  We consider possible resolutions of singularities in a contracting
anisotropic universe for a class of higher derivative gravity theories. We give
evidence that for our models the big crunch singularity may be replaced by a
nearly flat Minkowski-like phase before the Universe reenters an anisotropic
expansion in a time-symmetric manner.


  We study the covering path problem on a grid of R^{2}. We generalize earlier
results on a rectangular grid and prove that the covering path cost can be
bounded by the area and perimeter of the grid. We provide (2+\epsilon) and
(1+\epsilon)-approximations for the problem on a general grid and on a convex
grid, respectively.


  The existence of a Radius Valley in the Kepler size distribution stands as
one of the most important observational constraints to understand the origin
and composition of exoplanets with radii between that of Earth and Neptune. The
goal of this work is to provide insights into the existence of the Radius
Valley from, first, a pure formation point of view, and second, a combined
formation-evolution model. We run global planet formation simulations including
the evolution of dust by coagulation, drift and fragmentation; and the
evolution of the gaseous disc by viscous accretion and photoevaporation. A
planet grows from a moon-mass embryo by either silicate or icy pebble
accretion, depending on its position with respect to the water ice line. We
account for gas accretion and type-I/II migration. We perform an extensive
parameter study evaluating a wide range in disc properties and embryo's initial
location. We account for photoevaporation driven mass-loss after formation. We
find that due to the change in dust properties at the water ice line, rocky
cores form typically with $\sim$3 M$_{\oplus}$ and have a maximum mass of
$\sim$5 M$_{\oplus}$, while icy cores peak at $\sim$10 $M_{\oplus}$, with
masses lower than 5 M$_{\oplus}$ being scarce. When neglecting the gaseous
envelope, rocky and icy cores account naturally for the two peaks of the Kepler
size distribution. The presence of massive envelopes for cores more massive
than $\sim$10 M$_{\oplus}$ inflates the radii of those planets above 4
R$_{\oplus}$. While the first peak of the Kepler size distribution is
undoubtedly populated by bare rocky cores, the second peak can host water-rich
planets with thin H-He atmospheres. Some envelope-loss mechanism should operate
efficiently at short orbital periods to explain the presence of $\sim$10-40
M$_{\oplus}$ planets falling in the second peak of the size distribution.


  The classical bond-fluctuation model (BFM) is an efficient lattice Monte
Carlo algorithm for coarse-grained polymer chains where each monomer occupies
exclusively a certain number of lattice sites. In this paper we propose a
generalization of the BFM where we relax this constraint and allow the overlap
of monomers subject to a finite energy penalty $\overlap$. This is done to vary
systematically the dimensionless compressibility $g$ of the solution in order
to investigate the influence of density fluctuations in dense polymer melts on
various s tatic properties at constant overall monomer density. The
compressibility is obtained directly from the low-wavevector limit of the
static structure fa ctor. We consider, e.g., the intrachain bond-bond
correlation function, $P(s)$, of two bonds separated by $s$ monomers along the
chain. It is shown that the excluded volume interactions are never fully
screened for very long chains. If distances smaller than the thermal blob size
are probed ($s \ll g$) the chains are swollen acc ording to the classical
Fixman expansion where, e.g., $P(s) \sim g^{-1}s^{-1/2}$. More importantly, the
polymers behave on larger distances ($s \gg g$) like swollen chains of
incompressible blobs with $P(s) \si m g^0s^{-3/2}$.


  We consider the fate of the Dirac points in the spectrum of a honeycomb
optical lattice in the presence of a harmonic confining potential. By
numerically solving the tight binding model we calculate the density of states,
and find that the energy dependence can be understood from analytical
arguments. In addition, we show that the density of states of the harmonically
trapped lattice system can be understood by application of a local density
approximation based on the density of states of the homogeneous lattice. The
Dirac points are found to survive locally in the trap as evidenced by the local
density of states. They furthermore give rise to a distinct spatial profile of
a noninteracting Fermi gas.


  Deep, narrow-band \Ha\ and 6584 \AA\ [\Nii ] CCD images of the peculiar,
infrared excess B[e] star MWC~922 reveal a collimated, bipolar jet orthogonal
to the previously detected extended nebula. The jet consists of a pair of
$\sim$0.15 pc segments on either side of MWC~922 separated by gaps. The most
distant jet segments disappear $\sim$0.6 pc from the star. The northwest beam
points to a faint emission-line feature 1.65 pc from MWC~922 that may be a
terminal bow shock where the jet rams the ambient medium. The narrow
opening-angle of the jet combined with an estimated internal sound speed of
$\sim$10 \kms\ implies a jet speed $\sim$500 \kms . The previously detected
nebula extends up to 0.6~pc to the southwest of MWC~922 at right angles to the
jet and appears to be an extension of the compact, edge-on disk surrounding the
star. It points toward the HII region Messier 16 located $\sim$1\degr\
($\sim$30 pc in projection) to the southwest. This nebula and jet appear to be
externally ionized by the ambient Lyman continuum radiation field and have
electron densities of n$_e \sim$ 50 to 100 cm$^{-3}$. The southwest nebula and
jet have similar surface brightness in \Ha\ and [\Nii ]. Faint 70 $\mu$m
emission traces the southwest ejecta that likely originates from $\sim$50 K
dust embedded in the photo-ionized plasma which may shadow the dimmer ejecta
northeast of MWC~922. MWC~922 may be a massive member of the Serpens OB1 or OB2
associations surrounding Messier 16 and Sh2-54.


  We present a new library designed to provide a simple and straightforward way
to implement QM/AMOEBA and other polarizable QM/MM methods based on induced
point dipoles. The library, herein referred to as OpenMMPol, is free and
open-sourced and is engineered to address the increasing demand for accurate
and efficient QM/MM simulations. OpenMMPol is specifically designed to allow
polarizable QM/MM calculations of ground state energies and gradients, and
excitation properties. Key features of OpenMMPol include a modular architecture
facilitating extensibility, parallel computing capabilities for enhanced
performance on modern cluster architectures, and a user-friendly interface for
intuitive implementation and a simple and flexible structure for providing
input data. To show the capabilities of fered by the library we present an
interface with PySCF to perform QM/AMOEBA molecular dynamics, geometry
optimization and excited state calculation based on (TD)DFT.


  Superconducting fault current limiters (SFCLs) are new high-precision and
fast-response devices which help to reduce the fault current within the
breaking capacity of the protective relays. Nevertheless, the reconfigurable
structure of the distribution network can affect their performance negatively
by changing the supplying path of the electrical loads and thus keeping SFCL in
a useless point which cannot limit the high fault currents. This paper proposes
an aggregated approach to solve the optimal placement of SFCLs considering the
reconfiguration of feeders through the pre-located tie and sectionalizing
switches. While SFCL placement problem aims to minimize the number of SFCLs and
limit the high short circuit currents in the first seconds of the fault, the
reconfiguration strategy is used to minimize the total grid costs incorporating
the cost of power losses and customer interruptions. According to the high
non-linearity and complexity of the proposed problem, social spider algorithm
(SSA) with a two-phase modification method is developed to solve the proposed
problem. The feasibility and performance of the proposed method are examined on
an IEEE test system.


  An important subclass of hybrid Bayesian networks are those that represent
Conditional Linear Gaussian (CLG) distributions --- a distribution with a
multivariate Gaussian component for each instantiation of the discrete
variables. In this paper we explore the problem of inference in CLGs. We show
that inference in CLGs can be significantly harder than inference in Bayes
Nets. In particular, we prove that even if the CLG is restricted to an
extremely simple structure of a polytree in which every continuous node has at
most one discrete ancestor, the inference task is NP-hard.To deal with the
often prohibitive computational cost of the exact inference algorithm for CLGs,
we explore several approximate inference algorithms. These algorithms try to
find a small subset of Gaussians which are a good approximation to the full
mixture distribution. We consider two Monte Carlo approaches and a novel
approach that enumerates mixture components in order of prior probability. We
compare these methods on a variety of problems and show that our novel
algorithm is very promising for large, hybrid diagnosis problems.


  We discuss, from a theoretical point of view, excitonic phases at the
pressure induced semiconductor-semimetal transition in $\rm
TmSe_{0.45}Te_{0.55}$,focusing, in particular, on the stability against an
electron-hole liquid. The electron-hole pair density parameter $r_s(E_g,T)$ is
calculated within the quasi-static plasmon pole approximation as a function of
temperature $T$ and energy gap $E_g$ and converted into $-E_g(r_s,T)$. A
comparison of this quantity, which is the electron-hole pair chemical
potential, with the exciton binding energy reveals that excitons should be
suppressed in contrast to experimental evidence for excitonic phases. We
suspect therefore inter-valley exciton scattering and exciton-phonon scattering
to substantially stabilise excitons in $\rm TmSe_{0.45}Te_{0.55}$.


  In this paper we introduce the stochastic Ricci flow (SRF) in two spatial
dimensions. The flow is symmetric with respect to a measure induced by
Liouville Conformal Field Theory. Using the theory of Dirichlet forms, we
construct a weak solution to the associated equation of the area measure on a
flat torus, in the full "$L^1$ regime" $\sigma< \sigma_{L^1}=2\sqrt\pi$ where
$\sigma$ is the noise strength. We also describe the main necessary
modifications needed for the SRF on general compact surfaces, and list some
open questions.


  We discuss functoriality properties of the Ozsvath-Szabo contact invariant,
and expose a number of results which seemed destined for folklore. We clarify
the (in)dependence of the invariant on the basepoint, prove that it is
functorial with respect to contactomorphisms, and show that it is strongly
functorial under Stein cobordisms.


  We consider a planar heterostructure consisting of a normal metal in
proximity to an antiferromagnetic insulator, with an interlayer exchange
coupling between the metal and the insulator. The coupling to the two
sublattices of the antiferromagnetic insulator is allowed to be asymmetric. An
effective electron-electron interaction in the normal metal, mediated by
antiferromagnetic magnons in the insulator, is derived to second order in the
interlayer exchange coupling. Particular emphasis is placed on including
analytically derived expressions for the effective interactions including
Umklapp processes in the solutions to the superconducting gap equation. The gap
equation is first solved at the critical temperature as an eigenvalue problem
by linearizing the gap equation. The eigenvectors yield information on the
symmetry of the superconducting gap at the onset of superconductivity, and we
derive a phase diagram for the order parameter in this case. In the various
regimes of the phase diagram, we find $p$-wave, $f$-wave, and $d$-wave
superconductivity, with $p$-wave superconductivity in the dominant part of the
phase diagram. Umklapp processes, that come into play with increasing size of
the Fermi surface, yield $f$- and $d$-wave symmetries as the preferred
symmetries when band filling approaches half filling. To investigate the
stability of this order parameter symmetry as the temperature is lowered, we
also consider the nonlinear gap equation at zero temperature. We conclude that
the phase diagram and the symmetries of the superconducting order parameter
essentially are left intact as the temperature is lowered to zero temperature.


