  The quest for practical cryptographic primitives that are robust against
quantum computers is of vital importance for the field of cryptography. Among
the abundance of different cryptographic primitives one may consider, one-way
functions stand out as fundamental building blocks of more complex
cryptographic protocols, and they play a central role in modern asymmetric
cryptography. We propose a mathematical one-way function, which relies on
coarse-grained boson sampling. The evaluation and the inversion of the function
are discussed in the context of classical and quantum computers. The present
results suggest that the scope and power of boson sampling may go beyond the
proof of quantum supremacy, and pave the way towards cryptographic
applications.


  A novel, particle based, probabilistic approach for the simulation of cloud
microphysics is proposed, which is named the Super-Droplet Method (SDM). This
method enables accurate simulation of cloud microphysics with less demanding
cost in computation. SDM is applied to a warm-cloud system, which incorporates
sedimentation, condensation/evaporation, and stochastic coalescence. The
methodology to couple super-droplets and a non-hydrostatic model is also
developed. It is confirmed that the result of our Monte Carlo scheme for the
stochastic coalescence of super-droplets agrees fairly well with the solutions
of the stochastic coalescence equation. The behavior of the model is evaluated
using a simple test problem, that of a shallow maritime cumulus formation
initiated by a warm bubble. Possible extensions of SDM are briefly discussed. A
theoretical analysis suggests that the computational cost of SDM becomes lower
than the spectral (bin) method when the number of attributes - the variables
that identify the state of each super-droplet - becomes larger than some
critical value, which we estimate to be in the range $2\sim4$.


  I have recently shown that it is possible to formulate the Relativity
postulates in a way that does not lead to inconsistencies in the case of
space-times whose structure is governed by observer-independent scales of both
velocity and length. Here I give an update on the status of this proposal,
including a brief review of some very recent developments. I also emphasize the
role that one of the kappa-Poincare' Hopf algebras could play in the
realization of a particular example of the new type of postulates. I show that
the new ideas on Relativity require us to extend the set of tools provided by
kappa-Poincare' and to revise our understanding of certain already available
tools, such as the energy-momentum coproduct.


  Massive multiple-input multiple-output (MIMO) is a key technology for 5G
wireless communications with a promise of significant capacity increase. The
use of low-resolution data converters is crucial for massive MIMO to make the
overall transmission as cost- and energy-efficient as possible. In this work,
we consider a downlink millimeter-wave (mmWave) transmission scenario, where
multiple users are served simultaneously by massive MIMO with one-bit
digital-to-analog (D/A) converters. In particular, we propose a novel precoder
design based on signal-to-leakage-plus-noise ratio (SLNR), which minimizes
energy leakage into undesired users while taking into account impairments due
to nonlinear one-bit quantization. We show that well-known regularized
zero-forcing (RZF) precoder is a particular version of the proposed SLNR-based
precoder, which is obtained when quantization impairments are totally ignored.
Numerical results underscore significant performance improvements along with
the proposed SLNR-based precoder as compared to either RZF or zero-forcing (ZF)
precoders.


  In this article, we study the quantum field theoretic generalization of the
Caldeira-Leggett model in general curved space-time considering interactions
between two scalar fields in a classical gravitational background. The
thermalization phenomena is then studied from the obtained de Sitter solution
using quantum quench from one scalar field model obtained from path integrated
effective action. We consider an instantaneous quench in the time-dependent
mass protocol of the field of our interest. We find that the dynamics of the
field post-quench can be described in terms of the state of the generalized
Calabrese-Cardy (gCC) form and computed the different types of two-point
correlation functions in this context. We explicitly found the conserved
charges of $W_{\infty}$ algebra that represents the gCC state after a quench in
de Sitter space and found it to be significantly different from the flat
space-time results. We extend our study for the different two-point correlation
functions not only considering the pre-quench state as the ground state, but
also a squeezed state. We found that irrespective of the pre-quench state, the
post quench state can be written in terms of the gCC state showing that the
subsystem of our interest thermalizes in de Sitter space. Furthermore, we
provide a general expression for the two-point correlators and explicitly show
the thermalization process by considering a thermal Generalized Gibbs ensemble
(GGE). Finally, from the equal time momentum dependent counterpart of the
obtained results for the two-point correlators, we have studied the hidden
features of the power spectra and studied its consequences for different
choices of the quantum initial conditions.


  The spacelike reduction of the Chern-Simons Lagrangian yields a modified
Nonlinear Schr\"odinger Equation (jNLS) where in the non-linearity the particle
density is replaced by current. When the phase is linear in the position, this
latter is an ordinary NLS with time-dependent coefficients which admits
interesting solutions. Their arisal is explained by the conformal properties of
non-relativistic spacetime. Only the usual travelling soliton is consistent
with the jNLS, but the addition of a six-order potential converts it into an
integrable equation.


  We have performed an experiment demonstrating that loop
state-preparation-and-measurement (SPAM) tomography [C. Jackson and S. J. van
Enk, Phys. Rev. A 92, 042312 (2015)] is capable of detecting correlated errors
between the preparation and the measurement of a quantum system. Specifically,
we have prepared pure and mixed states of single qubits encoded in the
polarization of heralded individual photons. By performing measurements using
multiple state preparations and multiple measurement device settings we are
able to detect if there are any correlated errors between them, and are also
able to determine which state preparations are correlated with which
measurements. This is accomplished by going around a 'loop' in parameter space,
which allows us to check for self-consistency. No assumptions are made
concerning either the state preparations or the measurements, other than that
the dimensions of the states and the positive-operator-valued measures (POVM)
describing the detector are known. In cases where no correlations are found we
are able to perform quantum state tomography of the polarization qubits by
using knowledge of the detector POVMs, or quantum detector tomography by using
knowledge of the state preparations.


  We define and explore the classical counterpart of entanglement in complete
analogy with quantum mechanics. Using a basis independent measure of entropy in
the classical Hilbert space of densities that are propagated by the
Frobenius-Perron operator, we demonstrate that at short times the quantum and
classical entropies share identical power laws and qualitative behaviors.


  We propose collisionless damping of fast MHD waves as an important mechanism
for the heating and acceleration of winds from rotating stars. Stellar rotation
causes magnetic field lines anchored at the surface to form a spiral pattern
and magneto-rotational winds can be driven. If the structure is a magnetically
dominated, fast MHD waves generated at the surface can propagate almost
radially outward and cross the field lines. The propagating waves undergo
collisionless damping owing to interactions with particles surfing on magnetic
mirrors that are formed by the waves themselves. The damping is especially
effective where the angle between the wave propagation and the field lines
becomes moderately large ($\sim 20$ to $80^{\circ}$). The angle tends naturally
to increase into this range because the field in magneto-rotational winds
develops an increasingly large azimuthal component. The dissipation of the wave
energy produces heating and acceleration of the outflow. We show using
specified wind structures that this damping process can be important in both
solar-type stars and massive stars that have moderately large rotation rates.
This mechanism can play a role in coronae of young solar-type stars which are
rapidly rotating and show X-ray luminosities much larger than the sun. The
mechanism could also be important for producing the extended X-ray emitting
regions inferred to exist in massive stars of spectral type middle B and later.


  The duality relation between the electric and magnetic fields, in the
presence of an additional axion-like field, is considered. We derive the new
equations that describe the electrodynamics in this model, and we discuss the
implications for the conservation of the electric and magnetic four-currents
and for the propagation of waves.


  Petrosian magnitudes were designed to help with the difficult task of
determining a galaxy's total light. Although these magnitudes (taken here as
the flux within 2R_P, with the inverted Petrosian index 1/eta(R_P)=0.2) can
represent most of an object's flux, they do of course miss the light outside of
the Petrosian aperture (2R_P). The size of this flux deficit varies
monotonically with the shape of a galaxy's light-profile, i.e., its
concentration. In the case of a de Vaucouleurs R^{1/4} profile, the deficit is
0.20 mag; for an R^{1/8} profile this figure rises to 0.50 mag. Here we provide
a simple method for recovering total (Sersic) magnitudes from Petrosian
magnitudes using only the galaxy concentration (R_90/R_50 or R_80/R_20) within
the Petrosian aperture. The corrections hold to the extent that Sersic's model
provides a good description of a galaxy's luminosity profile. We show how the
concentration can also be used to convert Petrosian radii into effective
half-light radii, enabling a robust measure of the mean effective surface
brightness. Our technique is applied to the SDSS DR2 Petrosian parameters,
yielding good agreement with the total magnitudes, effective radii, and mean
effective surface brightnesses obtained from the NYU--VAGC Sersic R^{1/n} fits
by Blanton et al. (2005). Although the corrective procedure described here is
specifically applicable to the SDSS DR2 and DR3, it is generally applicable to
all imaging data where any Petrosian index and concentration can be
constructed.


  In this work, the Parareal algorithm is applied to evolution problems that
admit good low-rank approximations and for which the dynamical low-rank
approximation (DLRA) can be used as time stepper. Many discrete integrators for
DLRA have recently been proposed, based on splitting the projected vector field
or by applying projected Runge--Kutta methods. The cost and accuracy of these
methods are mostly governed by the rank chosen for the approximation. These
properties are used in a new method, called low-rank Parareal, in order to
obtain a time-parallel DLRA solver for evolution problems. The algorithm is
analyzed on affine linear problems and the results are illustrated numerically.


  Polar distortions in solids give rise to the well-known functionality of
switchable macroscopic polarisation in ferroelectrics and, when combined with
strong spin-orbit coupling, can mediate giant spin splittings of electronic
states. While typically found in insulators, ferroelectric-like distortions can
remain robust against increasing itineracy, giving rise to so-called "polar
metals". Here, we investigate the temperature-dependent electronic structure of
Ca$_3$Ru$_2$O$_7$, a correlated oxide metal in which octahedral tilts and
rotations combine to mediate pronounced polar distortions. Our angle-resolved
photoemission measurements reveal the destruction of a large hole-like Fermi
surface upon cooling through a coupled structural and spin-reorientation
transition at 48 K, accompanied by a sudden onset of quasiparticle coherence.
We demonstrate how these result from band hybridisation mediated by a hidden
Rashba-type spin-orbit coupling. This is enabled by the bulk structural
distortions and unlocked when the spin reorients perpendicular to the local
symmetry-breaking potential at the Ru sites. We argue that the electronic
energy gain associated with the band hybridisation is actually the key driver
for the phase transition, reflecting a delicate interplay between spin-orbit
coupling and strong electronic correlations, and revealing a new route to
control magnetic ordering in solids.


