as coplanar node clusters. We refer to this type of a deployment as a planar
deployment. When there is a planar deployment, the coplanarity causes
difficulties to the traditional range-based multilateration algorithms because
a node cannot be unambiguously localized if the distance measurements to that
node are from coplanar nodes. Thus, many already localized groups of nodes are
rendered ineffective in the process just because they are coplanar. We,
therefore propose an algorithm called Coplanarity Based Localization (CBL) that
can be used as an extension of any localization algorithm to avoid most flips
caused by coplanarity. CBL first performs a 2D localization among the nodes
that are clustered on the same surface, and then finds the positions of these
clusters in 3D. We have carried out experiments using trilateration for 2D
localization, and quadrilateration for 3D localization, and experimentally
verified that exploiting the clustering information leads to a more precise
localization than mere quadrilateration. We also propose a heuristic to extract
the clustering information in case it is not available, which is yet to be
improved in the future.


  Most Mahonian statistics can be expressed as a linear combination of vincular
patterns. This is not only true with statistics on the permutation set, but it
can also be applied for statistics on the permutation with repetition set. By
following the method extending the vincular patterns combinations presented by
Kitaev and Vajnovszki, we discover 8 vincular-patterns combinations of mad and
madl extensions that are possible to be Mahonian. Some of these have been
proved to be Mahonian on repetitive permutations by Clarke, Steingrimsson and
Zeng, while the rest are new statistics extensions. In this thesis, we
determine combinations of vincular pattern extension of mad and madl in Clarke,
Steingrimsson and Zeng s paper, which have been proved to be Mahonian on the
repetitive permutations. This result will be used to support the proof of
Mahonity of the new statistics extensions. We show that these new statistics
extensions are also Mahonian by constructing an involution {\Phi} on repetitive
permutations, which preserves the descents statistics and transforms new
statistics extensions to Mahonian mad and madl extensions of Clarke.


  Arc-annotated sequences are useful for representing structural information of
RNAs and have been extensively used for comparing RNA structures in both terms
of sequence and structural similarities. Among the many paradigms referring to
arc-annotated sequences and RNA structures comparison (see
\cite{IGMA_BliDenDul08} for more details), the most important one is the
general edit distance. The problem of computing an edit distance between two
non-crossing arc-annotated sequences was introduced in \cite{Evans99}. The
introduced model uses edit operations that involve either single letters or
pairs of letters (never considered separately) and is solvable in
polynomial-time \cite{ZhangShasha:1989}. To account for other possible RNA
structural evolutionary events, new edit operations, allowing to consider
either silmutaneously or separately letters of a pair were introduced in
\cite{jiangli}; unfortunately at the cost of computational tractability. It has
been proved that comparing two RNA secondary structures using a full set of
biologically relevant edit operations is {\sf\bf NP}-complete. Nevertheless, in
\cite{DBLP:conf/spire/GuignonCH05}, the authors have used a strong
combinatorial restriction in order to compare two RNA stem-loops with a full
set of biologically relevant edit operations; which have allowed them to design
a polynomial-time and space algorithm for comparing general secondary RNA
structures. In this paper we will prove theoretically that comparing two RNA
structures using a full set of biologically relevant edit operations cannot be
done without strong combinatorial restrictions.


  Light polarization is a key aspect of modern optics. Current methods for
polarization control utilize birefringence and dichroism of anisotropic
materials or of arrays of anisotropically shaped nanostructures. Based on
collective optical effects, the resulting components remain much larger than
the wavelength of light, which limits design strategies. Here, we present a
travelling-wave plasmonic antenna that overcomes this limit using a gold-coated
helical nanowire non-radiatively fed with a dipolar aperture nanoantenna. Our
non-resonant hybrid nanoantenna enables tightly confined circularly polarized
light by swirling surface plasmons on the subwavelength scale and taking
advantage of optical spin-orbit interaction. Four closely packed circularly
polarized light sources of opposite handedness and tunable intensities are
demonstrated. By reaching near-field interaction between neighboring
nanoantennas, we obtain a highly miniaturized wave plate whose polarization
properties have never previously been demonstrated.