  The main aim of this paper is to analyse minimally-coupled scalar-fields --
quintessence and phantom -- as the main candidates to explain the accelerated
expansion of the universe and compare its observables to current cosmological
observations; as a byproduct we present its python module. This work includes a
parameter $\epsilon$ which allows to incorporate both quintessence and phantom
fields within the same analysis. Examples of the potentials, so far included,
are $V(\phi)=V_0\phi^{\mu}e^{\beta \phi^\alpha}$ and $V(\phi)=V_0(\cosh(\alpha
\phi)+\beta)$ with $\alpha$, $\mu$ and $\beta$ being free parameters, but the
analysis can be easily extended to any other scalar field potential. Additional
to the field component and the standard content of matter, the study also
incorporates the contribution from spatial curvature ($\Omega_k$), as it has
been the focus in recent studies. The analysis contains the most up-to-date
datasets along with a nested sampler to produce posterior distributions along
with the Bayesian evidence, that allows to perform a model selection. In this
work we constrain the parameter-space describing the two generic potentials,
and among several combinations, we found that the best-fit to current datasets
is given by a model slightly favouring the quintessence field with potential
$V(\phi)=V_0\phi^\mu e^{\beta \phi}$ with $\beta=0.22\pm 1.56$, $\mu = -0.41\pm
1.90$, and slightly negative curvature $\Omega_{k,0}=-0.0016\pm0.0018$, which
presents deviations of $1.6\sigma$ from the standard $\Lambda$CDM model. Even
though this potential contains three extra parameters, the Bayesian evidence
$\mathcal{B}_{\Lambda, \phi} =2.0$ is unable to distinguish this model compared
to the $\Lambda$CDM with curvature ($\Omega_{k,0}=0.0013\pm0.0018$). The
potential that provides the minimal Bayesian evidence corresponds to
$V(\phi)=V_0 \cosh(\alpha \phi)$ with $\alpha=-0.61\pm 1.36$.


  I examine the form of the solution of the BFKL equation with running coupling
relevant for deep inelastic scattering. The evolution of structure functions is
precisely determined and well described by an effective coupling of the form
1/(beta_0(ln(Q^2/Lambda^2)+3.6(alpha_s(Q^2)ln(1/x))^1/2)) (until very small x).
Corrections to the LO equation are relatively small, and the perturbative
expansion is stable. Comparison to data via a global fit is very successful.


  Microscopic instability and macroscopic flow pattern resulting from colliding
plasmas are studied analytically in support of laboratory experiments. The
plasma flows are assumed to stream radially from two separate centers. In a
quasi-planar (2D) geometry, they may arise from an Ohmic explosion of two
parallel wires, but similar configurations emerge from other outflows, e.g.,
colliding winds in binary star systems. One objective of this paper is to
characterize the flow instabilities developing near the flow stagnation line.
An exact solution for the Buneman-type dispersion equation is obtained without
conventional simplifications. The unstable wave characteristics are key to
anomalous resistivity that determines the reconnection rate of opposite
magnetic fields transported with each flow toward the stagnation zone. The
second objective of the paper is to calculate the stream function of the plasma
shocked upon collision. We addressed this task by mapping the flow region to a
hodograph plane and solving a Dirichlet problem for the stream function. By
providing the instability growth rate, responsible for anomalous transport
coefficients, and the overall flow configuration, these studies lay the ground
for the next step. From there, we will examine the field reconnection scenarios
and emerging mesoscopic structures, such as radial striata observed in the
experiments.


  Ensemble Kalman inversion (EKI) is an ensemble-based method to solve inverse
problems. Its gradient-free formulation makes it an attractive tool for
problems with involved formulation. However, EKI suffers from the ''subspace
property'', i.e., the EKI solutions are confined in the subspace spanned by the
initial ensemble. It implies that the ensemble size should be larger than the
problem dimension to ensure EKI's convergence to the correct solution. Such
scaling of ensemble size is impractical and prevents the use of EKI in high
dimensional problems. To address this issue, we propose a novel approach using
dropout regularization to mitigate the subspace problem. We prove that
dropout-EKI converges in the small ensemble settings, and the computational
cost of the algorithm scales linearly with dimension. We also show that
dropout-EKI reaches the optimal query complexity, up to a constant factor.
Numerical examples demonstrate the effectiveness of our approach.


  We present a size analysis of a sample of $\sim$ 49,000 galaxies from the
CANDELS GOODS North and South fields using redshift-independent relative
surface brightness metrics to determine an unbiased measure of the differential
size evolution of galaxies at $1 \leq z \leq 7$. We introduce a novel method of
removing foreground objects from distant galaxy ($z > 3$) images that makes use
of the Lyman-break at 912{\AA}, in what we call `2-D Lyman-Break Imaging'. The
images used are in the rest-frame optical at $z < 3$ and progressively bluer
bands at $z > 3$. They are therefore subject to K-correction and cosmological
dimming effects which are tested and corrected for. We separately consider a
mass-selected sample (with masses in the range
10$^9$M$_{\odot}$$\leq$M$_*$$\leq$10$^{10.5}$M$_{\odot}$) and a number density
selected sample (using a constant number density of $n =
1\times10^{-4}$Mpc$^{-3}$). Instead of utilising the commonly used, but
potentially biased, effective radii for size measurements, we measure the
redshift-independent Petrosian radius, defined by the parameter $\eta$, for
each galaxy for three values of $\eta$ and use this as a proxy for size. The
evolution of the measured radii can be described by a power-law of the form
$R_{Petr} = \alpha(1+z)^\beta$kpc where $\beta < 0$. We find that the outer
radius increases more rapidly, suggesting that as a galaxy grows mass is added
to its outer regions via an inside-out growth. This growth is stronger for the
number density selected sample, with a growth rate of nearly three in the outer
radii compared to the inner. We test and confirm these results using a series
of image simulations.


  The study of fast, eruptive events in the low solar corona is one of the
science objectives of the Atmospheric Imaging Assembly (AIA) imagers on the
recently launched Solar Dynamics Observatory (SDO), which take full disk images
in ten wavelengths with arcsecond resolution and 12 sec cadence. We study with
AIA the formation of an impulsive coronal mass ejection (CME) which occurred on
June 13, 2010 and was associated with an M1.0 class flare. Specifically, we
analyze the formation of the CME EUV bubble and its initial dynamics and
thermal evolution in the low corona using AIA images in three wavelengths (171,
193 and 211 A). We derive the first ultra-high cadence measurements of the
temporal evolution of the CME bubble aspect ratio
(=bubble-height/bubble-radius). Our main result is that the CME formation
undergoes three phases: it starts with a slow self-similar expansion followed
by a fast but short-lived (~ 70 sec) period of strong lateral over-expansion
which essentially creates the CME. Then the CME undergoes another phase of
self-similar expansion until it exits the AIA field of view. During the studied
interval, the CME height-time profile shows a strong, short-lived, acceleration
followed by deceleration. The lateral overexpansion phase coincides with the
deceleration phase. The impulsive flare heating and CME acceleration are
closely coupled. However, the lateral overexpansion of the CME occurs during
the declining phase and is therefore not linked to flare reconnection. In
addition, the multi-thermal analysis of the bubble does not show significant
evidence of temperature change.


  The excitonic absorption spectrum for a disordered quantum well in presence
of exciton-acoustic phonon interaction is treated beyond the Markov
approximation. Realistic disorder exciton states are taken from a microscopic
simulation, and the deformation potential interaction is implemented. The
exciton Green's function is solved with a self energy in second order Born
quality. The calculated spectra differ from a superposition of Lorentzian
lineshapes by enhanced inter-peak absorption. This is a manifestation of pure
dephasing which should be possible to measure in near-field experiments.


  In this study we introduce Logarithmic Frequency Shift Keying (Log-FSK), a
novel frequency modulation for over-the-air computation (AirComp). Log-FSK
leverages non-linear signal processing to produce AirComp in the frequency
domain, this is, the maximum frequency of the received signal corresponds to
the sum of the individual transmitted frequencies. The demodulation procedure
relies on the inverse Discrete Cosine Transform (DCT) and the extraction of the
maximum frequency component. We provide the theoretical performance in terms of
error probability and mean squared error. To demonstrate its practicality, we
present specific applications and experimental results showcasing the
effectiveness of Log-FSK AirComp within linear Wireless Sensor Networks (WSN).
Our experiments show that Log-FSK outperforms linear AirComp, implemented with
double sideband (DSB), when working above the threshold SNR.


  Using three different approaches, Perturbation Theory (PT), the Lagrange Mesh
Method (Lag-Mesh) and the Variational Method (VM), we study the low-lying
states of the Yukawa potential $V(r)=-(\lambda/r)e^{-\alpha r}\,$. First orders
in PT in powers of $\alpha$ are calculated in the framework of the
Non-Linerization Procedure. It is found that the Pad\'e approximants to PT
series together with the Lag-Mesh provide highly accurate values of the energy
and the positions of the radial nodes of the wave function. The most accurate
results, at present, of the critical screening parameters ($\alpha_c$) for some
low-lying states and the first coefficients in the expansion of the energy at
$\alpha_c$ are presented. A locally-accurate and compact approximation for the
eigenfunctions of the low-lying states for any $r\in [ 0,\infty)$ is
discovered. This approximation used as a trial function in VM eventually leads
to energies as precise as those of PT and Lag-Mesh. Finally, a compact
analytical expression for the energy as a function of $\alpha$, that reproduce
at least $6$ decimal digits in the entire physical range of $\alpha$, is found.