  The electronics producing a few nanoseconds long LED pulses tuneable in the
amplitude and the optical system distributing the LED light to scintillators by
a single optical fibre are described. The properties of the LED pulses are
controlled by a computer connected via a CANbus to the controller on the board.
We produced a prototype with 6 LED pulse drivers placed on a 4-layer PCB with
dimension 250 x 147 mm2. The pulse width is constant and 3 ns long. Its
amplitude can be tuned from zero to 1.2 A. The pulse frequency can be set in
the range up to 100 kHz. The LED light is distributed by a 1 mm diameter
optical fibre. On the length of 2 m the fibre has every 30 mm a notch which
flashes light with homogeneity of \pm20%. The system is foreseen for
calibration of silicon photomultipliers embedded in scintillation tiles.


  Interfacial Dzyaloshinskii-Moriya interaction (iDMI) has been investigated in
Co2FeAl (CFA) ultrathin films of various thicknesses (0.8 nm<tCFA<2 nm) grown
on Si substrates, using Pt, W, Ir and MgO buffer or/and capping layers.
Vibrating sample magnetometry revealed that magnetization at saturation (Ms)
for the Pt and Ir buffered films is higher than the usual Ms of CFA due to the
proximity induced magnetization (PIM) in Ir and Pt, estimated to be 19% and
27%, respectively. The presence of PIM in these materials is confirmed using
x-ray resonant magnetic reflectivity. Moreover, while no PIM is induced in W,
higher PIM is obtained with Pt when it is used as buffer layer rather than
capping layer. Brillouin light scattering (BLS) in the Damon-Eshbach geometry
has been used to investigate iDMI constants and the perpendicular anisotropy
field versus the annealing temperature. The DMI sign has been found to be
negative for Pt/CFA and Ir/CFA while it is positive for W/CFA. The thickness
dependence of the effective iDMI constant for stacks involving Pt and W shows
the existence of two regimes similarly to that of the perpendicular anisotropy
constant due to the degradation of the interfaces as the CFA thickness
approaches the nanometer. The surface iDMI and anisotropy constants of each
stack have been determined for the thickest samples where a linear thickness
dependence of the effective iDMI constant and the effective magnetization has
been observed. The interface anisotropy and iDMI constants, investigated for
Pt/CFA/MgO system, showed different trends with the annealing temperature. The
decrease of iDMI constant with increasing annealing temperature is probably due
to the electronic structure changes at the interfaces, while the increase of
the interface anisotropy constant is coherent the interface quality and
disorder enhancement.


  We propose a new method to investigate signatures of a quantum gravity phase
in the primordial state of cosmological perturbations. We formulate and study a
quantum model of a perturbed Friedmann-Lemaitre-Robertson-Walker universe
beyond the conventional Born-Oppenheimer factorization, that is, without
restricting the wave function of the universe to the product of the background
and perturbation wave functions. We show that the quantum dynamics generically
does not preserve the product form of the universe's wave function, that
spontaneously evolves into a more general entangled state. Upon expanding this
state in a suitable basis of background wave functions and setting Gaussian
initial conditions for the perturbations, we numerically find that each of
these wave functions becomes associated to a non-Gaussian state of an
inhomogeneous perturbation.


  This paper focuses on safety critical control with sector-bounded
uncertainties at the plant input. The uncertainties can represent nonlinear
and/or time-varying components. We propose a new robust control barrier
function (RCBF) approach to enforce safety requirements in the presence of
these uncertainties. The primary objective is to minimally alter the given
baseline control command to guarantee safety in the presence of modeled
uncertainty. The resulting min-norm optimization problem can be recast as a
Second-Order Cone Program (SOCP) to enable online implementation. Properties of
this controller are studied and a numerical example is provided to illustrate
the effectiveness of this approach.


  The I-mode confinement regime can feature small edge temperature drops that
can lead to an increase in the energy deposited onto the divertor targets. In
this work, we show that these events are associated with a relaxation of both
electron temperature and density edge profiles, with the largest drop found at
the pedestal top position. Stability analysis of edge profiles reveals that the
operational points are far from the ideal peeling-ballooning boundary. Also, we
show that these events appear close to the H-mode transition in the typical
I-mode operational space in ASDEX Upgrade, and that no further enhancement of
energy confinement is found when they occur. Moreover, scrape-off layer
transport during these events is found to be very similar to type-I ELMs, with
regard to timescales ($\approx$ 800 $\mu$s), filament propagation, toroidally
asymmetric energy effluxes at the midplane and asymmetry between inner and
outer divertor deposited energy. In particular, the latter reveals that more
energy reaches the outer divertor target. Lastly, first measurements of the
divertor peak energy fluence are reported, and projections to ARC - a reactor
designed to operate in I-mode - are drawn.


  We present a study of triple Higgs boson (3H) production at the International
Linear Collider (ILC) within the general Two-Higgs-Doublet Model (2HDM). We
compute the production cross-sections at the leading-order for the 3H final
states and find values up to sigma ~ 0.1 pb. This result represents a large
enhancement with respect to the corresponding MSSM cross-sections, which stay
typically at the level of sigma ~ 10^(-6) pb or less. Furthermore, since the 3H
cross-sections in the general 2HDM can be of the order of the double Higgs
production cross-sections, such 3H processes could be a competitive (if not the
dominant) mechanism for Higgs boson production at the ILC. In practice, these
3H events could be identified through the tagging of 6 heavy-quark jet final
states and, in this case, they would provide strong evidence of an extended
Higgs boson sector -- likely of non-supersymmetric nature.


  Delineating the lesion area is an important task in image-based diagnosis.
Pixel-wise classification is a popular approach to segmenting the region of
interest. However, at fuzzy boundaries such methods usually result in glitches,
discontinuity, or disconnection, inconsistent with the fact that lesions are
solid and smooth. To overcome these undesirable artifacts, we propose the
BezierSeg model which outputs bezier curves encompassing the region of
interest. Directly modelling the contour with analytic equations ensures that
the segmentation is connected, continuous, and the boundary is smooth. In
addition, it offers sub-pixel accuracy. Without loss of accuracy, the bezier
contour can be resampled and overlaid with images of any resolution. Moreover,
a doctor can conveniently adjust the curve's control points to refine the
result. Our experiments show that the proposed method runs in real time and
achieves accuracy competitive with pixel-wise segmentation models.


  The nuclear response is evaluated in the frame of the bosonic loop expansion
in a purely nucleonic dynamical scheme, which seems to be reliable in handling
those channels where a direct excitation of a $\Delta$-resonance is not
allowed. It is shown that the response strongly depends upon the effective
interaction in the spin-transverse isovector channel. New experiments at CEBAF
on parity-violating electron scattering could further constrain the form of the
effective interaction.


  In this paper we study the Connes amenability of the second dual of Arens
regular Banach algebras. Of course we provide a partial answer to the question
posed by Volker Runde. Also we fined the necessary and sufficient conditions
for the second dual of an Arens regular module extension Banach algebra to be
Connes amenable when the module is reflexive.


  In the era of climate change, the distribution of climate variables evolves
with changes not limited to the mean value. Consequently, clustering algorithms
based on central tendency could produce misleading results when used to
summarize spatial and/or temporal patterns. We present a novel approach to
spatial clustering of time series based on quantiles using a Bayesian framework
that incorporates a spatial dependence layer based on a Markov random field. A
series of simulations tested the proposal, then applied to the sea surface
temperature of the Mediterranean Sea, one of the first seas to be affected by
the effects of climate change.


  We perform a search for neutrinos coincident with GRB 080319B, the brightest
GRB observed to date, in a +/- 1,000 s window. No statistically significant
coincidences were observed and we thereby obtain an upper limit on the fluence
of neutrino-induced muons from this source. From this we apply reasonable
assumptions to derive a limit on neutrino fluence from the GRB.


  The ATLAS collaboration (and also CMS) has recently reported an excess over
Standard Model expectations for gauge boson pair production in the invariant
mass region $1.8-2.2$ TeV. In the light of these results, we argue that such
signal might be the first manifestation of the production and further decay of
a heavy CP-even Higgs resulting from a type-I Two Higgs Doublet Model. We
demonstrate that in the presence of colored vector-like fermions, its gluon
fusion production cross-section is strongly enhanced, with the enhancement
depending on the color representation of the new fermion states. Our findings
show that barring the color triplet case, any QCD "exotic" representation can
fit the ATLAS result in fairly large portions of the parameter space. We have
found that if the diboson excess is confirmed and this mechanism is indeed
responsible for it, then the LHC Run-2 should find: (i) a CP-odd scalar with
mass below $\sim 2.3$ TeV, (ii) new colored states with masses below $\sim 2$
TeV, (iii) no statistically significant diboson events in the $W^\pm Z$
channel, (iv) events in the triboson channels $W^\pm W^\mp\,Z$ and $ZZZ$ with
invariant mass amounting to the mass of the CP-odd scalar.


  Hierarchical probabilistic models, such as mixture models, are used for
cluster analysis. These models have two types of variables: observable and
latent. In cluster analysis, the latent variable is estimated, and it is
expected that additional information will improve the accuracy of the
estimation of the latent variable. Many proposed learning methods are able to
use additional data; these include semi-supervised learning and transfer
learning. However, from a statistical point of view, a complex probabilistic
model that encompasses both the initial and additional data might be less
accurate due to having a higher-dimensional parameter. The present paper
presents a theoretical analysis of the accuracy of such a model and clarifies
which factor has the greatest effect on its accuracy, the advantages of
obtaining additional data, and the disadvantages of increasing the complexity.