  In the presented study we investigated the second order endpoints of the
lines of first order phase transitions which emerge for the QCD in the heavy
and light quark mass regime and for the three-dimensional three state Potts
model with an external field. We located the endpoints with Binder cumulants
and constructed the energy-like and ordering field like observables. The joint
probability distributions of these scaling fields and the values of the Binder
cumulant confirm that all three endpoints belong to the universality class of
the 3-dimensional Ising model.


  We report on a successful, simultaneous observation and modelling of the
millimeter (mm) to near-infrared (NIR) flare emission of the Sgr A* counterpart
associated with the supermassive black hole at the Galactic centre (GC). We
present a mm/sub-mm light curve of Sgr A* with one of the highest quality
continuous time coverages and study and model the physical processes giving
rise to the variable emission of Sgr A*.


  The real time exponential decay laws for meta-stable charged particles are
shown to require radiative corrections. The methods employed are well known to
be valid for radiatively correcting Breit-Wigner line shapes. Radiative
corrections contribute substantially to precision life time measurements of
muons and pions when initially stopped in condensed matter.


  Supernova fallback disks around neutron stars have been discussed to
influence the evolution of the diverse neutron star populations. Slowly
rotating neutron stars are most promising to find such disks. Searching for the
cold and warm debris of old fallback disks, we carried out Herschel PACS (70
$\mu$m, 160 $\mu$m) and Spitzer IRAC (3.6 $\mu$m, 4.5 $\mu$m) observations of
eight slowly rotating ($P\approx 3 - 11$ s) nearby ($<1$ kpc) isolated neutron
stars. Herschel detected 160 $\mu$m emission ($>5\sigma$) at locations
consistent with the positions of the neutron stars RX J0806.4-4123 and RX
J2143.0+0654. No other significant infrared emission was detected from the
eight neutron stars. We estimate probabilities of 63%, 33% and 3% that,
respectively, none, one, or both Herschel PACS 160 $\mu$m detections are
unrelated excess sources due to background source confusion or an interstellar
cirrus. If the 160 $\mu$m emission is indeed related to cold (10 K to 22 K)
dust around the neutron stars, this dust is absorbing and re-emitting $\sim
10$% to $\sim 20$% of the neutron stars' X-rays. Such high efficiencies would
be at least three orders of magnitude larger than the efficiencies of debris
disks around nondegenerate stars. While thin dusty disks around the neutron
stars can be excluded as counterparts of the 160 $\mu$m emission, dusty
asteroid belts constitute a viable option.


  In the framework of ab initio dynamical mean field theory for realistic
electronic structure calculations a new perturbation scheme which combine the
T-matrix and fluctuating exchange approximations has been proposed. This method
is less computationally expensive than numerically exact quantum Monte Carlo
technics and give an adequate description of the electronic structure and
exchange interactions for magnetic metals. We discuss a simple expression for
the exchange interactions corresponding to the neglecting of the vertex
corrections which becomes exact for the spin-wave stiffness in the local
approximation. Electronic structure, correlation effects and exchange
interactions for ferromagnetic nickel have been discussed.


  This paper is devoted to the asymptotic behavior of all eigenvalues of
Symmetric (in general non Hermitian) Toeplitz matrices with moderately smooth
symbols which trace out a simple loop on the complex plane line as the
dimension of the matrices increases to infinity. The main result describes the
asymptotic structure of all eigenvalues. The constructed expansion is uniform
with respect to the number of eigenvalues.
  Keywords: Toeplitz matrices, eigenvalues, asymptotic expansions


  We extend the techniques developed by Millson and Raghunathan to prove
nonvanishing results for the cohomology of compact arithmetic quotients of
hyperbolic n-space with values in the local coefficient systems associated to
finite dimensional irreducible representations of the group SO(n,1). We prove
that all possible nonvanishing results compatible with the vanishing theorems
of Vogan and Zuckerman can be realized by any sufficiently deep congruence
subgroup of the standard cocompact arithmetic examples.