  We study the effect of interlayer Coulomb interaction in an electronic double
layer. Assuming that each of the layers consists of a bipartite lattice, a
sufficiently strong interlayer interaction leads to an interlayer pairing of
electrons with a staggered order parameter. We show that the correlated pairing
state is dual to the excitonic pairing state with uniform order parameter in an
electron-hole double layer. The interlayer pairing of electrons leads to strong
current-current correlations between the layers. We also analyze the interlayer
conductivity and the fluctuations of the order parameter, which consists of a
gapped and a gapless mode.


  There has been a renewed interest in the description of dressed asymptotic
states a la Faddeev-Kulish. In this regard, a worldline representation for
asymptotic states dressed by radiation at subleading power in the soft
expansion, known as the Generalized Wilson Line (GWL) in the literature, has
been available for some time, and it recently found applications in the
derivation of factorization theorems for scattering processes of
phenomenological relevance. In this paper we revisit the derivation of the GWL
in the light of the well-known supersymmetric wordline formalism for the
relativistic spinning particle. In particular, we discuss the importance of
wordline supersymmetry to understand the contribution of the soft background
field to the asymptotic dynamics. We also provide a derivation of the GWL for
the gluon case, which was not previously available in the literature, thus
extending the exponentiation of next-to-soft gauge boson corrections to
Yang-Mills theory. Finally, we comment about possible applications in the
current research about asymptotic states in scattering amplitudes for gauge and
gravity theories and their classical limit.


  Granular media jam into a panoply of metastable states. The way in which
these states are achieved depends on the nature of local and global constraints
on grains; here we investigate this issue by means of a non-equilibrium
stochastic model of a hindered granular column near its jamming limit. Grains
feel the constraints of grains above and below them differently, depending on
their position. A rich phase diagram with four dynamical phases (ballistic,
activated, logarithmic and glassy) is revealed. The statistics of the jamming
time and of the metastable states reached as attractors of the zero-temperature
dynamics is investigated in each of these phases. Of particular interest is the
glassy phase, where intermittency and a strong deviation from Edwards' flatness
are manifest.


  This paper presents a search for a new $Z^\prime$ resonance decaying into a
pair of dark quarks which hadronise into dark hadrons before promptly decaying
back as Standard Model particles. This analysis is based on proton-proton
collision data recorded at $\sqrt{s}=13$ TeV with the ATLAS detector at the
Large Hadron Collider between 2015 and 2018, corresponding to an integrated
luminosity of 139 fb$^{-1}$. After selecting events containing large-radius
jets with high track multiplicity, the invariant mass distribution of the two
highest-transverse-momentum jets is scanned to look for an excess above a
data-driven estimate of the Standard Model multijet background. No significant
excess of events is observed and the results are thus used to set 95 %
confidence-level upper limits on the production cross-section times branching
ratio of the $Z^\prime$ to dark quarks as a function of the $Z^\prime$ mass for
various dark-quark scenarios.


  This work focuses on in-context data augmentation for intent detection.
Having found that augmentation via in-context prompting of large pre-trained
language models (PLMs) alone does not improve performance, we introduce a novel
approach based on PLMs and pointwise V-information (PVI), a metric that can
measure the usefulness of a datapoint for training a model. Our method first
fine-tunes a PLM on a small seed of training data and then synthesizes new
datapoints - utterances that correspond to given intents. It then employs
intent-aware filtering, based on PVI, to remove datapoints that are not helpful
to the downstream intent classifier. Our method is thus able to leverage the
expressive power of large language models to produce diverse training data.
Empirical results demonstrate that our method can produce synthetic training
data that achieve state-of-the-art performance on three challenging intent
detection datasets under few-shot settings (1.28% absolute improvement in
5-shot and 1.18% absolute in 10-shot, on average) and perform on par with the
state-of-the-art in full-shot settings (within 0.01% absolute, on average).


  The task of face reenactment is to transfer the head motion and facial
expressions from a driving video to the appearance of a source image, which may
be of a different person (cross-reenactment). Most existing methods are
CNN-based and estimate optical flow from the source image to the current
driving frame, which is then inpainted and refined to produce the output
animation. We propose a transformer-based encoder for computing a set-latent
representation of the source image(s). We then predict the output color of a
query pixel using a transformer-based decoder, which is conditioned with
keypoints and a facial expression vector extracted from the driving frame.
Latent representations of the source person are learned in a self-supervised
manner that factorize their appearance, head pose, and facial expressions.
Thus, they are perfectly suited for cross-reenactment. In contrast to most
related work, our method naturally extends to multiple source images and can
thus adapt to person-specific facial dynamics. We also propose data
augmentation and regularization schemes that are necessary to prevent
overfitting and support generalizability of the learned representations. We
evaluated our approach in a randomized user study. The results indicate
superior performance compared to the state-of-the-art in terms of motion
transfer quality and temporal consistency.


  Next-generation mobile networks promise to support high throughput, massive
connectivity, and improved energy efficiency. To achieve these ambitious goals,
extremely large-scale antenna arrays (ELAAs) and terahertz communications
constitute a pair of promising technologies. This will result in future
wireless communications occurring in the near-field regions. To accurately
portray the channel characteristics of near-field wireless propagation,
spherical wavefront-based models are required and present both opportunities as
well as challenges. Following the basics of near-field communications (NFC), we
contrast it to conventional far-field communications. Moreover, we cover the
key challenges of NFC, including its channel modeling and estimation,
near-field beamfocusing, as well as hardware design. Our numerical results
demonstrate the potential of NFC in improving the spatial multiplexing gain and
positioning accuracy. Finally, a suite of open issues are identified for
motivating future research.


  We searched for a correlation between the two anomalous properties of K
giants: Li enhancement and IR excess from an unbiased survey of a large sample
of RGB stars. A sample of 2000 low-mass K giants with accurate astrometry from
the Hipparcos catalog was chosen for which Li abundances have been determined
from low-resolution spectra. Far-infrared data were collected from the $WISE$
and $IRAS$ catalogs. To probe the correlation between the two anomalies, we
supplemented 15 Li-rich K giants discovered from this sample with 25 known
Li-rich K giants from other studies. Dust shell evolutionary models and
spectral energy distributions were constructed using the code DUSTY to estimate
different dust shell properties, such as dust evolutionary time scales, dust
temperatures, and mass-loss rates. Among 2000 K giants, we found about two
dozen K giants with detectable far-IR excess, and surprisingly, none of them
are Li-rich. Similarly, the 15 new Li-rich K giants that were identified from
the same sample show no evidence of IR excess. Of the total 40 Li-rich K
giants, only 7 show IR excess. Important is that K giants with Li enhancement
and/or IR excess begin to appear only at the bump on the RGB. Results show that
K giants with IR excess are very rare, similar to K giants with Li enhancement.
This may be due to the rapid differential evolution of dust shell and Li
depletion compared to RGB evolutionary time scales. We also infer from the
results that during the bump evolution, giants probably undergo some internal
changes, which are perhaps the cause of mass-loss and Li-enhancement events.
However, the available observational results do not ascertain that these
properties are correlated. That a few Li-rich giants have IR excess seems to be
pure coincidence.


  As defined by W. Thurston, the core entropy of a polynomial is the entropy of
the restriction to its Hubbard tree. For each d >= 2, we study the core entropy
as a function on the parameter space of polynomials of degree d, and prove it
varies continuously both as a function of the combinatorial data and of the
coefficients of the polynomials. This generalizes a conjecture of Thurston for
quadratic polynomials.


  The quantum world is described by a unit vector in the Hilbert space and the
Hamiltonian. Do they, as abstract basis-independent objects, give a complete
description of the physical world, or should we include observables like
positions and momenta and the decomposition into subsystems? According to
"Hilbert-space fundamentalism" they give a complete description, and all other
features of the physical world emerge from them (Carroll, arXiv:2103.09780).
This thesis was previously refuted in (arXiv:2102.08620) in full generality.
But being an abstract non-uniqueness proof, and not a constructive one, it may
not be convincing enough to the busy reader who wants to avoid mathematical
details.
  Here I give a simpler, intuitive and constructive refutation, by showing that
concrete physically distinct worlds can be described by the same unit vector
and evolve according to the same law.


  V697 Sco, the remnant of Nova Scorpii 1941 and currently at V ~ 20.0, is
found from photometric observations to have the characteristics of an
intermediate polar (IP) with an orbital period (Porb) of 4.49 h and a rotation
period (Prot) of 3.31 h. It therefore appears to be a member of the rare class
of IPs where Prot ~ Porb, which are probably discless systems. The prominence
of the modulation at 0.5 Prot, and its orbital sidebands, indicates two-pole
accretion.


  Many-photon interference in linear-optics setups can be exploited to generate
and detect multipartite entanglement. Without recurring to any inter-particle
interaction, many entangled states have been created experimentally, and a
panoply of theoretical schemes for the generation of various classes of
entangled states is available. Here, we present a unifying framework that
accommodates the present experiments and theoretical protocols for the creation
of multiparticle entanglement via interference. A general representation of the
states that can be created is provided for bosons and fermions, for any
particle number, and for any dimensionality of the entangled degree of freedom.
Using the framework, we derive an upper bound on the generalized Schmidt number
of the states that can be generated, and we establish bounds on the
dimensionality of the manifold of these states. We show that - at the expense
of a smaller success probability - more states can be created with bosons than
with fermions, and give an intuitive interpretation of the state representation
and of the established bounds in terms of superimposed many-particle paths.


  In this paper, we present a quantum algorithm for approximating multivariate
traces, i.e. the traces of matrix products. Our research is motivated by the
extensive utility of multivariate traces in elucidating spectral
characteristics of matrices, as well as by recent advancements in leveraging
quantum computing for faster numerical linear algebra. Central to our approach
is a direct translation of a multivariate trace formula into a quantum circuit,
achieved through a sequence of low-level circuit construction operations. To
facilitate this translation, we introduce \emph{quantum Matrix States Linear
Algebra} (qMSLA), a framework tailored for the efficient generation of state
preparation circuits via primitive matrix algebra operations. Our algorithm
relies on sets of state preparation circuits for input matrices as its primary
inputs and yields two state preparation circuits encoding the multivariate
trace as output. These circuits are constructed utilizing qMSLA operations,
which enact the aforementioned multivariate trace formula. We emphasize that
our algorithm's inputs consist solely of state preparation circuits, eschewing
harder to synthesize constructs such as Block Encodings. Furthermore, our
approach operates independently of the availability of specialized hardware
like QRAM, underscoring its versatility and practicality.