  Recovering the polarized cosmic microwave background (CMB) is crucial for
shading light on Cosmic Inflation. Methods with different characteristics
should be developed and optimized. We aim to use a neural network called CENN
and train it for recovering the E and B modes of the CMB. We train the network
with realistic simulations of 256x256 pixel squared patches at 100, 143 and 217
GHz Planck channels, which contain the CMB, thermal dust, synchrotron, PS and
noise. We make several trainings sets: 30, 25 and 20 arcmin resolution patches
at the same position in the sky. After being trained, CENN is able to recover
the CMB signal at 143 GHz in Q and U patches. Then, we use NaMaster for
estimating the EE and BB power spectrum for each input and output patches in
the test dataset, as well as the difference between input and output power
spectra and the residuals. We also test the methodology using a different
foreground model at 5 arcmin resolution without noise. We recover the E-mode
generally founding residuals bellow the input signal at all scales. In
particular, we found a value of about 0.1 muK2 at l<200, decreasing below 0.01
muK2 at smaller scales. For the B-mode, we similarly recover the CMB with
residuals between 0.01 and 0.001 muK2. We also train the network with 5 arcmin
Planck simulations without noise, obtaining clearly better results with respect
the previous cases. For a different foreground model, the recovery is similar,
although B-mode residuals increase above the input signal. In general, we found
that, the network performs better when training with the same resolution used
for testing. Based on the results, CENN seems to be a promising for recovering
both E and B modes at sub-degree scales in ground-base experiments such as
POLARBEAR, SO and CMB-S4. Once extending its applicability at all sky, it could
be an alternative component separation method for LiteBIRD satellite.


  We extend the antenna subtraction method to include initial states containing
one hadron at NNLO. We present results for all the necessary subtraction terms,
antenna functions, for the master integrals required to integrate them over the
relevant phase space and finally for the integrated antennae themselves. Where
applicable, our results are cross-checked against the known NNLO coefficient
functions for deep inelastic scattering processes.


  We extend results of Andrews and Bressoud on the vanishing of coefficients in
the series expansions of certain infinite products. These results have the form
that if \begin{equation*} \frac{(q^{r-tk}, q^{mk-(r-tk)};
q^{mk})_\infty}{(q^r,q^{mk-r}; q^{mk})_\infty} =: \sum_{n=0}^\infty c_nq^n,
\end{equation*} for certain integers $k$, $m$ $s$ and $t$, where $r=sm+t$, then
$c_{kn-rs}$ is always zero. Our theorems also partly give a simpler
reformulation of results of Alladi and Gordon, but also give results for cases
not covered by the theorems of Alladi and Gordon. We also give some
interpretations of the analytic results in terms of integer partitions.


  We prove a version of the Lefschetz hyperplane theorem for fppf cohomology
with coefficients in any finite commutative group scheme over the ground field.
As consequences, we establish new Lefschetz results for the Picard scheme.


  We review the various aspects of the 3D Einstein gravity theory with a
negative cosmological constant and its boundary description. We also explore
its connections to CFTs, modular symmetry, and holography. It is worth noting
that this particular theory is topological in nature, which means that all the
physical degrees of freedom are located on the boundary. Additionally, we can
derive the boundary description on a torus, which takes the form of a 2D
Schwarzian theory. This observation suggests that the relevant degrees of
freedom for the theory can be described using this 2D theory. Because of the
renormalizability of the 3D gravity theory, one can probe the quantum regime.
This suggests that it is possible to investigate quantum phenomena. Unlike the
conventional CFTs, when considering the AdS$_3$ background, the boundary theory
loses modular symmetry. This represents a departure from the usual behavior of
CFT and is quite intriguing. The Weyl transformation induces anomaly in CFTs,
and we indicate that applying this transformation to the 2D Schwarzian theory
leads to similar results. Summing over all geometries with the asymptotic
AdS$_3$ boundary condition is equivalent to summing over a modular group. The
partition function is one-loop exact and therefore an analytical expression
from the summation. This theory holds potential applications in Quantum
Information and is a recurring theme in the study of holography, where
gravitational theories are connected with CFTs.


  Rule extraction from black-box models is critical in domains that require
model validation before implementation, as can be the case in credit scoring
and medical diagnosis. Though already a challenging problem in statistical
learning in general, the difficulty is even greater when highly non-linear,
recursive models, such as recurrent neural networks (RNNs), are fit to data.
Here, we study the extraction of rules from second-order recurrent neural
networks trained to recognize the Tomita grammars. We show that production
rules can be stably extracted from trained RNNs and that in certain cases the
rules outperform the trained RNNs.


  We discuss how to search for a possibe signal of the recently observed 750
GeV enhancement in the diphoton channel in the four-jet production. In the
present studies we assume that the produced state is pseudoscalar. This fact,
when combined with specificity of the corresponding amplitude, allows to
improve the signal-to-background (S/B) ratio. We discuss in detail how to
impose cuts on jets in rapidity and transverse momenta in order to find optimal
S/B ratio and not to loose too much statistics. Our study suggest a measurement
of two soft (low cut on $p_t$) large-rapidity jets and two hard (high cut on
$p_t$) mid-rapidity jets. Azimuthal correlation between the soft external jets
may be useful to further improve the situation. Several differential
distributions in rapidities and transverse momenta of jets as well as dijet
invariant mass are shown. The integrated cross sections corresponding to
different cuts are collected in a table and number of events are presented.


  Inspired by the fact that the matrix formulated by nonlocal similar patches
in a natural image is of low rank, the rank approximation issue have been
extensively investigated over the past decades, among which weighted nuclear
norm minimization (WNNM) and weighted Schatten $p$-norm minimization (WSNM) are
two prevailing methods have shown great superiority in various image
restoration (IR) problems. Due to the physical characteristic of color images,
color image restoration (CIR) is often a much more difficult task than its
grayscale image counterpart. However, when applied to CIR, the traditional
WNNM/WSNM method only processes three color channels individually and fails to
consider their cross-channel correlations. Very recently, a quaternion-based
WNNM approach (QWNNM) has been developed to mitigate this issue, which is
capable of representing the color image as a whole in the quaternion domain and
preserving the inherent correlation among the three color channels. Despite its
empirical success, unfortunately, the convergence behavior of QWNNM has not
been strictly studied yet. In this paper, on the one side, we extend the WSNM
into quaternion domain and correspondingly propose a novel quaternion-based
WSNM model (QWSNM) for tackling the CIR problems. Extensive experiments on two
representative CIR tasks, including color image denoising and deblurring,
demonstrate that the proposed QWSNM method performs favorably against many
state-of-the-art alternatives, in both quantitative and qualitative
evaluations. On the other side, more importantly, we preliminarily provide a
theoretical convergence analysis, that is, by modifying the quaternion
alternating direction method of multipliers (QADMM) through a simple
continuation strategy, we theoretically prove that both the solution sequences
generated by the QWNNM and QWSNM have fixed-point convergence guarantees.


  We show that, for any fixed genus $g$, the ordinary generating function for
the genus $g$ partitions of an $n$-element set into $k$ blocks is algebraic.
The proof involves showing that each such partition may be reduced in a unique
way to a primitive partition and that the number of primitive partitions of a
given genus is finite. We illustrate our method by finding the generating
function for genus $2$ partitions, after identifying all genus $2$ primitive
partitions, using a computer-assisted search.


  We have searched the 1st-year WMAP W-Band CMB anisotropy map for evidence of
cosmic strings. We have set a limit of $\delta = 8 \pi G \mu / c^2 < 8.2 \times
10^{-6}$ at 95% CL for statistical search for a significant number of strings
in the map. We also have set a limit using the uniform distribution of strings
model in the WMAP data with $\delta = 8 \pi G \mu / c^2 < 7.34 \times 10^{-5}$
at 95% CL. And the pattern search technique we developed here set a limit
$\delta = 8 \pi G \mu / c^2 < 1.54 \times 10^{-5}$ at 95% CL.


  We present an alternative but intuitive method of obtaining the true or
intrinsic quasar luminosity function through the observed one in the framework
of gravitational lensing. Such a so-called inversion of the magnification bias
can be straightforwardly performed by means of the Mellin transformation
instead of other complex methods. Application of our approach to the well-known
form of the observed quasar luminosity function identifies the previous results
in literature.


  An operational perspective is used to understand the relationship between
source and channel coding. This is based on a direct reduction of one problem
to another that uses random coding (and hence common randomness) but unlike all
prior work, does not involve any functional computations, in particular, no
mutual-information computations. This result is then used to prove a universal
source-channel separation theorem in the rate-distortion context where
universality is in the sense of a compound ``general channel.''


  In this paper, we present a determinist Jordan normal form algorithms based
on the Fadeev formula: \[(\lambda \cdot I-A) \cdot B(\lambda)=P(\lambda) \cdot
I\] where $B(\lambda)$ is $(\lambda \cdot I-A)$'s comatrix and $P(\lambda)$ is
$A$'s characteristic polynomial. This rational Jordan normal form algorithm
differs from usual algorithms since it is not based on the Frobenius/Smith
normal form but rather on the idea already remarked in Gantmacher that the
non-zero column vectors of $B(\lambda_0)$ are eigenvectors of $A$ associated to
$\lambda_0$ for any root $\lambda_0$ of the characteristical polynomial. The
complexity of the algorithm is $O(n^4)$ field operations if we know the
factorization of the characteristic polynomial (or $O(n^5 \ln(n))$ operations
for a matrix of integers of fixed size). This algorithm has been implemented
using the Maple and Giac/Xcas computer algebra systems.


  Extending the parameter space of the three-dimensional (d=3) Ising model, we
search for a regime of eliminated corrections to finite-size scaling. For that
purpose, we consider a real-space renormalization group (RSRG) with respect to
a couple of clusters simulated with the transfer-matrix (TM) method. Imposing a
criterion of "scale invariance," we determine a location of the non-trivial
RSRG fixed point. Subsequent large-scale TM simulation around the fixed point
reveals eliminated corrections to finite-size scaling. As anticipated, such an
elimination of corrections admits systematic finite-size-scaling analysis. We
obtained the estimates for the critical indices as nu=0.6245(28) and
y_h=2.4709(73). As demonstrated, with the aid of the preliminary RSRG survey,
the transfer-matrix simulation provides rather reliable information on
criticality even for d=3, where the tractable system size is restricted
severely.


  This paper investigates a multilevel inverter with a capability that produces
a wide voltage range with high quality. The selective harmonic elimination
(SHE) method is considered for a single-phase 5-level cascaded H-bridge (CHB)
inverter, in which the particle swarm optimization (PSO) algorithm solves the
nonlinear equations. However, eliminating the low-order harmonics has been
challenging when a low range of output voltage is required. To surmount such
challenges and access to a wide range of output voltage, an adjustable dc-link
is introduced that allows the inverter to increase the modulation index,
resulting in a significant decrease in total harmonic distortion (THD). In this
paper, to regulate the dc-link voltage amount, a 12-pulse rectifier is employed
to allow the inverter to produce the output voltage requirements with less
distortion. To prove such claims, the PSO algorithm is modified to calculate
the optimal angles, as a result, the switching angles are applied in SIMULINK
MATLAB to generate a 5-level output voltage.