  We present a prototypical linear algebra compiler that automatically exploits
domain-specific knowledge to generate high-performance algorithms. The input to
the compiler is a target equation together with knowledge of both the structure
of the problem and the properties of the operands. The output is a variety of
high-performance algorithms, and the corresponding source code, to solve the
target equation. Our approach consists in the decomposition of the input
equation into a sequence of library-supported kernels. Since in general such a
decomposition is not unique, our compiler returns not one but a number of
algorithms. The potential of the compiler is shown by means of its application
to a challenging equation arising within the genome-wide association study. As
a result, the compiler produces multiple "best" algorithms that outperform the
best existing libraries.


  We propose a new analytical method to solve for the nonexactly solvable
Schrodinger equation. Successfully, it is applied to a class of spiked harmonic
oscillators and truncated Coulomb potentials. The utility of this method could
be extended to study other systems of atomic, molecular and nuclear physics
interest.


  Nonparametric models are versatile, albeit computationally expensive, tool
for modeling mixture models. In this paper, we introduce spectral methods for
the two most popular nonparametric models: the Indian Buffet Process (IBP) and
the Hierarchical Dirichlet Process (HDP). We show that using spectral methods
for the inference of nonparametric models are computationally and statistically
efficient. In particular, we derive the lower-order moments of the IBP and the
HDP, propose spectral algorithms for both models, and provide reconstruction
guarantees for the algorithms. For the HDP, we further show that applying
hierarchical models on dataset with hierarchical structure, which can be solved
with the generalized spectral HDP, produces better solutions to that of flat
models regarding likelihood performance.


  Recent models for learned image compression are based on autoencoders,
learning approximately invertible mappings from pixels to a quantized latent
representation. These are combined with an entropy model, a prior on the latent
representation that can be used with standard arithmetic coding algorithms to
yield a compressed bitstream. Recently, hierarchical entropy models have been
introduced as a way to exploit more structure in the latents than simple fully
factorized priors, improving compression performance while maintaining
end-to-end optimization. Inspired by the success of autoregressive priors in
probabilistic generative models, we examine autoregressive, hierarchical, as
well as combined priors as alternatives, weighing their costs and benefits in
the context of image compression. While it is well known that autoregressive
models come with a significant computational penalty, we find that in terms of
compression performance, autoregressive and hierarchical priors are
complementary and, together, exploit the probabilistic structure in the latents
better than all previous learned models. The combined model yields
state-of-the-art rate--distortion performance, providing a 15.8% average
reduction in file size over the previous state-of-the-art method based on deep
learning, which corresponds to a 59.8% size reduction over JPEG, more than 35%
reduction compared to WebP and JPEG2000, and bitstreams 8.4% smaller than BPG,
the current state-of-the-art image codec. To the best of our knowledge, our
model is the first learning-based method to outperform BPG on both PSNR and
MS-SSIM distortion metrics.


  We consider in this paper a perturbation of the standard semilinear heat
equation by a term involving the space derivative and a non-local term. We
prove the existence of a blow-up solution, and give its blow-up profile. Our
proof relies on the following method: we linearize the equation (in similarity
variables) around the expected profile, then, we control the nonpositive
directions of the spectrum thanks to the decreasing properties of the kernel.
Finally, we use a topological argument to control the positive directions of
the spectrum.


  This article aims at providing insights for a comprehensive understanding of
terahertz (THz) propagation channels. Specifically, we discuss essential THz
channel characteristics to be well understood for the success of THz
communications. The methodology of establishing realistic and 6G-compliant THz
channel models based on measurements is then elaborated on, followed by a
discussion on existing THz channel measurements in the literature. Finally,
future research directions, challenges and measures to enrich the understanding
of THz channels are discussed.


  We present here the iteration procedure for the determination of free energy
$\epsilon^{2}$-expansion using the theory of KdV - type equations. In our
approach we use the conservation laws for KdV - type equations depending
explicitly on times $t_{1}, t_{2}, ...$ to find the $\epsilon^{2}$-expansion of
$u(x,t_{1},t_{2},...)$ after the infinite number of shifts of $u(x,0,0,...)
\equiv x$ along $t_{1}, t_{2}, ...$ in recurrent form. The formulas for the
free energy expansion are just obtained then as a result of quite simple
integration procedure applied to $u_{n}(x)$.