  In this paper, we present a device-to-device (D2D) transmission scheme for
aiding long-range frequency hopping spread spectrum (LR-FHSS) LoRaWAN protocol
with application in direct-to-satellite IoT networks. We consider a practical
ground-to-satellite fading model, i.e. shadowed-Rice channel, and derive the
outage performance of the LR-FHSS network. With the help of network coding,
D2D-aided LR-FHSS transmission scheme is proposed to improve the network
capacity for which a closed-form outage probability expression is also derived.
The obtained analytical expressions for both LR-FHSS and D2D-aided LR-FHSS
outage probabilities are validated by computer simulations for different parts
of the analysis capturing the effects of noise, fading, unslotted ALOHA-based
time scheduling, the receiver's capture effect, IoT device distributions, and
distance from node to satellite. The total outage probability for the D2D-aided
LR-FHSS shows a considerable increase of 249.9% and 150.1% in network capacity
at a typical outage of 10^-2 for DR6 and DR5, respectively, when compared to
LR-FHSS. This is obtained at the cost of minimum of one and maximum of two
additional transmissions per each IoT end device imposed by the D2D scheme in
each time-slot.


  The Hilbert Huang Transform is a new technique for the analysis of
non--stationary signals. It comprises two distinct parts: Empirical Mode
Decomposition (EMD) and the Hilbert Transform of each of the modes found from
the first step to produce a Hilbert Spectrum. The EMD is an adaptive
decomposition of the data, which results in the extraction of Intrinsic Mode
Functions (IMFs). We discuss the application of the EMD to the calibration of
two optical scintillometers that have been used to measure C_n^2 over
horizontal paths on a building rooftop, and discuss the advantage of using the
Marginal Hilbert Spectrum over the traditional Fourier Power Spectrum.


  One important problem in genome science is to determine sets of co-regulated
genes based on measurements of gene expression levels across samples, where the
quantification of expression levels includes substantial technical and
biological noise. To address this problem, we developed a Bayesian sparse
latent factor model that uses a three parameter beta prior to flexibly model
shrinkage in the loading matrix. By applying three layers of shrinkage to the
loading matrix (global, factor-specific, and element-wise), this model has
non-parametric properties in that it estimates the appropriate number of
factors from the data. We added a two-component mixture to model each factor
loading as being generated from either a sparse or a dense mixture component;
this allows dense factors that capture confounding noise, and sparse factors
that capture local gene interactions. We developed two statistics to quantify
the stability of the recovered matrices for both sparse and dense matrices. We
tested our model on simulated data and found that we successfully recovered the
true latent structure as compared to related models. We applied our model to a
large gene expression study and found that we recovered known covariates and
small groups of co-regulated genes. We validated these gene subsets by testing
for associations between genotype data and these latent factors, and we found a
substantial number of biologically important genetic regulators for the
recovered gene subsets.


  A new type of simplified cloaks with matched exterior boundaries is proposed.
The cloak uses non-magnetic material for the TM polarization and can function
with a relatively thin thickness. It is shown that the $zero^{th}$ order
scattering of such cloak is dominant among all cylindrical scattering terms. A
gap is added at the cloak's inner surface to eliminate the zero-th order
scattering, through the mechanism of scattering resonance. The reduction in
scattering is relatively smooth, indicating that the proposed scattering
reduction method has good tolerance to perturbations. Numerical simulations
also confirm that the proposed structure has very low scattering.


  Recent observations of a large number of DA and DB white dwarfs show evidence
of debris disks, which are the remnants of old planetary systems. The infrared
excess detected with \emph{Spitzer} and the lines of heavy elements observed in
their atmospheres with high-resolution spectroscopy converge on the idea that
planetary material accretes onto these stars. Accretion rates have been derived
by several authors with the assumption of a steady state between accretion and
gravitational settling. The results are unrealistically different for DA and DB
white dwarfs. When heavy matter is accreted onto stars, it induces an inverse
$\mu$-gradient that leads to fingering (thermohaline) convection. The aim of
this letter is to study the impact of this specific process on the derived
accretion rates in white dwarfs and on the difference between DA and DB. We
solve the diffusion equation for the accreted heavy elements with a
time-dependent method. The models we use have been obtained both with the IRAP
code, which computes static models, and the La Plata code, which computes
evolutionary sequences. Computations with pure gravitational settling are
compared with computations that include fingering convection. The most
important result is that fingering convection has very important effects on DAs
but is inefficient in DBs. When only gravitational settling is taken into
account, the time-dependent computations lead to a steady state, as postulated
by previous authors. When fingering convection is added, this steady state
occurs much later. The surprising difference found in the past for the
accretion rates derived for DA and DB white dwarfs disappears. The derived
accretion rates for DAs are increased when fingering convection is taken into
account, whereas those for DBs are not modified. More precise and developed
results will be given in a forthcoming paper.


  We determine the general conditions for the existence of Godel, Einstein
static, and de Sitter universes in gravity theories derived from a Lagrangian
that is an arbitrary function of the scalar curvature and Ricci and Riemann
curvature invariants. Explicit expressions for the solutions are found in terms
of the parameters defining the Lagrangian. We also determine the conditions on
the Lagrangian of the theory under which time-travel is allowed in the Godel
universes.


  Bayesian statistical calculations and linear-bisector calculations for
obtaining Cepheid distances and radii by the infrared surface brightness method
have been compared for a set of 38 Cepheids. The distances obtained by the two
techniques agree to 1.5%+/-0.6% and the radii agree to 1.1%+/-0.7%. Thus the
two methods yield the same distances and radii at the 2 sigma level. This
implies that the short distance to the LMC found in recent linearbisector
studies of Cepheids is not a result of simplifications in the mathematical
approach. The computed uncertainties in distance and radius are larger in the
Bayesian calculation typically by a factor of three.


  We show that every group $H$ of at most exponential growth with respect to
some left invariant metric admits a bi-Lipschitz embedding into a finitely
generated group $G$ such that $G$ is amenable (respectively, solvable,
satisfies a non-trivial identity, elementary amenable, of finite decomposition
complexity, etc.) whenever $H$ is. We also discuss some applications to
compression functions of Lipschitz embeddings into uniformly convex Banach
spaces, F{\o}lner functions, and elementary classes of amenable groups.


  Charge migration is a ubiquitous phenomenon with profound implications
throughout many areas of chemistry, physics, biology and materials science. The
long-term vision of designing functional materials with tailored molecular
scale properties has triggered an increasing quest to identify prototypical
systems where truly molecular conduction pathways play a fundamental role. Such
pathways can be formed due to the molecular organization of various organic
materials and are widely used to discuss electronic properties at the nanometer
scale. Here, we present a computational methodology to study charge propagation
in organic molecular stacks at nano and sub-nanoscales and exploit this
methodology to demonstrate that moving charge carriers strongly affect the
values of the physical quantities controlling their motion. The approach is
also expected to find broad application in the field of charge migration in
soft matter systems.


  There are racial disparities in the COVID-19 test positivity rate, suggesting
that minorities may be under-tested. Here, drawing on the literature on
statistically assessing racial disparities in policing, we 1) illuminate a
statistical flaw, known as infra-marginality, in using the positivity rate as a
metric for assessing racial disparities in under-testing; 2) develop a new type
of Bayesian threshold test to measure disparities in COVID-19 testing and 3)
apply the test to measure racial disparities in testing thresholds in a
real-world COVID-19 dataset.


  While most classic studies of function in experimental neuroscience have
focused on the coding properties of individual neurons, recent developments in
recording technologies have resulted in an increasing emphasis on the dynamics
of neural populations. This has given rise to a wide variety of models for
analyzing population activity in relation to experimental variables, but direct
testing of many neural population hypotheses requires intervening in the system
based on current neural state, necessitating models capable of inferring neural
state online. Existing approaches, primarily based on dynamical systems,
require strong parametric assumptions that are easily violated in the
noise-dominated regime and do not scale well to the thousands of data channels
in modern experiments. To address this problem, we propose a method that
combines fast, stable dimensionality reduction with a soft tiling of the
resulting neural manifold, allowing dynamics to be approximated as a
probability flow between tiles. This method can be fit efficiently using online
expectation maximization, scales to tens of thousands of tiles, and outperforms
existing methods when dynamics are noise-dominated or feature multi-modal
transition probabilities. The resulting model can be trained at kiloHertz data
rates, produces accurate approximations of neural dynamics within minutes, and
generates predictions on submillisecond time scales. It retains predictive
performance throughout many time steps into the future and is fast enough to
serve as a component of closed-loop causal experiments.


  Dark (hidden) photons are widely recognised as well motivated candidates for
physics beyond the standard model, and have been invoked for the solution of
several outstanding problems, including to account for the dark matter in the
universe. In this paper, we consider a simple model for dark photons, which is
coupled to ordinary matter only through kinetic mixing with ordinary photons.
Within this framework, we calculate the flux of solar dark photons on Earth and
revise the potential to detect it with the next generation of axion
helioscopes, particularly with the International AXion Observatory (IAXO). This
paper extends on previous theoretical analyses in two main ways. Firstly, it
includes a more complete analysis of the possible sources of dark photons from
the sun, including the contribution of the solar magnetic field and of nuclear
processes, and secondly it includes predictions on the parameter space
accessible in the gas-filled phase of IAXO.


  Recently our group analyzed how the probability distribution for the jet
opening angle is modified in an ensemble of jets that has propagated through an
expanding cooling droplet of plasma [1]. Each jet in the ensemble is
represented holographically by a string in the dual 4+1- dimensional
gravitational theory with the distribution of initial energies and opening
angles in the ensemble given by perturbative QCD. In [1], the full string
dynamics were approximated by assuming that the string moves at the speed of
light. We are now able to analyze the full string dynamics for a range of
possible initial conditions, giving us access to the dynamics of holographic
jets just after their creation. The nullification timescale and the features of
the string when it has nullified are all results of the string evolution. This
emboldens us to analyze the full jet shape modification, rather than just the
opening angle modification of each jet in the ensemble as in [1]. We find the
result that the jet shape scales with the opening angle at any particular
energy. We construct an ensemble of dijets with energies and energy asymmetry
distributions taken from events in proton-proton collisions, opening angle
distribution as in [1], and jet shape taken from proton-proton collisions and
scaled according to our result. We study how these observables are modified
after we send the ensemble of dijets through the strongly-coupled plasma.