  Variational quantum algorithms are believed to be promising for solving
computationally hard problems and are often comprised of repeated layers of
quantum gates. An example thereof is the quantum approximate optimization
algorithm (QAOA), an approach to solve combinatorial optimization problems on
noisy intermediate-scale quantum (NISQ) systems. Gaining computational power
from QAOA critically relies on the mitigation of errors during the execution of
the algorithm, which for coherence-limited operations is achievable by reducing
the gate count. Here, we demonstrate an improvement of up to a factor of 3 in
algorithmic performance as measured by the success probability, by implementing
a continuous hardware-efficient gate set using superconducting quantum
circuits. This gate set allows us to perform the phase separation step in QAOA
with a single physical gate for each pair of qubits instead of decomposing it
into two C$Z$-gates and single-qubit gates. With this reduced number of
physical gates, which scales with the number of layers employed in the
algorithm, we experimentally investigate the circuit-depth-dependent
performance of QAOA applied to exact-cover problem instances mapped onto three
and seven qubits, using up to a total of 399 operations and up to 9 layers. Our
results demonstrate that the use of continuous gate sets may be a key component
in extending the impact of near-term quantum computers.


  Recently, substantial amount of activity in Quantum General Relativity (QGR)
has focussed on the semiclassical analysis of the theory. In this paper we want
to comment on two such developments: 1) Polymer-like states for Maxwell theory
and linearized gravity constructed by Varadarajan which use much of the Hilbert
space machinery that has proved useful in QGR and 2) coherent states for QGR,
based on the general complexifier method, with built-in semiclassical
properties. We show the following: A) Varadarajan's states {\it are}
complexifier coherent states. This unifies all states constructed so far under
the general complexifier principle. B) Ashtekar and Lewandowski suggested a
non-Abelean generalization of Varadarajan's states to QGR which, however, are
no longer of the complexifier type. We construct a new class of non-Abelean
complexifiers which come close to the one underlying Varadarajan's
construction. C) Non-Abelean complexifiers close to Varadarajan's induce new
types of Hilbert spaces which do not support the operator algebra of QGR. The
analysis suggests that if one sticks to the present kinematical framework of
QGR and if kinematical coherent states are at all useful, then normalizable,
graph dependent states must be used which are produced by the complexifier
method as well. D) Present proposals for states with mildened graph dependence,
obtained by performing a graph average, do not approximate well coordinate
dependent observables. However, graph dependent states, whether averaged or
not, seem to be well suited for the semiclassical analysis of QGR with respect
to coordinate independent operators.


  Fractal grids generate turbulence by exciting many length scales of different
sizes simultaneously rather than using the nonlinear cascade mechanism to
obtain multi-scale structures, as it is the case for regular grids. The
interest in these grids has been further building up since the surprising
findings stemming from the experimental and computational studies conducted on
these grids. This work presents experimental wind tunnel and computational
fluid dynamics (CFD) studies of the turbulent flow generated by a space-filling
fractal square grid. The experimental work includes Particle Image Velocimetry
(PIV) and hot-wire measurements. In addition, Delayed Detached Eddy Simulations
(DDES) with a Spalart-Allmaras background turbulence model are conducted using
the open-source package OpenFOAM. This is the first time DDES simulations are
used to simulate and characterize the turbulent flow generated by a fractal
grid. Finally, this article reports on the extensive statistical study and the
direct comparison between the experimentally and numerically acquired time
series to investigate and compare one-point- and two-point statistics. Our goal
is to validate our computational results and provide enhanced insight into the
complexity of the multi-scale generation of turbulence using a fractal grid
with a low number of fractal iterations. In particular, we investigate the
different turbulent structures and their complex interaction in the near-grid
region or the production regime of the fractal grid flow.


  This document contains supplementary material for the main articles in our
Random Cayley Graphs project.
  We prove refined results about simple random walks on the integers and on the
cycle. We are primarily interested in the entropy of these random walks at
certain times and how this entropy changes when the time changes slightly.
Additionally, we prove some large deviation and exit time estimates.
  We prove some results on the size of discrete lattice balls and how this size
changes when the radius changes slightly. We do this in a general $L_q$ norm,
with $q \in [1,\infty]$.
  We also prove some other technical results deferred from the main papers.
  We hope that some of the results, particularly the simple random walk
estimates, will be useful in their own right for other researchers.


  The Exoplanet Characterisation Observatory (EChO) has been studied as a space
mission concept by the European Space Agency in the context of the M3 selection
process. Through direct measurement of the atmospheric chemical composition of
hundreds of exoplanets, EChO would address fundamental questions such as: What
are exoplanets made of? How do planets form and evolve? What is the origin of
exoplanet diversity?
  More specifically, EChO is a dedicated survey mission for transit and eclipse
spectroscopy capable of observing a large, diverse and well-defined planetary
sample within its four to six year mission lifetime.
  In this paper we use the end-to-end instrument simulator EChOSim to model the
currently discovered targets, to gauge which targets are observable and assess
the EChO performances obtainable for each observing tier and time. We show that
EChO would be capable of observing over 170 relativity diverse planets if it
were launched today, and the wealth of optimal targets for EChO expected to be
discovered in the next 10 years by space and ground-based facilities is simply
overwhelming.
  In addition, we build on previous molecular detectability studies to show
what molecules and abundances will be detectable by EChO for a selection of
real targets with various molecular compositions and abundances.
  EChO's unique contribution to exoplanetary science will be in identifying the
main constituents of hundreds of exoplanets in various mass/temperature
regimes, meaning that we will be looking no longer at individual cases but at
populations. Such a universal view is critical if we truly want to understand
the processes of planet formation and evolution in various environments.
  In this paper we present a selection of key results. The full results are
available online (http://www.ucl.ac.uk/exoplanets/echotargetlist/).


  In this paper we investigate the propagation of the weak representation
property (WRP) to an independently enlarged filtration. More precisely, we
consider an $\mathbb{F}$-semimartingale $X$ possessing the WRP with respect to
$\mathbb{F}$ and an $\mathbb{H}$-semimartingale $Y$ possessing the WRP with
respect to $\mathbb{H}$. Assuming that $\mathbb{F}$ and $\mathbb{H}$ are
independent, we show that the $\mathbb{G}$-semimartingale $Z=(X,Y)$ has the WRP
with respect to $\mathbb{G}$, where $\mathbb{G}:=\mathbb{F}\vee\mathbb{H}$. In
our setting, $X$ and $Y$ may have simultaneous jump-times. Furthermore, their
jumps may charge predictable times. This generalizes all available results
about the propagation of the WRP to independently enlarged filtrations.


  Social media is an area where users often experience censorship through a
variety of means such as the restriction of search terms or active and
retroactive deletion of messages. In this paper we examine the feasibility of
automatically detecting censorship of microblogs. We use a network growing
model to simulate discussion over a microblog follow network and compare two
censorship strategies to simulate varying levels of message deletion. Using
topological features extracted from the resulting graphs, a classifier is
trained to detect whether or not a given communication graph has been censored.
The results show that censorship detection is feasible under empirically
measured levels of message deletion. The proposed framework can enable
automated censorship measurement and tracking, which, when combined with
aggregated citizen reports of censorship, can allow users to make informed
decisions about online communication habits.


  If stable electroweak strings are copiously produced during the electroweak
phase transition, they may contribute significantly to the presently observed
baryon to entropy ratio of the Universe. This analysis establishes the
feasibility of implementing an electroweak baryogenesis scenario without a
first order phase transition.


  QCD instantons are known to produce deeply bound diquarks which may be used
as building blocks in the formation of multiquark states, in particular
pentaquarks and dibaryons. We suggest a simple model in which the lowest scalar
diquark (and possibly the tensor one) can be treated as an independent
``body'', with the same color and (approximately) the mass as a constituent
(anti)quark. In this model a new symmetry between states with the same number
of ``bodies'' but different number of quarks appear, in particular the
3-``body'' pentaquarks can be naturally related to decuplet baryons. We
estimate both the masses and widths of such states, and then discuss the
limitations of this model.


  A simulation study of the energy released by extensive air showers in the
form of MHz radiation is performed using the CoREAS simulation code. We develop
an efficient method to extract this radiation energy from air-shower
simulations. We determine the longitudinal profile of the radiation energy
release and compare it to the longitudinal profile of the energy deposit by the
electromagnetic component of the air shower. We find that the radiation energy
corrected for the geometric dependence of the geomagnetic emission scales
quadratically with the energy in the electromagnetic component of the air
shower with a second order dependency on the atmospheric density at the
position of the maximum of the shower development $X_\mathrm{max}$. In a
measurement where $X_\mathrm{max}$ is not accessible, this second order
dependence can be approximated using the zenith angle of the incoming direction
of the air shower with only a minor deterioration in accuracy. This method
results in an intrinsic uncertainty of 4% with respect to the electromagnetic
shower energy which is well below current experimental uncertainties.


  In this paper we revisit the subject of stationary flows of Lax hierarchies
of a coupled KdV class. We explain the main ideas in the standard KdV case and
then consider the dispersive water waves (DWW) case, with respectively 2 and 3
Hamiltonian representations. Each Hamiltonian representation gives us a
different form of stationary flow. Comparing these, we construct Poisson maps,
which, being non-canonical, give rise to bi-Hamiltonian representations of the
stationary flows. An alternative approach is to use the Miura maps, which we do
in the case of the DWW hierarchy, which has two ''modifications''. This
structure gives us 3 sequences of Poisson related stationary flows. We use the
Poisson maps to build a tri-Hamiltonian representation of each of the three
stationary hierarchies. One of the Hamiltonian representations allows a
multi-component squared eigenfunction expansion, which gives $N$ degrees of
freedom Hamiltonians, with first integrals. A Lax representation for each of
the stationary flows is derived from the coupled KdV matrices. In the case of 3
degrees of freedom, we give a generalisation of our Lax matrices and
Hamiltonian functions, which allows a connection with the rational
Calogero-Moser (CM) system. This gives a coupling of the CM system with other
potentials, along with a Lax representation. We present the particular case of
coupling one of the integrable H\'enon-Heiles systems to CM.