  The development of generative design driven by artificial intelligence
algorithms is speedy. There are two research gaps in the current research: 1)
Most studies only focus on the relationship between design elements and pay
little attention to the external information of the site; 2) GAN and other
traditional generative algorithms generate results with low resolution and
insufficient details. To address these two problems, we integrate GAN, Stable
diffusion multimodal large-scale image pre-training model to construct a
full-process park generative design method: 1) First, construct a
high-precision remote sensing object extraction system for automated extraction
of urban environmental information; 2) Secondly, use GAN to construct a park
design generation system based on the external environment, which can quickly
infer and generate design schemes from urban environmental information; 3)
Finally, introduce Stable Diffusion to optimize the design plan, fill in
details, and expand the resolution of the plan by 64 times. This method can
achieve a fully unmanned design automation workflow. The research results show
that: 1) The relationship between the inside and outside of the site will
affect the algorithm generation results. 2) Compared with traditional GAN
algorithms, Stable diffusion significantly improve the information richness of
the generated results.


  It is expected that conformal symmetry is an emergent property of many
systems at their critical point. This imposes strong constraints on the
critical behavior of a given system. Taking them into account in theoretical
approaches can lead to a better understanding of the critical physics or
improve approximation schemes. However, within the framework of the
non-perturbative or functional renormalization group and, in particular, of one
of its most used approximation schemes, the Derivative Expansion (DE),
non-trivial constraints only apply from third order (usually denoted
$\mathcal{O}(\partial^4)$), at least in the usual formulation of the DE that
includes correlation functions involving only the order parameter. In this
work, we implement conformal constraints on a generalized DE including
composite operators and show that new constraints already appear at second
order of the DE (or $\mathcal{O}(\partial^2)$). We show how these constraints
can be used to fix nonphysical regulator parameters.


  Echocardiography has become routinely used in the diagnosis of cardiomyopathy
and abnormal cardiac blood flow. However, manually measuring myocardial motion
and cardiac blood flow from echocardiogram is time-consuming and error-prone.
Computer algorithms that can automatically track and quantify myocardial motion
and cardiac blood flow are highly sought after, but have not been very
successful due to noise and high variability of echocardiography. In this work,
we propose a neural multi-scale self-supervised registration (NMSR) method for
automated myocardial and cardiac blood flow dense tracking. NMSR incorporates
two novel components: 1) utilizing a deep neural net to parameterize the
velocity field between two image frames, and 2) optimizing the parameters of
the neural net in a sequential multi-scale fashion to account for large
variations within the velocity field. Experiments demonstrate that NMSR yields
significantly better registration accuracy than state-of-the-art methods, such
as advanced normalization tools (ANTs) and VoxelMorph, for both myocardial and
cardiac blood flow dense tracking. Our approach promises to provide a fully
automated method for fast and accurate analyses of echocardiograms.


  A conjecture due to Gompf asserts that no nontrivial Brieskorn homology
sphere admits a pseudoconvex embedding in ${\mathbb C}^2$, with either
orientation. A related question asks whether every compact contractible
4-manifold admits the structure of a Stein domain. We verify Gompf's
conjecture, with one orientation, for a family of Brieskorn spheres of which
some are known to admit a smooth embedding in ${\mathbb C}^2$. With the other
orientation our methods do not resolve the question, but do give rise to an
example of a contractible, boundary-irreducible 4-manifold that admits no Stein
structure with either orientation, though its boundary has Stein fillings with
both orientations.


  In this study, we introduce the natural mate and conjugate mate of a Frenet
curve in a three dimensional Lie group $ \mathbb{G} $ with bi-invariant metric.
Also, we give some relationships between a Frenet curve and its natural mate or
its conjugate mate in $ \mathbb{G} $. Especially, we obtain some results for
the natural mate and the conjugate mate of a Frenet curve in $ \mathbb{G} $
when the Frenet curve is a general helix, a slant helix, a spherical curve, a
rectifying curve, a Salkowski (constant curvature and non-constant torsion),
anti-Salkowski (non-constant curvature and constant torsion), Bertrand curve.
Finally, we give nice graphics with numeric solution in Euclidean 3-space as a
commutative Lie group.