  We investigate cosmological evolution and implications of cosmic strings with
time-dependent tension. We derive basic equations of time development of the
correlation length and the velocity of such strings, based on the one scale
model. Then, we find that, in the case where the tension depends on some power
of the cosmic time, cosmic strings with time-dependent tension goes into the
scaling solution if the power is lower than a critical value. We also discuss
cosmic microwave background anisotropy and matter power spectra produced by
these strings. The constraints on their tensions from the Wilkinson microwave
anisotropy probe (WMAP) three year data and Sloan digital sky survey (SDSS)
data are also given.


  The acceleration gradients generated in a laser- or beam-driven plasma
wakefield accelerator are typically three orders of magnitude greater than
those produced by a conventional accelerator, and hence plasma accelerators can
open a route to a new generation of very compact machines. In addition,
plasma-based accelerators can generate beams with unique properties, such as
tens of kiloamp peak currents, attosecond bunch duration, ultrahigh brightness
and intrinsic particle beam-laser pulse synchronization.
  In this roadmap we review the status of plasma accelerator research in the
UK. We outline potential applications, describe the research and development
required to enable those applications, and discuss synergies with related areas
of research. We also set-out the resources required to realise these ambitions
and provide a timeline for advances in the key areas.


  Acoustic bianisotropy, also known as the Willis parameter, expands the field
of acoustics by providing nonconventional couplings between momentum and strain
in constitutive relations. Sharing the common ground with electromagnetics, the
realization of acoustic bianisotropy enables the exotic manipulation of
acoustic waves in cooperation with a properly designed inverse bulk modulus and
mass density. While the control of entire constitutive parameters substantiates
intriguing theoretical and practical applications, a Willis metamaterial that
enables independently and precisely designed polarizabilities has yet to be
developed to overcome the present restrictions of the maximum Willis bound and
the nonreciprocity inherent to the passivity of metamaterials. Here, by
extending the recently developed concept of virtualized metamaterials, we
propose acoustic Willis metamaterials that break the passivity and reciprocity
limit while also achieving decoupled control of all constitutive parameters
with designed frequency responses. By instituting basis convolution kernels
based on parity symmetry for each polarization response, we experimentally
demonstrate bianisotropy beyond the limit of passive media. Furthermore, based
on the notion of inverse design of the frequency dispersion by means of digital
convolution, purely nonreciprocal media and media with a broadband,
flat-response Willis coupling are also demonstrated. Our approach offers all
possible independently programmable extreme constitutive parameters and
frequency dispersion tunability accessible within the causality condition and
provides a flexible platform for realizing the full capabilities of acoustic
metamaterials.


  The discovery of quantum key distribution by Bennett and Brassard (BB84)
bases on the fundamental quantum feature: incompatibility of measurements of
quantum non-commuting observables. In 1991 Ekert showed that cryptographic key
can be generated at a distance with help of entangled (correlated) quantum
particles. Recently Barrett, Hardy and Kent showed that the non-locality used
by Ekert is itself a good resource of cryptographic key even beyond quantum
mechanics. Their result paved the way to new generation of quantum
cryptographic protocols - secure even if the devices are built by the very
eavesdropper. However, there is a question, which is fundamental from both
practical and philosophical point of view: does Nature offer security on
operational level based on the original concept behind quantum cryptography -
that information gain about one bservables must cause disturbance to another,
incompatible one?
  Here we resolve this problem by using in place of non-locality another
striking feature of quantum world - contextuality. It is a strong version of
incompatibility manifested in the famous Kochen-Specker paradox. The crucial
concept is the use of a new class of families of bipartite probability
distributions which locally exhibit the Kochen-Specker paradox conditions and,
in addition, exhibit perfect correlations. We show that if two persons share
systems described by such a family then they can extract secure key.
  This is the first operational protocol that directly implements the
fundamental feature of Nature: the information gain vs. disturbance trade-off.
At the same time it provides natural device-independent cryptographic scheme
within quantum mechanics suitable for current technology.


  Large-scale distributions of hot-gas temperature and Fe abundance in the
Perseus cluster have been studied with multi-pointing observations by the GIS
instrument on ASCA. Within a radius of 20' from the cluster center, the energy
spectra requires two temperature components, in which the cool component
indicates kT ~ 2 keV and the hot-component temperature shows a significant
decline from about 8 keV to 6 keV toward the center. In the outer region of the
cluster, the temperature shows a fluctuation with an amplitude of about 2 keV
and suggest that a western region at ~16' from the cluster center is relatively
hotter. As for the Fe abundance, a significant decline with radius is detected
from 0.44 solar at the center to ~0.1 solar at a 50' offset region. If observed
Fe-K line intensity within 4' from the center is suppressed by a factor of 2
due to the resonance scattering effect, the corrected Fe mass density follows
the galaxy distribution. Finally, our results do not support the large-scale
velocity gradients previously reported from the same GIS data.


  In contrast to the optomechanically induced transparency (OMIT) defined
conventionally, the inverse OMIT behaves as coherent absorption of the input
lights in the optomechanical systems. We characterize a feasible inverse OMIT
in a multi-channel fashion with a double-sided optomechanical cavity system
coupled to a nearby charged nanomechanical resonator via Coulomb interaction,
where two counter-propagating probe lights can be absorbed via one of the
channels or even via three channels simultaneously with the assistance of a
strong pump light. Under realistic conditions, we demonstrate the experimental
feasibility of our model using two slightly different nanomechanical resonators
and the possibility of detecting the energy dissipation of the system. In
particular, we find that our model turns to be an unilateral inverse OMIT once
the two probe lights are different with a relative phase, and in this case we
show the possibility to measure the relative phase precisely.


  In this paper we first discuss the analysis regarding the role of Lorentz
symmetry in the perturbative non-gravitational anomalies for a family of
fermions, which has been recently performed in arXiv:0809.0184. The theory is
assumed to be translational invariant, power-counting renormalizable and based
on a local action, but is allowed to have general Lorentz violating operators,
including those that break CPT. The main result is that Lorentz symmetry does
not participate in the clash of symmetries that leads to the anomalies.
Moreover, here we provide a simple "semiclassical" argument that shortly
illustrates the origin of this fact.


  We compare two widespread formulations of the mean-field approximation, based
on minimizing an appropriately built mean-field free energy. We use the example
of the antiferromagnetic Ising model to show that one of these formulations
does not guarantee the existence of an underlying variational principle. This
results in a severe failure where straightforward minimization of the
corresponding mean-field free energy leads to incorrect results.


  With the black hole mass function (BHMF; assuming an exponential cutoff at a
mass of $\sim 40\,M_\odot$) of coalescing binary black hole systems constructed
with the events detected in the O1 run of the advanced LIGO/Virgo network,
Liang et al.(2017) predicted that the birth of the lightest intermediate mass
black holes (LIMBHs; with a final mass of $\gtrsim 100\,M_\odot$) is very
likely to be caught by the advanced LIGO/Virgo detectors in their O3 run. The
O1 and O2 observation run data, however, strongly favor a cutoff of the BHMF
much sharper than the exponential one. In this work we show that a power-law
function followed by a sudden drop at $\sim 40\,M_\odot$ by a factor of $\sim
$a few tens and then a new power-law component extending to $\geq 100M_\odot$
are consistent with the O1 and O2 observation run data. With this new BHMF,
quite a few LIMBH events can be detected in the O3 observation run of advanced
LIGO/Virgo. The first LIMBH born in GW190521, an event detected in the early
stage of the O3 run of advanced LIGO/Virgo network, provides additional
motivation for our hypothesis.


  As it has become common to use many computer cores in routine applications,
finding good ways to parallelize popular algorithms has become increasingly
important. In this paper, we present a parallelization scheme for Markov chain
Monte Carlo (MCMC) methods based on spectral clustering of the underlying state
space, generalizing earlier work on parallelization of MCMC methods by state
space partitioning. We show empirically that this approach speeds up MCMC
sampling for multimodal distributions and that it can be usefully applied in
greater generality than several related algorithms. Our algorithm converges
under reasonable conditions to an `optimal' MCMC algorithm. We also show that
our approach can be asymptotically far more efficient than naive
parallelization, even in situations such as completely flat target
distributions where no unique optimal algorithm exists. Finally, we combine
theoretical and empirical bounds to provide practical guidance on the choice of
tuning parameters.


  The normal form and zero dynamics are powerful tools useful in analysis and
control of both linear and nonlinear systems. There are no simple closed form
solutions to the general zero dynamics problem for nonlinear systems. A few
algorithms exist for determining the zero dynamics, but none is straightforward
and all are difficult to apply to large dimensional problems. A Closed form
solution to the zero dynamics problem would motivate more usage of this
powerful technique. The author presents here a simple algebraic methodology for
the normal form and zero dynamics calculation of a class of nonlinear systems,
mostly found in dynamical mechanical systems. The solution is in closed form so
that application of the theorem presented is straight forward. As an
illustration, the zero dynamics calculations for the complex dynamics of a
flexible spacecraft is presented to demonstrate the simplicity and usefulness
of the proposed closed form solution.
  Keywords: Control, Differential Geometry, Normal Form, Zero Dynamics,
Nonlinear Systems, Feedback Linearization, Attitude Dynamics, Flexible
Spacecraft.


  Recently, discrepancies of up to $4\,\sigma$ between the different
determinations of the Cabibbo angle were observed. This "Cabibbo-angle anomaly"
could be explained by lepton flavour universality (LFU) violating New Physics
(NP) in the neutrino sector. However, modified neutrino couplings to Standard
Model gauge bosons also affect many other observables sensitive to LFU
violation which have to be taken into account in order to assess the viability
of this explanation. Therefore, we perform a model-independent global analysis
in a Bayesian approach and find that the tension in the Cabibbo angle is
significantly reduced, while the agreement with other data is also mostly
improved. In fact, non-zero modifications of electron and muon neutrino
couplings are preferred at more than 99\% CL. Still, since constructive effects
in the muon sector are necessary, simple models with right-handed neutrinos
(whose global fit we update as a by-product) cannot fully explain data,
pointing towards more sophisticated NP models.