  Ultralow amplitude (ULA) and strange mode Cepheids are thought to be
pulsating variable stars that are near to or are at the edges of the classical
instability strip. Until now, a few dozen such variable star candidates have
been found both in the Large Magellanic Cloud and the Milky Way. For the
present work, we studied six ULA Cepheid candidates in the Milky Way,
identified by using CoRoT and 2MASS data. In order to identify their positions
in the period--luminosity and color--magnitude diagrams, we used the Gaia DR3
parallax and brightness data of each star to calculate their reddening-free
absolute magnitudes and distances. Furthermore, we calculated the Fourier
parameters (e.g., period and amplitude) of the light variations based on CoRoT
and TESS measurements, and established the long-term phase shifts for four out
of six stars. Based on the results, we conclude that none of the six ULA
Cepheid candidates are pulsating variable stars, but rather rotation-induced
variable stars (rotational spotted and $\alpha^2$~Canum Venaticorum variables)
that are either bluer or fainter than Cepheids would be.


  This text is reproduced with the kind permission of Fran\c{c}ois Ap\'ery.
  It was originally edited by Fran\c{c}ois Gu\'enard and Gilbert Leli\`evre for
the book "Penser les math\'ematiques".
  It is the modified and abridged version of a text that appeared previously as
S\'eminaire de philosophie et math\'ematiques de l'\'Ecole normale sup\'erieure
(s\'eance du 26 avril 1976), Paris, IREM Paris-Nord, 1980, 15 pp.,
http://www.numdam.org/item?id=SPHM_1976___1_A1_0, as well as in Langage et
pens\'ee math\'ematiques: actes du colloque international (Luxembourg, 9-11
juin 1976), Luxembourg, Centre universitaire de Luxembourg, 1976, pp. 391--410.
  In its introduction, Ap\'ery writes: "In default of convincing, this text can
set the record straight: we show that the constructive conception does not
mutilate, on the contrary, it enriches classical mathematics."


  This work is devoted to the causal perturbative Quantum Field Theory (QFT)
due to Bogoliubov, including QED and other realistic QFT. The white noise
analysis and the Hida operators as the annihilation-creation operators for free
fields are used. The whole Bogoliubov method is unchanged. Causal axioms of
such QFT make sense on any globally causal space-times. It is proved that on
the flat Minkowski spacetime realistic QFT, including QED, lead to the
scattering operator and interacting fields understood as generalized operators
in the white noise theory of Hida-Obata-Sait\^o with the perturbative series
equal to the Fock expansion of these operators in the sense of the white noise
calculus and make perfect sense in the adiabatic limit as the generalized
operators. But in case of the flat Minkowski space-time the realistic QFT,
including QED, can be applied only to the scattering phenomena with the
many-particle plane wave generalized states as the \emph{in} and \emph{out}
states. Theory is mathematically consistent without any infrared or ultraviolet
infinities. Feynman rules are replaced with other much more effective
recurrence rules for the higher order contributions to the scattering operator.
It is shown that realistic QFT, e.g. QED, are quite singular on the flat
Minkowski spacetime with the interacting fields as generalized operators, which
are quite singular, which after smearing with test function are not equal to
ordinary operators. Bound state problems cannot be treated entirely within QED
on the Minkowski space-time. It is proved that on space-times with compact
Cauchy surfaces and non-zero curvature realistic causal perturbative QFT,
including QED, behave much better. Perturbative series for some realistic QFT
are proved to be convergent on the globally causal space-times with nonzero
curvature and compact Cauchy surfaces.


  We investigate the contributions coming from the penguin operators in the
nonresonant $B^- \to M \bar M \pi^-$ ($M =\pi^-, K^-, K^0$) decays. The
effective Wilson coefficients of the the strong penguin operators $O_{4,6}$ are
found to be relatively larger. We calculate the contributions arising from the
$O_4$ and $O_6$ operators in the nonresonant decays $B^- \to M \bar M\pi^-$ ($M
= \pi^-, K^-, \bar K^0$) using a model combining heavy quark symmetry and the
chiral symmetry, developed previously. We find that the forbidden nonresonant
$B^- \to K^0 \bar K^0 \pi^-$ decay occurs through the strong penguin operators.
These penguin contributions affect the branching ratios for $B^- \to M \bar
M\pi^-$ ($M = \pi^-, K^-$) by only a few percent. The branching ratio for $B^-
\to K^0 \bar K^0 \pi^-$ is estimated to be of the order $ 10^{-6}$.


  We consider the asymptotic dynamics of the Einstein-Maxwell field equations
for the class of non-tilted Bianchi cosmologies with a barotropic perfect fluid
and a pure homogeneous source-free magnetic field, with emphasis on models of
Bianchi type VII_{0}, which have not been previously studied. Using the
orthonormal frame formalism and Hubble-normalized variables, we show that, as
is the case for the previously studied class A magnetic Bianchi models, the
magnetic Bianchi VII_{0} cosmologies also exhibit an oscillatory approach to
the initial singularity. However, in contrast to the other magnetic Bianchi
models, we rigorously establish that typical magnetic Bianchi VII_{0}
cosmologies exhibit the phenomena of asymptotic self-similarity breaking and
Weyl curvature dominance in the late-time regime.


  In this article a relation between curvature functionals for surfaces in the
Euclidean space and area functionals in relative differential geometry will be
given. Relative differential geometry can be described as the geometry of
surfaces in the affine space, endowed with a distinguished "relative normal
vector field" which generalises the notion of unit normal vector field N from
Euclidean differential geometry. A concise review of relative differential
geometry will be presented. The main result, to which the title of this article
refers, will be given in the third section. Here we consider, for a function
$f$ of two variables, relative normal vector fields of the form
$f(H,K)\,N-\grad_{\II}(f(H,K))$ for non-degenerate surfaces in the Euclidean
three-dimensional space. A comparison of the variation of the curvature
functional $\int f(H,K)\,\dd\Omega$ with the relative area functional obtained
from the above relative normal vector field, results in a distinguishing
property for the one-parameter family of relative normal vector fields which
was introduced by F.\ Manhart, and which is obtained by choosing
$f(H,K)=|K|^{\alpha}$ (where we will assume that $\alpha\neq 1$). More
precisely, the following will be shown in theorem~6: ``{The curvature
functionals $(\ast)$ for which the critical points coincide with the
relative-minimal surfaces with respect to the relative normal vector field
$(\dagger)$, are essentially those obtained from Manhart's family}." In the
fourth section, we give a characterisation of the sphere by means of relations
between the support function and the curvatures. In the last section, we
combine the previously described results and arrive at a variational
characterisation of the sphere.


  The hadronic corrections to the muon anomalous magnetic moment a_mu, due to
the gauge-invariant set of diagrams with dynamical quark loop light-by-light
scattering insertions, are calculated in the framework of the nonlocal chiral
quark model. These results complete calculations of all hadronic light-by-light
scattering contributions to a_mu in the leading order in the 1/Nc expansion.
The result for the quark loop contribution is
a_mu^{HLbL,Loop}=(11.0+-0.9)*10^(-10), and the total result is
a_mu^{HLbL,NxQM}=(16.8+-1.2)*10^(-10).


  We present here an overview of the Fourier Transform Scanning Tunneling
spectroscopy technique (FT-STS). This technique allows one to probe the
electronic properties of a two-dimensional system by analyzing the standing
waves formed in the vicinity of defects. We review both the experimental and
theoretical aspects of this approach, basing our analysis on some of our
previous results, as well as on other results described in the literature. We
explain how the topology of the constant energy maps can be deduced from the FT
of dI/dV map images which exhibit standing waves patterns. We show that not
only the position of the features observed in the FT maps, but also their shape
can be explained using different theoretical models of different levels of
approximation. Thus, starting with the classical and well known expression of
the Lindhard susceptibility which describes the screening of electron in a free
electron gas, we show that from the momentum dependence of the susceptibility
we can deduce the topology of the constant energy maps in a joint density of
states approximation (JDOS). We describe how some of the specific features
predicted by the JDOS are (or are not) observed experimentally in the FT maps.
The role of the phase factors which are neglected in the rough JDOS
approximation is described using the stationary phase conditions. We present
also the technique of the T-matrix approximation, which takes into account
accurately these phase factors. This technique has been successfully applied to
normal metals, as well as to systems with more complicated constant energy
contours. We present results recently obtained on graphene systems which
demonstrate the power of this technique, and the usefulness of local
measurements for determining the band structure, the map of the Fermi energy
and the constant-energy maps.


  Motivated by recent developments in perturbative calculations of the
nonlinear evolution of large-scale structure, we present an iterative algorithm
to reconstruct the initial conditions in a given volume starting from the dark
matter distribution in real space. In our algorithm, objects are first moved
back iteratively along estimated potential gradients, with a progressively
reduced smoothing scale, until a nearly uniform catalog is obtained. The linear
initial density is then estimated as the divergence of the cumulative
displacement, with an optional second-order correction. This algorithm should
undo nonlinear effects up to one-loop order, including the higher-order
infrared resummation piece. We test the method using dark matter simulations in
real space. At redshift $z=0$, we find that after eight iterations the
reconstructed density is more than $95\%$ correlated with the initial density
at $k\le 0.35\; h\mathrm{Mpc}^{-1}$. The reconstruction also reduces the power
in the difference between reconstructed and initial fields by more than 2
orders of magnitude at $k\le 0.2\; h\mathrm{Mpc}^{-1}$, and it extends the
range of scales where the full broadband shape of the power spectrum matches
linear theory by a factor of 2-3. As a specific application, we consider
measurements of the baryonic acoustic oscillation (BAO) scale that can be
improved by reducing the degradation effects of large-scale flows. In our
idealized dark matter simulations, the method improves the BAO signal-to-noise
ratio by a factor of 2.7 at $z=0$ and by a factor of 2.5 at $z=0.6$, improving
standard BAO reconstruction by $70\%$ at $z=0$ and $30\%$ at $z=0.6$, and
matching the optimal BAO signal and signal-to-noise ratio of the linear density
in the same volume. For BAO, the iterative nature of the reconstruction is the
most important aspect.


  A special class of generalized Jacobi operators which are self-adjoint in
Krein spaces is presented. A description of the resolvent set of such operators
in terms of solutions of the corresponding recurrence relations is given. In
particular, special attention is paid to the periodic generalized Jacobi
operators. Finally, the spectral properties of generalized Jacobi operators are
applied to prove convergence results for Pad\'e approximants.