  Preliminary data from the Beam-Energy Scan II measurements by the STAR
Collaboration at the Relativistic Heavy Ion Collider suggest a dip in the
fourth-to-second-order cumulant ratio when plotted vs. beam energy. At the same
energy range where the structure appears, a transition from hadrons to quarks
is expected, the deconfinement transition. In this paper, the role of quark
deconfinement in establishing fluctuaitions in the early stages of the
collision is considered. Two models are compared: one with stopping occurring
on a baryon-by-baryon basis, and a second where stopping proceeds through quark
degrees of freedom. In the latter model, the fluctuation of baryon number is
significantly reduced and this signal is found to survive recombination into
hadrons and the subsequent diffusion. The transformation from baryon to quark
stopping thus produces a dip in the fourth-to-second-order cumulant ratio when
plotted vs. beam energy, consistent with observations.


  In this paper, we prove a theorem about the integer solutions to the
Diophantine equation $x^{4}-q^{4}=py^{r}$, extending previous work of K.Gy\H
ory, and F.Luca and A.Togbe, and of the author.


  By means of the property of effective local connectivity, the computability
of finding the Carath\'eodory extension of a conformal map of a Jordan domain
onto the unit disk is demonstrated.


  Fairness is an important topic for medical image analysis, driven by the
challenge of unbalanced training data among diverse target groups and the
societal demand for equitable medical quality. In response to this issue, our
research adopts a data-driven strategy-enhancing data balance by integrating
synthetic images. However, in terms of generating synthetic images, previous
works either lack paired labels or fail to precisely control the boundaries of
synthetic images to be aligned with those labels. To address this, we formulate
the problem in a joint optimization manner, in which three networks are
optimized towards the goal of empirical risk minimization and fairness
maximization. On the implementation side, our solution features an innovative
Point-Image Diffusion architecture, which leverages 3D point clouds for
improved control over mask boundaries through a point-mask-image synthesis
pipeline. This method outperforms significantly existing techniques in
synthesizing scanning laser ophthalmoscopy (SLO) fundus images. By combining
synthetic data with real data during the training phase using a proposed Equal
Scale approach, our model achieves superior fairness segmentation performance
compared to the state-of-the-art fairness learning models. Code is available at
https://github.com/wenyi-li/FairDiff.


  The multiple-ionization energy difference of 163Ho and 163Dy atoms is
evaluated for the ionization degree q = 30, 48, 56. The calculations are
performed by means of the large-scale relativistic configuration interaction
method combined with the many-body perturbation theory. The quantum
electrodynamics, nuclear recoil, and frequency-dependent Breit interaction
corrections are taken into account. The obtained theoretical values are within
1 eV uncertainty. These results can help to increase accuracy of the laboratory
neutrino mass limit, provided they are accompanied by the corresponding
experiment on electron capture in Ho and a precise measurement of the ion mass
difference.


  In this paper, we make a close comparison of a covariant definition of an
energy/entropy in general relativity, recently proposed by a collaboration
including the present authors, with existing definitions of energies such as
the one from the pseudo-tensor and the quasi-local energy. We show that
existing definitions of energies in general relativity are conserved charges
from the Noether's 2nd theorem for the general coordinate transformation, whose
conservations are merely identities implied by the local symmetry and always
hold without using equations of motion. Thus none of existing definitions in
general relativity reflects the dynamical properties of the system, need for a
physical definition of an energy. In contrast, our new definition of the
energy/entropy in general relativity is generically a conserved non-Noether
charge and gives physically sensible results for various cases such as the
black hole mass, the gravitational collapse, and the expanding universe, while
existing definitions sometimes lead to unphysical ones including zero and
infinity. We conclude that our proposal is more physical than existing
definitions of energies. Our proposal makes it possible to define almost
uniquely the covariant and conserved energy/entropy in general relativity,
which brings some implications to future investigations.