  Finite W-algebras are certain associative algebras arising in Lie theory.
Each W-algebra is constructed from a pair of a semisimple Lie algebra g (our
base field is algebraically closed and of characteristic 0) and its nilpotent
element e. In this paper we classify finite dimensional irreducible modules
with integral central character over W-algebras. In more detail, in a previous
paper the first author proved that the component group A(e) of the centralizer
of the nilpotent element under consideration acts on the set of finite
dimensional irreducible modules over the W-algebra and the quotient set is
naturally identified with the set of primitive ideals in U(g) whose associated
variety is the closure of the adjoint orbit of e. In this paper for a given
primitive ideal with integral central character we compute the corresponding
A(e)-orbit. The answer is that the stabilizer of that orbit is basically a
subgroup of A(e) introduced by G. Lusztig. In the proof we use a variety of
different ingredients: the structure theory of primitive ideals and
Harish-Chandra bimodules of semisimple Lie algebras, the representation theory
of W-algebras, the structure theory of cells and Springer representations, and
multi-fusion monoidal categories.


  We show a parallel repetition theorem for the entangled value $\omega^*(G)$
of any two-player one-round game $G$ where the questions $(x,y) \in
\mathcal{X}\times\mathcal{Y}$ to Alice and Bob are drawn from a product
distribution on $\mathcal{X}\times\mathcal{Y}$. We show that for the $k$-fold
product $G^k$ of the game $G$ (which represents the game $G$ played in parallel
$k$ times independently),
  $ \omega^*(G^k)
=\left(1-(1-\omega^*(G))^3\right)^{\Omega\left(\frac{k}{\log(|\mathcal{A}|
\cdot |\mathcal{B}|)}\right)} $, where $\mathcal{A}$ and $\mathcal{B}$
represent the sets from which the answers of Alice and Bob are drawn.


  We present a new method for treating the inner Cauchy boundary of a black
hole spacetime by matching to a characteristic evolution. We discuss the
advantages and disadvantages of such a scheme relative to Cauchy-only
approaches. A prototype code, for the spherically symmetric collapse of a
self-gravitating scalar field, shows that matching performs at least as well as
other approaches to handling the inner boundary.


  Electrical transfer from a room temperature power source to a superconducting
system is done via conventional or superconducting current leads and
superconducting buses or links. The principles of optimization of these devices
are presented, with emphasis on the cryogenic, electrical, and superconductor
related aspects that drive choices for a system.


  We characterize the dissipative phase transition in a driven dissipative
Bose-Einstein condensate of neutral atoms. Our results generalize the work on
dissipative nonlinear Kerr resonators towards many modes and stronger
interactions. We measure the effective Liouvillian gap and analyze the
microscopic system dynamics, where we identify a non-equilibrium condensation
process.


  Knowledge graphs have been demonstrated to be an effective tool for numerous
intelligent applications. However, a large amount of valuable knowledge still
exists implicitly in the knowledge graphs. To enrich the existing knowledge
graphs, recent years witness that many algorithms for link prediction and
knowledge graphs embedding have been designed to infer new facts. But most of
these studies focus on the static knowledge graphs and ignore the temporal
information that reflects the validity of knowledge. Developing the model for
temporal knowledge graphs completion is an increasingly important task. In this
paper, we build a new tensor decomposition model for temporal knowledge graphs
completion inspired by the Tucker decomposition of order 4 tensor. We
demonstrate that the proposed model is fully expressive and report
state-of-the-art results for several public benchmarks. Additionally, we
present several regularization schemes to improve the strategy and study their
impact on the proposed model. Experimental studies on three temporal datasets
(i.e. ICEWS2014, ICEWS2005-15, GDELT) justify our design and demonstrate that
our model outperforms baselines with an explicit margin on link prediction
task.


  We consider quadratic Weyl sums $S_N(x;\alpha,\beta)=\sum_{n=1}^N
\exp\!\left[2\pi i\left( \left(\tfrac{1}{2}n^2+\beta n\right)\!x+\alpha
n\right)\right]$ for $(\alpha,\beta)\in\mathbb{Q}^2$, where $x\in\mathbb{R}$ is
randomly distributed according to a probability measure absolutely continuous
with respect to the Lebesgue measure. We prove that the limiting distribution
in the complex plane of $\frac{1}{\sqrt{N}}S_N(x;\alpha,\beta)$ as $N\to\infty$
is either heavy tailed or compactly supported, depending solely on
$\alpha,\beta$. In the heavy tailed case, the probability (according to the
limiting distribution) of landing outside a ball of radius $R$ is shown to be
asymptotic to $\mathcal{T}(\alpha,\beta)R^{-4}$, where the constant
$\mathcal{T}(\alpha,\beta)>0$ is explicit. The result follows from an analogous
statement for products of generalized quadratic Weyl sums of the form
$S_N^f(x;\alpha,\beta)=\sum_{n\in\mathbb{Z}}
f\left(\frac{n}{N}\right)\exp\!\left[2\pi i\left( \left(\tfrac{1}{2}n^2+\beta
n\right)\!x+\alpha n\right)\right]$ where $f$ is regular. The precise tails of
the limiting distribution of
$\frac{1}{N}S_N^{f_1}\bar{S_N^{f_2}}(x;\alpha,\beta)$ as $N\to\infty$ can be
described in terms of a measure -- which depends on $(\alpha,\beta)$ -- of a
super level set of a product of two Jacobi theta functions on a noncompact
homogenous space. Such measures are obtained by means of an equidistribution
theorem for rational horocycle lifts to a torus bundle over the unit tangent
bundle to a cover of the classical modular surface. The cardinality and the
geometry of orbits of rational points of the torus under the affine action of
the theta group play a crucial role in the computation of
$\mathcal{T}(\alpha,\beta)$. This paper complements and extends the works of
Cellarosi and Marklof [6] and Marklof [32], where
$(\alpha,\beta)\notin\mathbb{Q}^2$ and $\alpha=\beta=0$ are considered.


  We demonstrate a quantum random number generator based on the random nature
of the phase difference between two independent laser sources. The speed of
random bit generation is determined by the photodetector bandwidth and the
linewidth of the lasers used. The system implemented is robust and generates a
probability distribution of quantum origin which is intrinsically uniform and
thus in principle needs no randomness extraction. The phase is measured with
telecom equipment routinely used for high capacity coherent optical
communications, which allows to keep track of the phase drift of the lasers and
is readily available in the telecommunication industry.


  The functional form of Coulomb interactions in the transition metal
dichalcogenides and other van der Waals solids is critical to many of their
unique properties, e.g. strongly-correlated electron states, superconductivity
and emergent ferromagnetism. This paper presents measurements of key excitonic
energy levels in MoSe2/WSe2 heterostructures. These measurements are obtained
from resonance Raman experiments on specific Raman peaks only observed at
excited states of the excitons. This data is used to validate a model of the
Coulomb potential in these structures which predicts the exciton energies to
within ~5 meV / 2.5%. This model is used to determine the effect of
heterostructure formation on the single-particle band gaps of the layers and
will have a wide applicability in designing the next generation of more complex
transition metal dichalcogenide structures.


  We present results of a study of intermittency and multifractality of
magnetic structures in solar active regions (ARs). Line-of-sight magnetograms
for 214 ARs of different flare productivity observed at the center of the solar
disk from January 1997 until December 2006 are utilized. Data from the
Michelson Doppler Imager (MDI) instrument on-board the {\it Solar and
Heliospheric Observatory} (SOHO) operating in the high resolution mode, the Big
Bear Solar Observatory digital magnetograph and {\it Hinode} SOT/SP instrument
were used. Intermittency spectra were derived via high-order structure
functions and flatness functions. The flatness function exponent is a measure
of the degree of intermittency. We found that the flatness function exponent at
scales below approximately 10 Mm is correlated to the flare productivity (the
correlation coefficient is - 0.63). {\it Hinode} data show that the
intermittency regime is extended toward the small scales (below 2 Mm) as
compared to the MDI data. The spectra of multifractality, derived from the
structure functions and flatness functions, are found to be more broad for ARs
of highest flare productivity as compared to that of low flare productivity.
The magnetic structure of high-flaring ARs consists of a voluminous set of
monofractals, and this set is much richer than that for low-flaring ARs. The
results indicate relevance of the multifractal organization of the photospheric
magnetic fields to the flaring activity. Strong intermittency observed in
complex and high-flaring ARs is a hint that we observe a photospheric imprint
of enhanced sub-photospheric dynamics.


  In 2011 the Nobel Prize in Physics was awarded for the 1998 discovery of the
nonzero cosmological constant. This discovery is very important and surely
worth to receive the Nobel Prize. However, years earlier several papers had
been published (Paal, Horvath, & Lukacs 1992; Holba et al. 1992, Holba et al.
1994) about a very similar discovery from observational data.


  A set of bi-orthogonal potential-density basis functions is introduced to
model the density and its associated gravitational field of three dimensional
stellar systems. Radial components of our basis functions are weighted integral
forms of spherical Bessel functions. We discuss the properties of our basis
functions and demonstrate their shapes for the latitudinal Fourier number
$l=2$.


  This paper studies the problem of remote state estimation in the presence of
a passive eavesdropper. A sensor measures a linear plant's state and transmits
it to an authorized user over a packet-dropping channel, which is susceptible
to eavesdropping. Our goal is to design a coding scheme such that the
eavesdropper cannot infer the plant's current state, while the user
successfully decodes the sent messages. We employ a novel class of codes,
termed State-Secrecy Codes, which are fast and efficient for dynamical systems.
They apply linear time-varying transformations to the current and past states
received by the user. In this way, they force the eavesdropper's information
matrix to decrease with asymptotically the same rate as in the open-loop
prediction case, i.e. when the eavesdropper misses all messages. As a result,
the eavesdropper's minimum mean square error (mmse) for the unstable states
grows unbounded, while the respective error for the stable states converges to
the open-loop prediction one. These secrecy guarantees are achieved under
minimal conditions, which require that, at least once, the user receives the
corresponding packet while the eavesdropper fails to intercept it. Meanwhile,
the user's estimation performance remains optimal. The theoretical results are
illustrated in simulations.


  An extended study of exclusive vector meson production in e,p interactions
has been performed by the H1 and the ZEUS collaborations at the HERA collider.
Recent measurements are reported and discussed within the framework of the
dipole model and pQCD.