  In this paper we show that if we want to obtain human evidence about
conventionalization of some phrases, we should ask native speakers about
associations they have to a given phrase and its component words. We have shown
that if component words of a phrase have each other as frequent associations,
then this phrase can be considered as conventionalized. Another type of
conventionalized phrases can be revealed using two factors: low entropy of
phrase associations and low intersection of component word and phrase
associations. The association experiments were performed for the Russian
language.


  This paper considers the support of grant-free massive access and solves the
challenge of active user detection and channel estimation in the case of a
massive number of users. By exploiting the sparsity of user activities, the
concerned problems are formulated as a compressive sensing problem, whose
solution is acquired by approximate message passing (AMP) algorithm.
Considering the cooperation of multiple access points, for the deployment of
AMP algorithm, we compare two processing paradigms, cloud computing and fog
computing, in terms of their effectiveness in guaranteeing ultra reliable
low-latency access. For cloud computing, the access points are connected in a
cloud radio access network (C-RAN) manner, and the signals received at all
access points are concentrated and jointly processed in the cloud baseband
unit. While for fog computing, based on fog radio access network (F-RAN), the
estimation of user activity and corresponding channels for the whole network is
split, and the related processing tasks are performed at the access points and
fog processing units in proximity to users. Compared to the cloud computing
paradigm based on traditional C-RAN, simulation results demonstrate the
superiority of the proposed fog computing deployment based on F-RAN.


  Empathy is often understood as the ability to share and understand another
individual's state of mind or emotion. With the increasing use of chatbots in
various domains, e.g., children seeking help with homework, individuals looking
for medical advice, and people using the chatbot as a daily source of everyday
companionship, the importance of empathy in human-computer interaction has
become more apparent. Therefore, our study investigates the extent to which
ChatGPT based on GPT-3.5 can exhibit empathetic responses and emotional
expressions. We analyzed the following three aspects: (1) understanding and
expressing emotions, (2) parallel emotional response, and (3) empathic
personality. Thus, we not only evaluate ChatGPT on various empathy aspects and
compare it with human behavior but also show a possible way to analyze the
empathy of chatbots in general. Our results show, that in 91.7% of the cases,
ChatGPT was able to correctly identify emotions and produces appropriate
answers. In conversations, ChatGPT reacted with a parallel emotion in 70.7% of
cases. The empathic capabilities of ChatGPT were evaluated using a set of five
questionnaires covering different aspects of empathy. Even though the results
show, that the scores of ChatGPT are still worse than the average of healthy
humans, it scores better than people who have been diagnosed with Asperger
syndrome / high-functioning autism.


  We apply the fermion renormalization group method, implemented numerically by
Honerkamp et.al., to a two-band model of FeAs-based materials. At half filling
we find the $(\pi,0)$ or $(0,\pi)$ spin density wave order and a sub-dominant
superconducting pairing tendency. Due to a topological reason, the spin density
wave gap has nodes on the fermi surfaces. Away from half filling we find an
unconventional s-wave and a sub-dominant $d_{x^2-y^2}$ pairing instability. The
former has $s$ symmetry around the hole fermi surface but exhibits
$s+d_{x^2-y^2}$ symmetry around the electron pockets where the 90 degree
rotation is broken. The pairing mechanism is inter-pocket pair hopping.
Interestingly, the same interaction also drives the antiferromagnetism.


  Single-domain particles of SrFe8Al4O19 were prepared by thermal treatment at
1473 K of porous products of citrate-nitrate auto-combustion, and the influence
of synthesis time on the particle morphology and magnetic properties was
studied. The procedure allows to obtain SrFe8Al4O19 particles with mean
diameters 100 - 460 nm, and their coercivity ranges from 14.5 to 18.4 kOe,
while ferromagnetic resonance frequencies vary from 149 to 164 GHz.


  Some quantal systems require only a small part of the full quantum theory for
their analysis in classical terms. In such understanding we review some recent
literature on semiclassical treatments.
  An analysis of it allows one to see that some important quantum features of
the harmonic oscillator can indeed be already encountered at the classical or
semiclassical statistical levels.


  We describe the results of an experiment to test for spacetime anisotropy
terms that might exist from Lorentz violations. The apparatus consists of a
pair of cylindrical superconducting cavity-stabilized oscillators operating in
the TM_{010} mode with one axis east-west and the other vertical. Spatial
anisotropy is detected by monitoring the beat frequency at the sidereal rate
and its first harmonic. We see no anisotropy to a part in 10^{13}. This puts a
comparable bound on four linear combinations of parameters in the general
Standard Model extension, and a weaker bound of <4 x 10^{-9} on three others.


  Human feedback has become the de facto standard for evaluating the
performance of Large Language Models, and is increasingly being used as a
training objective. However, it is not clear which properties of a generated
output this single `preference' score captures. We hypothesise that preference
scores are subjective and open to undesirable biases. We critically analyse the
use of human feedback for both training and evaluation, to verify whether it
fully captures a range of crucial error criteria. We find that while preference
scores have fairly good coverage, they under-represent important aspects like
factuality. We further hypothesise that both preference scores and error
annotation may be affected by confounders, and leverage instruction-tuned
models to generate outputs that vary along two possible confounding dimensions:
assertiveness and complexity. We find that the assertiveness of an output skews
the perceived rate of factuality errors, indicating that human annotations are
not a fully reliable evaluation metric or training objective. Finally, we offer
preliminary evidence that using human feedback as a training objective
disproportionately increases the assertiveness of model outputs. We encourage
future work to carefully consider whether preference scores are well aligned
with the desired objective.


  Set partitions and permutations with restrictions on the size of the blocks
and cycles are important combinatorial sequences. Counting these objects lead
to the sequences generalizing the classical Stirling and Bell numbers. The main
focus of the present article is the analysis of combinatorial and arithmetical
properties of them. The results include several combinatorial identities and
recurrences as well as some properties of their $p$-adic valuations.


  In kaon physics, several new precision measurements on flavour variables and
CP violation have performed in the recent years. Presented are a new precise
determination of the CKM parameter |V_us|, which combines the results of all
experiments together with recent theoretical progress, and new measurements of
the ratio R_K = Gamma(K+ -> e+ nu)/Gamma(K+ -> mu+ nu), which is sensitive to
contributions of a possible charged Higgs in the SUSY framework. Also, final
results of a precision search for direct CP violation in charged kaon decays
are presented.


  By introducing diffeomorphism and local Lorentz gauge invariant holonomy
fields, we study in the recent article [S.-S. Xue, Phys. Rev. D82 (2010)
064039] the quantum Einstein-Cartan gravity in the framework of Regge calculus.
On the basis of strong coupling expansion, mean-field approximation and
dynamical equations satisfied by holonomy fields, we present in this Letter
calculations and discussions to show the phase structure of the quantum
Einstein-Cartan gravity, (i) the order phase: long-range condensations of
holonomy fields in strong gauge couplings; (ii) the disorder phase: short-range
fluctuations of holonomy fields in weak gauge couplings. According to the
competition of the activation energy of holonomy fields and their entropy, we
give a simple estimate of the possible ultra-violet critical point and
correlation length for the second-order phase transition from the order phase
to disorder one. At this critical point, we discuss whether the continuum field
theory of quantum Einstein-Cartan gravity can be possibly approached when the
macroscopic correlation length of holonomy field condensations is much larger
than the Planck length.


  We develop a definitive physical-space scattering theory for the scalar wave
equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In
particular, we prove results corresponding to "existence and uniqueness of
scattering states" and "asymptotic completeness" and we show moreover that the
resulting "scattering matrix" mapping radiation fields on the past horizon and
past null infinity to radiation fields on the future horizon and future null
infinity is a bounded operator. The latter allows us to give a time-domain
theory of superradiant reflection. The boundedness of the scattering matrix
shows in particular that the maximal amplification of solutions associated to
ingoing finite-energy wave packets on past null infinity is bounded. On the
frequency side, this corresponds to the novel statement that the suitably
normalised reflection and transmission coefficients are uniformly bounded
independently of the frequency parameters. We further complement this with a
demonstration that superradiant reflection indeed amplifies the energy radiated
to future null infinity of suitable wave-packets as above. The results make
essential use of a refinement of our recent proof [M. Dafermos, I. Rodnianski
and Y. Shlapentokh-Rothman, Decay for solutions of the wave equation on Kerr
exterior spacetimes III: the full subextremal case |a|<M, arXiv:1402.6034] of
boundedness and decay for solutions of the Cauchy problem so as to apply in the
class of solutions where only a degenerate energy is assumed finite. We show in
contrast that the analogous scattering maps cannot be defined for the class of
finite non-degenerate energy solutions. This is due to the fact that the
celebrated horizon red-shift effect acts as a blue-shift instability when
solving the wave equation backwards.


  Nine years ago, superconductors based on the magnetic element iron were
discovered. A flurry of research activity has revealed an unprecedented
diversity of chemical structures and physical properties. Similarly to other
unconventional superconductors, stripe-type antiferromagnetism seems to play an
important role. Particularly interesting is its strong coupling to the crystal
lattice. The systematic comparison of different compounds may allow to identify
key elements in the mechanism of superconductivity and provide guidelines for
the search for new and better superconductors.


  The quantum spin Hall insulators predicted ten years ago and now
experimentally observed are instrumental for a breakthrough in nanoelectronics
due to non-dissipative spin-polarized electron transport through their edges.
For this transport to persist at normal conditions, the insulators should
possess a sufficiently large band gap in a stable topological phase. Here, we
theoretically show that quantum spin Hall insulators can be realized in
ultra-thin films constructed from a trivial band insulator with strong
spin-orbit coupling. The thinnest film with an inverted gap large enough for
practical applications is a centrosymmetric sextuple layer built out of two
inversely stacked non-centrosymmetric BiTeI trilayers. This nontrivial sextuple
layer turns out to be the structure element of an artificially designed strong
three-dimensional topological insulator Bi$_2$Te$_2$I$_2$. We reveal general
principles of how a topological insulator can be composed from the structure
elements of the BiTeX family (X=I, Br, Cl), which opens new perspectives
towards engineering of topological phases.