  In this paper, the effectiveness and capability of convolutional neural
networks have been studied in the classification of 8 skin diseases. Different
pre-trained state-of-the-art architectures (DenseNet 201, ResNet 152, Inception
v3, InceptionResNet v2) were used and applied on 10135 dermoscopy skin images
in total (HAM10000: 10015, PH2: 120). The utilized dataset includes 8
diagnostic categories - melanoma, melanocytic nevi, basal cell carcinoma,
benign keratosis, actinic keratosis and intraepithelial carcinoma,
dermatofibroma, vascular lesions, and atypical nevi. The aim is to compare the
ability of deep learning with the performance of highly trained dermatologists.
Overall, the mean results show that all deep learning models outperformed
dermatologists (at least 11%). The best ROC AUC values for melanoma and basal
cell carcinoma are 94.40% (ResNet 152) and 99.30% (DenseNet 201) versus 82.26%
and 88.82% of dermatologists, respectively. Also, DenseNet 201 had the highest
macro and micro averaged AUC values for overall classification (98.16%, 98.79%,
respectively).


  We consider random Gaussian eigenfunctions of the Laplacian on the standard
torus, and investigate the number of nodal intersections against a line
segment. The expected intersection number, against any smooth curve, is
universally proportional to the length of the reference curve, times the
wavenumber, independent of the geometry. We found an upper bound for the nodal
intersections variance, depending on whether the slope of the straight line is
rational or irrational. Our findings exhibit a close relation between this
problem and the theory of lattice points on circles.


  Precession driven flows are found in any rotating container filled with
liquid, when the rotation axis itself rotates about a secondary axis that is
fixed in an inertial frame of reference. Because of its relevance for planetary
fluid layers, many works consider spheroidal containers, where the uniform
vorticity component of the bulk flow is reliably given by the well-known
equations obtained by Busse in 1968. So far however, no analytical result on
the solutions is available. Moreover, the cases where multiple flows can
coexist have not been investigated in details since their discovery by Noir et
al. (2003). In this work, we aim at deriving analytical results on the
solutions, aiming in particular at, first estimating the ranges of parameters
where multiple solutions exist, and second studying quantitatively their
stability. Using the models recently proposed by Noir \& C{\'e}bron (2013),
which are more generic in the inviscid limit than the equations of Busse, we
analytically describe these solutions, their conditions of existence, and their
stability in a systematic manner. We then successfully compare these analytical
results with the theory of Busse (1968). Dynamical model equations are finally
proposed to investigate the stability of the solutions, which allows to
describe the bifurcation of the unstable flow solution. We also report for the
first time the possibility that time-dependent multiple flows can coexist in
precessing triaxial ellipsoids. Numerical integrations of the algebraic and
differential equations have been efficiently performed with the dedicated
script FLIPPER (supplementary material).


  We introduce the notion of families of n-marked smooth rational tropical
curves over smooth tropical varieties and establish a one-to-one correspondence
between (equivalence classes of) these families and morphisms from smooth
tropical varieties into the moduli space of n-marked abstract rational tropical
curves.


  Counterfactual reasoning, a fundamental aspect of human cognition, involves
contemplating alternatives to established facts or past events, significantly
enhancing our abilities in planning and decision-making. In light of the
advancements in current multi-modal large language models, we explore their
effectiveness in counterfactual reasoning. To facilitate this investigation, we
introduce a novel dataset, C-VQA, specifically designed to test the
counterfactual reasoning capabilities of modern multi-modal large language
models. This dataset is constructed by infusing original questions with
counterfactual presuppositions, spanning various types such as numerical and
boolean queries. It encompasses a mix of real and synthetic data, representing
a wide range of difficulty levels. Our thorough evaluations of contemporary
vision-language models using this dataset have revealed substantial performance
drops, with some models showing up to a 40% decrease, highlighting a
significant gap between current models and human-like vision reasoning
capabilities. We hope our dataset will serve as a vital benchmark for
evaluating the counterfactual reasoning capabilities of models. Code and
dataset are publicly available at https://bzhao.me/C-VQA/.