  Since FRB 200428 has been found to be associated with an X-ray burst from the
Galactic magnetar SGR J1935+2154, it is interesting to explore whether the
magnetar bursts also follow the similar active periodic behavior as some
repeating FRBs. Previous studies show that there is possible period about 230
day in SGR J1935+2154 bursts. Here, we collected an updated burst sample from
SGR J1935+2154, including all bursts reported by Fermi/GBM and GECAM till 2022
January. We also developed a targeted search pipeline to reveal more bursts
from SGR J1935+2154 in the Fermi/GBM data from 2008 August to 2014 December
(i.e. before the first burst detected by Swift/BAT). With this burst sample, we
re-analyzed the possible periodicity of SGR J1935+2154 bursts using the Period
Folding and Lomb-Scargle Periodogram methods. Our results show that the
periodicity $\sim$238 day reported in literature is probably fake and the
observation effects may introduce false periods (i.e. 55 day) according to
simulation tests. We find that, for the current burst sample, the most probable
period is 126.88$\pm$2.05 day, which could be interpreted as the precession of
the magnetar. However, we note that the whole burst history is very complicated
and difficult to be perfectly accommodated with any period reported thus far,
therefore more monitoring observations of SGR J1935+2154 are required to test
any periodicity hypothesis.


  The canonical-type connection on the almost contact manifolds with B-metric
is constructed. It is proved that its torsion is invariant with respect to a
subgroup of the general conformal transformations of the almost contact
B-metric structure. The basic classes of the considered manifolds are
characterized in terms of the torsion of the canonical-type connection.


  Open charm production at the initial and the pre-equilibrium stages in
nuclear collisions is studied. The pre-equilibrium contribution to open charm
production in $A+A$ collisions at $\sqrt s=200 AGeV$ is shown to be very
sensitive to correlations between momenta and space-time coordinates of the
minijets produced after the initial collision. A minimal correlation model
based on the uncertainty principle is introduced, and leads only to a small
pre-equilibrium charm yield as compared with initial yields. Opposite-sign
lepton pairs $ee, e\mu$ and $\mu\mu$ from open charm decay in $p+A$ reactions
at $\sqrt s=200$ AGeV are proposed as a measure of nuclear shadowing effects.
Via an approximate scaling, the ratio of the spectra from $p+A$ collisions to
those from $pp$ collisions is shown to reflect the shadowing function well.
Finally it is shown that the required measurements are feasible at RHIC.


  Anatomical consistency in biomarker segmentation is crucial for many medical
image analysis tasks. A promising paradigm for achieving anatomically
consistent segmentation via deep networks is incorporating pixel connectivity,
a basic concept in digital topology, to model inter-pixel relationships.
However, previous works on connectivity modeling have ignored the rich
channel-wise directional information in the latent space. In this work, we
demonstrate that effective disentanglement of directional sub-space from the
shared latent space can significantly enhance the feature representation in the
connectivity-based network. To this end, we propose a directional connectivity
modeling scheme for segmentation that decouples, tracks, and utilizes the
directional information across the network. Experiments on various public
medical image segmentation benchmarks show the effectiveness of our model as
compared to the state-of-the-art methods. Code is available at
https://github.com/Zyun-Y/DconnNet.


  Using the theory of exponential Riordan arrays and orthogonal polynomials, we
demonstrate that the "descending power" Eulerian polynomials, and their once
shifted sequence, are moment sequences for simple families of orthogonal
polynomials, which we characterize in terms of their three-term recurrence. We
obtain the generating functions of the polynomial sequences in terms of
continued fractions, and we also calculate their Hankel transforms.


  The donor in the microquasar GRS 1915+105 is a low-mass giant. Such a star
consists of a degenerate helium core and a hydrogen-rich envelope. Both
components are separated by a hydrogen burning shell. The structure of such an
object is relatively simple and easy to model. Making use of the observational
constraints on the luminosity and the radius of the donor, we constrain the
mass of this star with evolutionary models. We find a very good agreement
between the constraints from those models and from the observed rotational
broadening and the NIR magnitude. Combining the constraints, we find solutions
with stripped giants of the mass of $\geq\!0.28{\rm M}_{\odot}$ and of the
spectral class K5 III, independent of the distance to the system, and a
distance-dependent upper limit, $\lesssim\!1{\rm M}_{\odot}$. We also calculate
the average mass transfer rate and the duty cycle of the system as a function
of the donor mass. This rate is much below the critical rate (at which the
system would become persistent), and the duty cycle is less than 20 per cent.


  We present a new efficient method to compute Uehling-Uhlenbeck collision
integral for all two-particle interactions in relativistic plasma with drastic
improvement in computation time with respect to existing methods. Plasma is
assumed isotropic in momentum space. The set of reactions consists of: Moeller
and Bhabha scattering, Compton scattering, two-photon pair annihilation, and
two-photon pair production, which are described by QED matrix elements. In our
method exact energy and particle number conservation laws are satisfied.
Reaction rates are compared, where possible, with the corresponding analytical
expressions and convergence of numerical rates is demonstrated.


  Fe2O3 nanoparticles of different sizes ranging from 22 to 56nm were
synthesized chemically by a modified sol-gel method. Pure alpha phase particles
as well as particles with admixture of alpha and gamma phase were obtained and
identified by x-ray and M\"ossbauer measurements. Different size and phase
controlling parameters have been identified. The average size of the particles
decreases with increased annealing temperature of the gel and decreases with
the increase in the concentrations of the (citric acid). The annealing
temperature affects the relative fractions of the two phases and consequently
the magnetization of the particles. The magnetization of the particles (Ms) and
coercivity (Hc) increase consistently with the increase in the annealing
temperature. For the same relative amount of the two phases, the coercivity
(Hc) and the moment of the particles increase with the decrease in the size of
the particles, indicating the role of surface effects in the magnetic
behaviour.


  Hydrogen embrittlement can cause a dramatic deterioration of the mechanical
properties of high-strength metallic materials. Despite decades of experimental
and modelling studies, the exact underlying mechanisms behind hydrogen
embrittlement remain elusive. To unlock understanding of the mechanism and
thereby help mitigate the influence of hydrogen and the associated
embrittlement, it is essential to examine the interactions of hydrogen with
structural defects such as grain boundaries, dislocations and stacking faults.
Atom probe tomography (APT) can, in principle, analyse hydrogen located
specifically at such microstructural features but faces strong challenges when
it comes to charging specimens with hydrogen or deuterium. Here, we describe
three different workflows enabling hydrogen/deuterium charging of site-specific
APT specimens: namely cathodic, plasma and gas charging. We discuss in detail
the caveats of the different approaches in order to help with future research
efforts and facilitate further studies of hydrogen in metals. Our study
demonstrates successful cathodic and gas charging, with the latter being more
promising for the analysis of the high-strength steels at the core of our work.


  Internet of Things devices such as the Amazon Echo are undoubtedly great
sources of potential digital evidence due to their ubiquitous use and their
always on mode of operation, constituting a human life black box. The Amazon
Echo in particular plays a centric role for the cloud based intelligent virtual
assistant Alexa developed by Amazon Lab126. The Alexa enabled wireless smart
speaker is the gateway for all voice commands submitted to Alexa. Moreover, the
IVA interacts with a plethora of compatible IoT devices and third party
applications that leverage cloud resources. Understanding the complex cloud
ecosystem that allows ubiquitous use of Alexa is paramount on supporting
digital investigations when need raises. This paper discusses methods for
digital forensics pertaining to the IVA Alexa ecosystem. The primary
contribution of this paper consists of a new efficient approach of combining
cloud native forensics with client side forensics, to support practical digital
investigations. Based on a deep understanding of the targeted ecosystem, we
propose a proof of concept tool, CIFT, that supports identification,
acquisition and analysis of both native artifacts from the cloud and client
centric artifacts from local devices.


  This work shows that the following problems are equivalent, both in theory
and in practice:
  - median filtering: given an $n$-element vector, compute the sliding window
median with window size $k$,
  - piecewise sorting: given an $n$-element vector, divide it in $n/k$ blocks
of length $k$ and sort each block.
  By prior work, median filtering is known to be at least as hard as piecewise
sorting: with a single median filter operation we can sort $\Theta(n/k)$ blocks
of length $\Theta(k)$. The present work shows that median filtering is also as
easy as piecewise sorting: we can do median filtering with one piecewise
sorting operation and linear-time postprocessing. In particular, median
filtering can directly benefit from the vast literature on sorting
algorithms---for example, adaptive sorting algorithms imply adaptive median
filtering algorithms.
  The reduction is very efficient in practice---for random inputs the
performance of the new sorting-based algorithm is on a par with the fastest
heap-based algorithms, and for benign data distributions it typically
outperforms prior algorithms.
  The key technical idea is that we can represent the sliding window with a
pair of sorted doubly-linked lists: we delete items from one list and add items
to the other list. Deletions are easy; additions can be done efficiently if we
reverse the time twice: First we construct the full list and delete the items
in the reverse order. Then we undo each deletion with Knuth's dancing links
technique.


  We formulate a unifying framework for unsupervised continual learning (UCL),
which disentangles learning objectives that are specific to the present and the
past data, encompassing stability, plasticity, and cross-task consolidation.
The framework reveals that many existing UCL approaches overlook cross-task
consolidation and try to balance plasticity and stability in a shared embedding
space. This results in worse performance due to a lack of within-task data
diversity and reduced effectiveness in learning the current task. Our method,
Osiris, which explicitly optimizes all three objectives on separate embedding
spaces, achieves state-of-the-art performance on all benchmarks, including two
novel benchmarks proposed in this paper featuring semantically structured task
sequences. Compared to standard benchmarks, these two structured benchmarks
more closely resemble visual signals received by humans and animals when
navigating real-world environments. Finally, we show some preliminary evidence
that continual models can benefit from such realistic learning scenarios.


  We study the combinatorial properties of a tropical hyperplane arrangement.
We define tropical oriented matroids, and prove that they share many of the
properties of ordinary oriented matroids. We show that a tropical oriented
matroid determines a subdivision of a product of two simplices, and conjecture
that this correspondence is a bijection.