  We give a representation-theoretic interpretation of the Langlands character
duality of Frenkel and Hernandez, and show that the "Langlands branching
multiplicities" for symmetrizable Kac-Moody Lie algebras are equal to certain
tensor product multiplicities. For finite type quantum groups, the connection
with tensor products can be explained in terms of tilting modules.


  The thermal, chemical, and kinematic properties of the potentially
multi-phase circum/inter-galactic medium at the virial radii of galaxy clusters
remain largely uncertain. We present an X-ray study of Abell 2246 and GMBCG
J255.34805+64.23661 (z=0.23 and 0.45), two foreground clusters of the UV-bright
QSO HS 1700+6416, based on 240 ks Chandra/ACIS-I observations. We detect
enhanced diffuse X-ray emission to the projected distances beyond r_{200} radii
of these two clusters. The large-scale X-ray emission is consistent with being
azimuthally symmetric at the projected radii of the QSO (0.36 and 0.8 times the
radii of the two clusters). Assuming a spherical symmetry, we obtain the
de-projected temperature and density profiles of the X-ray-emitting gas.
Excluding the cool cores that are detected, we find that the mean temperature
of the hot gas is about 4.0 keV for Abell 2246 and 5.5 keV for GMBCG
J255.34805+64.23661, although there are indications for temperature drop at
large radii. From these results, we can estimate the density and pressure
distributions of the hot gas along the QSO sightline. We further infer the
radial entropy profile of Abell 2246 and compare it with the one expected from
purely gravitational hierarchical structure formation. This comparison shows
that the ICM in the outer region of the clusters is likely in a clumpy and
multi-phased state. These results, together with the upcoming HST/COS
observations of the QSO sightline, will enable a comprehensive investigation of
the multi-phase medium associated with the clusters.


  We study the phase-covariant quantum cloning machine for qudits, i.e. the
input states in d-level quantum system have complex coefficients with arbitrary
phase but constant module. A cloning unitary transformation is proposed. After
optimizing the fidelity between input state and single qudit reduced density
opertor of output state, we obtain the optimal fidelity for 1 to 2
phase-covariant quantum cloning of qudits and the corresponding cloning
transformation.


  This paper considers a secure multigroup multicast multiple-input
single-output (MISO) communication system aided by an intelligent reflecting
surface (IRS). Specifically, we aim to minimize the transmit power at the Alice
via jointly optimizing the transmit beamformer, AN vector and phase shifts at
the IRS subject to the secrecy rate constraints as well as the unit modulus
constraints of IRS phase shifts. However, the optimization problem is
non-convex and directly solving it is intractable. To tackle the optimization
problem, we first transform it into a semidefinite relaxation (SDR) problem,
and then alternately update the transmit beamformer and AN matrix as well as
the phase shifts at the IRS. In order to reduce the high computational
complexity, we further propose a low-complexity algorithm based on second-order
cone programming (SOCP). We decouple the optimization problem into two
sub-problems and optimize the transmit beamformer, AN vector and the phase
shifts alternately by solving two corresponding SOCP sub-problem. Simulation
results show that the proposed SDR and SOCP schemes require half or less
transmit power than the scheme without IRS, which demonstrates the advantages
of introducing IRS and the effectiveness of the proposed methods.


  Let $B$ be a sixth-power-free integer and $P$ be a non-torsion point on the
Mordell curve $E_B:y^2=x^3+B$. In this paper, we study integral multiples
$[n]P$ of $P$. Among other results, we show that $P$ has at most three integral
multiples with $n>1$. This result is sharp in the sense that there are points
$P$ with exactly three integral multiples $[n]P$ and $n>1$. As an application,
we discuss the number of integral points on the quasi-minimal model of rank 1
Mordell curves.


  Poly-L-lactide (PLLA) is a popular choice for medical devices due to its
bioresorbability and superior mechanical properties compared with other
polymers. However, although PLLA has been investigated for use in bioresorbable
cardiovascular stents, it presents application-specific limitations which
hamper device therapies. These include low toughness and strength compared with
metals used for this purpose, and slow degradation. Blending PLLA with novel
polyethylene glycol functionalised
poly(L-lactide-co-$\varepsilon$-caprolactone) (PLCL-PEG) materials has been
investigated here to tailor the mechanical properties and degradation behaviour
of PLLA. This exciting approach provides a foundation for a next generation of
bioresorbable materials whose properties can be rapidly tuned. The degradation
of PLLA was significantly accelerated by addition of PLCL-PEG. After 30 days of
degradation, several structural changes were observed in the polymer blends,
which were dependent on the level of PLCL-PEG addition. Blends with low
PLCL-PEG content displayed enthalpy relaxation, resulting in embrittlement,
while blends with high PLCL-PEG content displayed crystallisation, due to
enhanced chain mobility brought on by chain scission, also causing
embrittlement. Moderate PLCL-PEG additions (10% PLCL(70:30)-PEG and 20 - 30%
PLCL(80:20)-PEG) stabilised the structure, reducing the extent of enthalpy
relaxation and crystallisation and thus retaining ductility. Compositional
optimisation identified a sweet spot for this blend strategy, whereby the
ductility was enhanced while maintaining strength. Our results indicate that
blending PLLA with PLCL-PEG provides an effective method of tuning the
degradation timescale and mechanical properties of PLLA, and provides important
new insight into the mechanisms of structural relaxations that occur during
degradation, and strategies for regulating these.


  Two methods for determining the potential (\psi) around a discretely charged
rod have been devised. The methods utilize the potential around the
continuously charged rod (\bar{\psi}) as the reference where \bar{\psi}
isdetermined by the Poisson-Boltzmann equation. The potential data are used to
determine the theoretical radial distribution function (RDF) which is compared
with MD simulation data. It is shown that the magnitude of the charge and size
parameters very strongly affects the shape of the RDF's and consequently the
thermodynamics.


  I try to argue that the only way out of the black hole information paradox is
through a unified quantum field theory of gravity and other interactions.
Superstring theory is especially interesting, since in a special limit, the
classical picture of 't Hooft emerges.


  The online bipartite matching problem has offline buyers desiring to be
matched to online items. The analysis of online bipartite matching of Eden et
al. (2021) is a smoothness proof (Syrgkanis and Tardos, 2013). Moreover, it can
be interpreted as combining a $\lambda = 1-1/e$ value covering (which holds for
single-dimensional agents and randomized auctions) and $\mu = 1$ revenue
covering (Hartline et al., 2014). Note that value covering is a fact about
single-dimensional agents and has nothing to do with the underlying feasibility
setting. Thus, the essential new result from Eden et al. (2021) is that online
bipartite matching is $\mu=1$ revenue covered. A number of old and new
observations follow from this perspective.


  In this paper, we propose a new dense retrieval model which learns diverse
document representations with deep query interactions. Our model encodes each
document with a set of generated pseudo-queries to get query-informed,
multi-view document representations. It not only enjoys high inference
efficiency like the vanilla dual-encoder models, but also enables deep
query-document interactions in document encoding and provides multi-faceted
representations to better match different queries. Experiments on several
benchmarks demonstrate the effectiveness of the proposed method, out-performing
strong dual encoder baselines.The code is available at
\url{https://github.com/jordane95/dual-cross-encoder


  In this paper, we discuss a distributed control architecture, aimed at
networks with linear and time-invariant dynamics, which is amenable to convex
formulations for controller design. The proposed approach is well suited for
large scale systems, since the resulting feedback schemes completely avoid the
exchange of internal states, i.e., plant or controller states, among
sub-controllers. Additionally, we provide state-space formulas for these
sub-controllers, able to be implemented in a distributed manner.


  We present the first X-ray detections of ultracool dwarfs (UCDs) from the
first all-sky survey of the extended ROentgen Survey with an Imaging Telescope
Array (eROSITA) onboard the Russian Spektrum-Roentgen-Gamma (SRG) mission. We
use three publicly available input catalogs of spectroscopically confirmed UCDs
and Gaia-selected UCD candidates that together comprise nearly 20000 objects.
We first extracted all X-ray sources from the catalog of the first eROSITA
survey, eRASS1, that have a UCD or candidate within three times their
positional uncertainty. Then we examined all Gaia objects in the vicinity of
these 96 X-ray sources and we associated them to the most plausible counterpart
on the basis of their spatial separation to the X-ray position and their
multiwavelength properties. This way we find 40 UCDs that have a secure
identification with an X-ray source and 18 plausible UCD X-ray emitters.
Twenty-one of these X-ray emitting UCDs have a spectroscopic confirmation,
while the others have been selected based on Gaia photometry and we computed
spectral types from the G-J color. The spectral types of the X-ray emitting
UCDs and candidates range between M5 and M9, and the distances range from 3.5
to 190 pc. The majority of the UCDs from the eRASS1 sample show a ratio of
X-ray to bolometric luminosity well above the canonical saturation limit of log
(Lx/Lbol) ~ -3. For the two most extreme outliers, we showed through an
analysis of the eRASS1 light curve that these high values are due to flaring
activity. The X-ray spectra of the two brightest objects both reveal an
emission-measure weighted plasma temperature of kT ~ 0.75 keV. These
observations demonstrate the potential of eROSITA for advancing our knowledge
on the faint coronal X-ray emission from UCDs by building statistical samples
for which the average X-ray brightness, flares, and coronal temperatures can be
derived.


  Many peer-review venues are either using or looking to use algorithms to
assign submissions to reviewers. The crux of such automated approaches is the
notion of the "similarity score"--a numerical estimate of the expertise of a
reviewer in reviewing a paper--and many algorithms have been proposed to
compute these scores. However, these algorithms have not been subjected to a
principled comparison, making it difficult for stakeholders to choose the
algorithm in an evidence-based manner. The key challenge in comparing existing
algorithms and developing better algorithms is the lack of the publicly
available gold-standard data that would be needed to perform reproducible
research. We address this challenge by collecting a novel dataset of similarity
scores that we release to the research community. Our dataset consists of 477
self-reported expertise scores provided by 58 researchers who evaluated their
expertise in reviewing papers they have read previously.
  We use this data to compare several popular algorithms employed in computer
science conferences and come up with recommendations for stakeholders. Our main
findings are as follows. First, all algorithms make a non-trivial amount of
error. For the task of ordering two papers in terms of their relevance for a
reviewer, the error rates range from 12%-30% in easy cases to 36%-43% in hard
cases, highlighting the vital need for more research on the
similarity-computation problem. Second, most existing algorithms are designed
to work with titles and abstracts of papers, and in this regime the Specter+MFR
algorithm performs best. Third, to improve performance, it may be important to
develop modern deep-learning based algorithms that can make use of the full
texts of papers: the classical TD-IDF algorithm enhanced with full texts of
papers is on par with the deep-learning based Specter+MFR that cannot make use
of this information.