  We have analysed ground-based multi-colour Stromgren photometry and
single-filter photometry from the star tracker on the WIRE satellite of the
delta scuti star Epsilon Cephei. The ground-based data set consists of 16
nights of data collected over 164 days, while the satellite data are nearly
continuous coverage of the star during 14 days. The spectral window and noise
level of the satellite data are superior to the ground-based data and this data
set is used to locate the frequencies. However, we can use the ground-based
data to improve the accuracy of the frequencies due to the much longer time
baseline. We detect 26 oscillation frequencies in the WIRE data set, but only
some of these can be seen clearly in the ground-based data. We have used the
multi-colour ground-based photometry to determine amplitude and phase
differences in the Stromgren b-y colour and the y filter in an attempt to
identify the radial degree of the oscillation frequencies. We conclude that the
accuracies of the amplitudes and phases are not sufficient to constrain
theoretical models of Epsilon Cephei. We find no evidence for rotational
splitting or the large separation among the frequencies detected in the WIRE
data set. To be able to identify oscillation frequencies in delta scuti stars
with the method we have applied, it is crucial to obtain more complete coverage
from multi-site campaigns with a long time baseline and in multiple filters.
This is important when planning photometric and spectroscopic ground-based
support for future satellite missions like COROT and KEPLER.


  Intra-day price variations in financial markets are driven by the sequence of
orders, called the order flow, that is submitted at high frequency by traders.
This paper introduces a novel application of the Sequence Generative
Adversarial Networks framework to model the order flow, such that random
sequences of the order flow can then be generated to simulate the intra-day
variation of prices. As a benchmark, a well-known parametric model from the
quantitative finance literature is selected. The models are fitted, and then
multiple random paths of the order flow sequences are sampled from each model.
Model performances are then evaluated by using the generated sequences to
simulate price variations, and we compare the empirical regularities between
the price variations produced by the generated and real sequences. The
empirical regularities considered include the distribution of the price
log-returns, the price volatility, and the heavy-tail of the log-returns
distributions. The results show that the order sequences from the generative
model are better able to reproduce the statistical behaviour of real price
variations than the sequences from the benchmark.


  Traditional Byzantine Fault Tolerance (BFT) state machine replication
protocols assume a partial synchrony model, leading to a design where a leader
replica drives the protocol and is replaced after a timeout. Recently, we
witnessed a surge of asynchronous BFT protocols, which use randomization to
remove the need for bounds on message delivery times, making them more
resilient to adverse network conditions. However, existing research proposals
still fall short of gaining practical adoption, plausibly because they are not
able to combine good performance with a simple design that can be readily
understood and adopted. In this paper, we present Alea-BFT, a simple and highly
efficient asynchronous BFT protocol, which is gaining practical adoption,
namely in Ethereum distributed validators. Alea-BFT brings the key design
insight from classical protocols of concentrating part of the work on a single
designated replica and incorporates this principle in a simple two-stage
pipelined design, with an efficient broadcast led by the designated replica,
followed by an inexpensive binary agreement. The evaluation of our research
prototype implementation and two real-world integrations in cryptocurrency
ecosystems shows excellent performance, improving on the fastest protocol
(Dumbo-NG) in terms of latency and displaying good performance under faults.


  We present an interpretation of the recent Daniel K. Inouye Solar Telescope
(DKIST) observations of propagating wavefronts in the lower solar atmosphere.
Using MPS/University of Chicago MHD (MURaM) radiative magnetohydrodynamic
simulations spanning solar photosphere, overshoot region, and lower
chromosphere, we identify three acoustic-wave source mechanisms, each occurring
at a different atmospheric height. We synthesize the DKIST Visible Broadband
Imager (VBI) G-band, blue-continuum, and CaIIK signatures of these waves at
high spatial and temporal resolution, and conclude that the wavefronts observed
by DKIST likely originate from acoustic sources at the top of the solar
photosphere overshoot region and in the chromosphere proper. The overall
importance of these local sources to the atmospheric energy and momentum budget
of the solar atmosphere is unknown, but one of the excitation mechanism
identified (upward propagating shock interaction with down-welling
chromospheric plasma resulting in acoustic radiation) appears to be an
important shock dissipation mechanism. Additionally, the observed wavefronts
may prove useful for ultra-local helioseismological inversions and promise to
play an important diagnostic role at multiple atmospheric heights.