  Let G be an infinitesimal group scheme over a field k of positive
characteristic p. We introduce the global p-nilpotent operator $\Theta_G: k[G]
\to k[V(G)]$, where V(G) is the scheme which represents 1-parameter subgroups
of G. This operator applied to M encodes the local Jordan type of M, and leads
to computational insights into the representation theory of G. For certain
G-modules (including those of constant Jordan type), we employ the global
p-nilpotent operator to associate various algebraic vector bundles on the
projective scheme $\bP(G)$, the projectivization of the scheme of one-parameter
subgroups of G. These vector bundles not only distinguish certain
representations with the same local Jordan type, but also provide a method of
constructing algebraic vector bundles on $\bP(G)$.


  We present a detailed analysis of the usefulness of ultracold atomic
collisions for sensing the strength of an external magnetic field as well as
its spatial gradient. The core idea of the sensor, which we recently proposed
in K. Jachymski \emph{et al.}, Phys. Rev. Lett. {\bf 120}, 013401 (2018), is to
probe the transmission of the atoms through a set of quasi-one-dimensional
waveguides that contain an impurity. Magnetic field-dependent interactions
between the incoming atoms and the impurity naturally lead to narrow resonances
that can act as sensitive field probes since they strongly affect the
transmission. We illustrate our findings with concrete examples of experimental
relevance, demonstrating that a sensitivity of the order of 1 nT for the field
strength and $100\,\mathrm{nT}/\mathrm{mm}$ for the gradient can be reached
using our scheme.


  Advances in satellite imaging and GPS tracking devices have given rise to a
new era of remote sensing and geospatial analysis. In environmental science and
conservation ecology, biotelemetric data is often high-dimensional, spatially
and/or temporally, and functional in nature, meaning that there is an
underlying continuity to the biological process of interest. GPS-tracking of
animal movement is commonly characterized by irregular time-recording of animal
position, and the movement relationships between animals are prone to sudden
change. In this paper, I propose a measure of localized mutual information
(LMI) to derive a correlation function for monitoring changes in the pairwise
association between animal movement trajectories. The properties of the LMI
measure are assessed analytically and by simulation under a variety of
circumstances. Advantages and disadvantages of the LMI measure are assessed and
an alternate measure of LMI is proposed to handle potential disadvantages. The
measure of LMI is shown to be an effective tool for detecting shifts in the
correlation of animal movements, and seasonal/phasal correlatory structure.


  We present the theory, the experimental evidence, and fundamental physical
consequences concerning the existence of families of undistorted progressive
waves (UPWs) of arbitrary speeds $0\leq v < \infty$, which are solutions of the
homogeneous wave equation, Maxwell equations, and Dirac and Weyl equations.


  We present a study of eclipsing binary J064726.39+223431.6 using spectra from
the LAMOST-MRS and TESS photometry. We use full-spectrum fitting to derive
radial velocities and spectral parameters: ${T_{\rm eff}}_{A,B}=6177,\,5820$ K,
$v \sin{i}_{A,B}=59,\,50~\kms$ and ${\rm [Fe/H]}_{A,B}=-0.19$ dex. The orbital
solution and light curve analysis suggest that it is a close pair of fast
rotating stars on circular orbit. We measure their masses to be
$M_{A,B}=1.307\pm0.007,\, 1.129\pm0.005\,M_\odot$ and their radii to be
$R_{A,B}=1.405\pm0.052,\, 1.219\pm0.060\,R_\odot$ resulting in surface
gravities of $\log{g}_{A,B}=4.259\pm0.033,\,4.319\pm0.042$ (cgs). Theoretical
models cannot match all of these properties, predicting significantly higher
${T_{\rm eff}}$ for a given metallicity. Derived age of the system 1.56 Gyr
indicates that both components are younger than Sun, which contradicts to much
longer orbit's circularisation timescale.


  We develop an approach to utilize anisotropic metamaterials to solve one of
the fundamental problems of modern plasmonics -- parasitic scattering of
surface waves into free-space modes, opening the road to truly two-dimensional
plasmonic optics. We illustrate the developed formalism on examples of
plasmonic refractor and plasmonic crystal, and discuss limitations of the
developed technique and its possible applications for sensing and imaging
structures, high-performance mode couplers, optical cloaking structures, and
dynamically reconfigurable electro-plasmonic circuits.


  We exactly calculate the thermal distribution and temperature of Hawking
radiation for a two-dimensional charged dilatonic black hole after it has
settled down to an "equilibrium" state. The calculation is carried out using
the Bogoliubov coefficients. The background of the process is furnished by a
preexisting black hole and not by collapsing matter as considered by Giddings
and Nelson for the case of a Schwarzschild black hole. Furthermore, the
vanishing of the temperature and/or the Hawking radiation in the extremal case
is obtained as a regular limit of the general case.


  We present the first analytic scheme-independent series calculations of
anomalous dimensions of several types of baryon operators at an infrared fixed
point (IRFP) in an asymptotically free SU(3) gauge theory with $N_f$ fermions.
Separately, for an asymptotically free gauge theory with a gauge group $G$ and
$N_f$ fermions in a representation $R$ of $G$, we consider physical quantities
at an IRFP, including the anomalous dimension of gauge-invariant fermion
bilinears and the derivative of the beta function. These quantities have been
calculated in series expansions whose coefficients have been proved to be
scheme-independent at each order. We illustrate the scheme independence using a
variety of schemes, including the RI$^\prime$ scheme and several types of
momentum subtraction (MOM) schemes.


  This paper explores the assumption that Large Language Models (LLMs) skilled
in generation tasks are equally adept as evaluators. We assess the performance
of three LLMs and one open-source LM in Question-Answering (QA) and evaluation
tasks using the TriviaQA (Joshi et al., 2017) dataset. Results indicate a
significant disparity, with LLMs exhibiting lower performance in evaluation
tasks compared to generation tasks. Intriguingly, we discover instances of
unfaithful evaluation where models accurately evaluate answers in areas where
they lack competence, underscoring the need to examine the faithfulness and
trustworthiness of LLMs as evaluators. This study contributes to the
understanding of "the Generative AI Paradox" (West et al., 2023), highlighting
a need to explore the correlation between generative excellence and evaluation
proficiency, and the necessity to scrutinize the faithfulness aspect in model
evaluations.


  In this paper, we propose a generalization of Continuous Logic ([BBHU08])
where the distances take values in suitable co-quantales (in the way as it was
proposed in [Fla97]). By assuming suitable conditions (e.g., being
co-divisible, co-Girard and a V-domain), we provide, as test questions, a proof
of a version of the Tarski-Vaught test (Proposition 4.2) and {\L}o\'s Theorem
(Theorem 5.27) in our setting. Iovino proved in [Iov01] that there is no any
logic extending (equivalent logics to) Continuous Logic satisfying both
Countable Tarski-Vaught chain Theorem and Compactness Theorem. Since [0, 1]
satisfies all of the assumptions given above, we get new logics by dropping any
of those assumptions.


  We analyze the symmetry and the nodal structure of the superconducting order
parameter in a cubic ferromagnet, such as ZrZn$_2$. We demonstrate how the
order parameter symmetry evolves when the electromagnetic interaction of the
conduction electrons with the internal magnetic induction and the spin-orbit
coupling are taken into account. These interactions break the cubic symmetry
and lift the degeneracy of the order parameter. It is shown that the order
parameter which appears immediately below the critical temperature has two
components, and its symmetry is described by {\em co-representations} of the
magnetic point groups. This allows us to make predictions about the location of
the gap nodes.


  Performing exact Bayesian inference for complex models is computationally
intractable. Markov chain Monte Carlo (MCMC) algorithms can provide reliable
approximations of the posterior distribution but are expensive for large
datasets and high-dimensional models. A standard approach to mitigate this
complexity consists in using subsampling techniques or distributing the data
across a cluster. However, these approaches are typically unreliable in
high-dimensional scenarios. We focus here on a recent alternative class of MCMC
schemes exploiting a splitting strategy akin to the one used by the celebrated
alternating direction of multipliers (ADMM) optimization algorithm. These
methods appear to provide empirically state-of-the-art performance but their
theoretical behavior in high dimension is currently unknown. In this paper, we
propose a detailed theoretical study of one of these algorithms known as the
split Gibbs sampler. Under regularity conditions, we establish explicit
convergence rates for this scheme using Ricci curvature and coupling ideas. We
support our theory with numerical illustrations.


  We extensively study the growing behavior of the energy and the pressure
components depending on the space-time rapidity in the framework of the Glasma,
which describes the early-time dynamics in the ultra-relativistic heavy-ion
collisions. We simulate the Glasma solving the classical equations of motion in
the SU(2) Yang-Mills theory and systematically investigate the dependence of
the Glasma instability on the model parameters. We have checked that the
transverse and longitudinal grid sizes in our simulation are large enough to
handle cutoff effects under control. By comparing the numerical results from
several initial conditions with different magnitudes of instability seed and
also those with different wave-numbers for rapidity fluctuations, we clearly
see that unstable modes dominantly grow up in the linear regime and we also
confirm non-linear effects in the time evolution. To extract more detailed
information on the evolving Glasma, we decompose the energy into the components
in terms of rapidity wave-numbers. We observe an energy flow from low
wave-number modes into higher wave-number modes due to non-linearity in the
equations of motion. We find that the energy spectrum approaches an asymptotic
scaling that is consistent with Kolmogorov's power-law form even in the
expanding system of the Glasma.


  We inserted non-magnetic layers of Au and Cu into sputtered AlOx-based
magnetic tunnel junctions and Meservey-Tedrow junctions in order to study their
effect on tunnelling magnetoresistance (TMR) and spin polarization (TSP). When
either Au or Cu are inserted into a Co/AlOx interface, we find that TMR and TSP
remain finite and measurable for thicknesses up to several nanometres.
High-resolution transmission electron microscopy shows that the Cu and Au
interface layers are fully continuous when their thickness exceeds ~3 nm,
implying that spin-polarized carriers penetrate the interface noble metal to
dis- tances exceeding this value. A power law model based on exchange
scattering is found to fit the data better than a phenomenological exponential
decay. The discrepancy between these length scales and the much shorter ones
reported from x-ray magnetic circular dichroism studies of magnetic
proximitization is ascribed to the fact that our tunnelling transport
measurements selectively probe s-like electrons close to the Fermi level. When
a 0.1 nm thick Cu or Au layer is inserted within the Co, we find that the
suppression of TMR and TSP is restored on a length scale of <=1 nm, indicating
that this is a sufficient quantity of Co to form a fully spin-polarized band
structure at the interface with the tunnel barrier.