  Using the div-curl inequalities of Bourgain-Brezis [?MR2057026] and van
Schaftingen [?MR2078071], we prove an improved Strichartz estimate for systems
of inhomogeneous wave and Schrodinger equations, for which the inhomogeneity is
a divergence-free vector field at each given time. The novelty of the result is
that one can allow $L^1_x$ norms of the inhomogeneity in the right hand side of
the estimate.


  This tutorial offers a comprehensive overview of photonic time crystals -
artificial materials whose electromagnetic properties are periodically
modulated in time at scales comparable to the oscillation period of light while
remaining spatially uniform. Being the temporal analogs to traditional photonic
crystals, photonic time crystals differ in that they exhibit momentum bandgaps
instead of energy bandgaps. The energy is not conserved within momentum
bandgaps, and eigenmodes with exponentially growing amplitudes exist in the
momentum bandgap. Such properties make photonic time crystals a fascinating
novel class of artificial materials from a basic science and applied
perspective. This tutorial overviews the fundamental electromagnetic equations
governing photonic time crystals and explores the groundbreaking physical
phenomena they support. Based on these properties, we also oversee a diverse
range of applications they unlock. Different material platforms suitable for
creating photonic time crystals are discussed and compared. Furthermore, we
elaborate on the connections between wave amplification in photonic time
crystals and parametric amplification mechanisms in electrical circuits and
nonlinear optics. The tutorial will be helpful for readers with physics or
engineering backgrounds. It is designed to serve as an introductory guide for
beginners and to establish a reference baseline reflecting the current
understanding for researchers in the field.


  Scholars studying organizations often work with multiple datasets lacking
shared identifiers or covariates. In such situations, researchers usually use
approximate string ("fuzzy") matching methods to combine datasets. String
matching, although useful, faces fundamental challenges. Even where two strings
appear similar to humans, fuzzy matching often struggles because it fails to
adapt to the informativeness of the character combinations. In response, a
number of machine learning methods have been developed to refine string
matching. Yet, the effectiveness of these methods is limited by the size and
diversity of training data. This paper introduces data from a prominent
employment networking site (LinkedIn) as a massive training corpus to address
these limitations. By leveraging information from the LinkedIn corpus regarding
organizational name-to-name links, we incorporate trillions of name pair
examples into various methods to enhance existing matching benchmarks and
performance by explicitly maximizing match probabilities. We also show how
relationships between organization names can be modeled using a network
representation of the LinkedIn data. In illustrative merging tasks involving
lobbying firms, we document improvements when using the LinkedIn corpus in
matching calibration and make all data and methods open source.


  We continue the study of the impact of baryon physics on the small scale
problems of the $\Lambda$CDM model, based on a semi-analytical model (Del
Popolo, 2009). Withsuch model, we show how the cusp/core, missing satellite
(MSP), Too Big to Fail (TBTF) problems and the angular momentum catastrophe can
be reconciled with observations, adding parent-satellite interaction. Such
interaction between darkmatter (DM) and baryons through dynamical friction (DF)
can sufficiently flattenthe inner cusp of the density profiles to solve the
cusp/core problem. Combining, in our model, a Zolotov et al. (2012)-like
correction, similarly to Brooks et al. (2013), and effects of UV heating and
tidal stripping, the number of massive, luminous satellites, as seen in the Via
Lactea 2 (VL2) subhaloes,is in agreement with the numbers observed in the MW,
thus resolving the MSP and TBTF problems. The model also produces a
distribution of the angular spin parameter and angular momentum in agreement
with observations of the dwarfs studied by van den Bosch, Burkert, \\& Swaters
(2001).


  We give a brief and a critical review of the Barret-Crane spin foam models of
quantum gravity. Then we describe two new spin foam models which are obtained
by direct quantization of General Relativity and do not have some of the
drawbacks of the Barret-Crane models. These are the model of spin foam
invariants for the embedded spin networks in loop quantum gravity and the spin
foam model based on the integration of the tetrads in the path integral for the
Palatini action.