  This work analyses the effect of the Helium content on synthetic
Period-Luminosity Relations (PLRs) and Period-Wesenheit Relations (PWRs) of
Cepheids and the systematic uncertainties on the derived distances that a
hidden population of He-enhanced Cepheids may generate. We use new stellar and
pulsation models to build a homogeneous and consistent framework to derive the
Cepheid features. The Cepheid populations expected in synthetic color-magnitude
diagrams of young stellar systems (from 20 Myr to 250 Myr) are computed in
several photometric bands for Y = 0.25 and Y = 0.35, at a fixed metallicity (Z
= 0.008). The PLRs appear to be very similar in the two cases, with negligible
effects (few %) on distances, while PWRs differ somewhat, with systematic
uncertainties in deriving distances as high as about 7% at log P < 1.5.
Statistical effects due to the number of variables used to determine the
relations contribute to a distance systematic error of the order of few
percent, with values decreasing from optical to near-infrared bands. The
empirical PWRs derived from multi-wavelength datasets for the Large Magellanic
Cloud (LMC) is in a very good agreement with our theoretical PWRs obtained with
a standard He content, supporting the evidence that LMC Cepheids do not show
any He effect.


  The Cluster Wideband Data instrument has been used to determine the locations
of auroral kilometric radiation (AKR) using very long baseline interferometry.
The technique involves cross-correlating individual AKR bursts from all six
Cluster baselines using time and frequency filtered waveforms. We report the
locations of over 1,700 individual AKR bursts during six observing epochs
between 10 July 2002 and 22 January 2003 when the Cluster constellation was
high above the southern or northern hemisphere. In general we find that the AKR
burst locations lie along magnetic field lines which map onto the nighttime
auroral zone as expected from previous AKR studies. The distribution of AKR
auroral footprint locations at each epoch had a overall spatial scale between
1000 - 2000 km, much larger than the positional uncertainty of an individual
AKR burst location magnetic footprint, but a small fraction of the auroral
oval. For two of the six epochs, there was a significant drift in the mean
location of AKR activity over a period of 1-2 hours. The drift was
predominantly in latitude at one epoch and in longitude at the other, with
average drift speed V ~ 80-90 m s-1 at the AKR emission location.


  A discrete version of the symmetric duality of Caputo-Torres, to relate left
and right Riemann-Liouville and Caputo fractional differences, is considered.
As a corollary, we provide an evidence to the fact that in case of right
fractional differences, one has to mix between nabla and delta operators. As an
application, we derive right fractional summation by parts formulas and left
fractional difference Euler-Lagrange equations for discrete fractional
variational problems whose Lagrangians depend on right fractional differences.


  We study reinforcement learning in an infinite-horizon average-reward setting
with linear function approximation, where the transition probability function
of the underlying Markov Decision Process (MDP) admits a linear form over a
feature mapping of the current state, action, and next state. We propose a new
algorithm UCRL2-VTR, which can be seen as an extension of the UCRL2 algorithm
with linear function approximation. We show that UCRL2-VTR with Bernstein-type
bonus can achieve a regret of $\tilde{O}(d\sqrt{DT})$, where $d$ is the
dimension of the feature mapping, $T$ is the horizon, and $\sqrt{D}$ is the
diameter of the MDP. We also prove a matching lower bound
$\tilde{\Omega}(d\sqrt{DT})$, which suggests that the proposed UCRL2-VTR is
minimax optimal up to logarithmic factors. To the best of our knowledge, our
algorithm is the first nearly minimax optimal RL algorithm with function
approximation in the infinite-horizon average-reward setting.


  The Bianchi IX model has been used often to investigate the structure close
to singularities of general relativity. Its classical chaos is expected to
have, via the BKL scenario, implications even for the approach to general
inhomogeneous singularities. Thus, it is a popular model to test consequences
of modifications to general relativity suggested by quantum theories of
gravity. This paper presents a detailed proof that modifications coming from
loop quantum gravity lead to a non-chaotic effective behavior. The way this is
realized, independently of quantization ambiguities, suggests a new look at
initial and final singularities.


  It is shown that the processes of electron(positron) scattering and $e^+e^-$
pair production in the Coulomb fields of two relativistic ions, can be
expressed through the amplitudes of lepton scattering off the ion Coulomb field
via Watson expansion. We obtained the compact expressions for these amplitudes
valid in the high energy limit and discuss the crossing symmetry relations
among the considered processes.


  In this paper, for each graph G, a free edge set F is defined. To study the
existence of cycle double cover, the naive cycle double cover of G and F have
been defined and studied. In the main theorem, the paper, based on the
Kuratowski minor properties, presents a condition to guarantee the existence of
a naive cycle double cover for couple (G,F). As a result, the cycle double
cover conjecture has been concluded. Moreover, Goddyn's conjecture - asserting
if C is a cycle in bridgeless graph G, there is a cycle double cover of G
containing C - will have been proved.


  This work establishes that the physical layer can be used to perform
information-theoretic authentication in additive white Gaussian noise channels,
as long as the adversary is not omniscient. The model considered consists of an
encoder, decoder, and adversary, where the adversary has access to the message,
a non-causal noisy observation of the encoder's transmission, and unlimited
transmission power, while the decoder observes a noisy version of the sum of
the encoder and adversary's outputs. A method to modify a generic existing
channel code to enable authentication is presented. It is shown that this
modification costs an asymptotically negligible amount of the coding rate,
while still enabling authentication as long as the adversary's observation is
not noiseless. Also notable is that this modification is not (asymptotically) a
function of the statistical characterization of the adversary's channel and
furthermore no secret key is required, hence paving the way for a robust
practical implementation. Using these results, the channel-authenticated
capacity is calculated and shown to be equal to the non-adversarial channel
capacity. While this modular scheme is designed for use in the given channel
model, it is applicable to a wide range of settings.


  In this study, we demonstrate that the flyby anomaly, an unexpected
acceleration detected in some of the gravitational assists of the Galileo,
NEAR, Cassini and Rosetta spacecraft, could be probed by accurate orbital
tracking available in the proposed Space-Time Explorer and Quantum Equivalence
Principle Space Test (STE- QUEST); following a recent work, we focus on the
similarity between an hyperbolic flyby and the perigee passage in a highly
elliptic orbit of the latter, as well as its Global Navigation Satellite System
precise orbital determination capabilities.


  Let $G$ be a locally compact group with cocompact connected component. We
prove that the assembly map from the topological $\k$-theory of $G$ to the
$\k$-theory of the reduced $C^*$-algebra of $G$ is an isomorphism.


  We investigate possible realization of the phantom-like behavior in the
framework of $f(R)$-gravity models where there are no phantom fields in the
matter sector of the theory. By adopting some observationally reliable ansatz
for $f(R)$, we show that it is possible to realize phantom-like behavior in
$f(R)$-gravity without introduction of phantom fields that suffer from
instabilities and violation of the null energy condition. Depending on the
choice of $f(R)$, the null energy condition is fulfilled in some subspaces of
each model parameter space.


  Truth discovery is to resolve conflicts and find the truth from
multiple-source statements. Conventional methods mostly research based on the
mutual effect between the reliability of sources and the credibility of
statements, however, pay no attention to the mutual effect among the
credibility of statements about the same object. We propose memory network
based models to incorporate these two ideas to do the truth discovery. We use
feedforward memory network and feedback memory network to learn the
representation of the credibility of statements which are about the same
object. Specially, we adopt memory mechanism to learn source reliability and
use it through truth prediction. During learning models, we use multiple types
of data (categorical data and continuous data) by assigning different weights
automatically in the loss function based on their own effect on truth discovery
prediction. The experiment results show that the memory network based models
much outperform the state-of-the-art method and other baseline methods.


  Vision-language alignment learned from image-caption pairs has been shown to
benefit tasks like object recognition and detection. Methods are mostly
evaluated in terms of how well object class names are learned, but captions
also contain rich attribute context that should be considered when learning
object alignment. It is unclear how methods use this context in learning, as
well as whether models succeed when tasks require attribute and object
understanding. To address this gap, we conduct extensive analysis of the role
of attributes in vision-language models. We specifically measure model
sensitivity to the presence and meaning of attribute context, gauging influence
on object embeddings through unsupervised phrase grounding and classification
via description methods. We further evaluate the utility of attribute context
in training for open-vocabulary object detection, fine-grained text-region
retrieval, and attribution tasks. Our results show that attribute context can
be wasted when learning alignment for detection, attribute meaning is not
adequately considered in embeddings, and describing classes by only their
attributes is ineffective. A viable strategy that we find to increase benefits
from attributes is contrastive training with adjective-based negative captions.


  Magnetic ordering in topological insulators (TI) is crucial for breaking
time-reversal symmetry (TRS) and thereby opening a gap in the topological
surface states (TSSs) [1-6], which is the key for realizing useful topological
properties such as the quantum anomalous Hall (QAH) effect, axion insulator
state and the topological magnetoelectric effect. Combining TIs with magnetic
materials can be expected to yield interfaces [26-28] with unique topological
and magnetic phases but such interfaces largely remain unexplored. Here, we
report the discovery of a novel antiferromagnetic (AFM) Van der Waals (VdW)
phase at the interface of a sputtered c-axis oriented TI/FM (Bi2Te3/Ni80Fe20)
heterostructure due to the formation of a Ni-intercalated Bi2Te3 VdW
interfacial layer. The TI/FM heterostructure is shown to possess a significant
spontaneous exchange bias and the presence of an AFM order at the interface via
measurements of the hysteresis loop as well as the observation of compensated
magnetic moments at the interface using polarized neutron reflectometry (PNR).
An in-depth analysis of the structural and chemical properties of the
interfacial AFM phase was carried out using selected area electron diffraction
(SAED), electron energy loss spectroscopy (EELS), and X-ray photoelectron
spectroscopy (XPS). These studies show evidence of solid-state reaction between
the intercalated Ni atoms and Bi2Te3 layers and of the formation of
topologically nontrivial magnetic VdW compounds. The N\'eel temperature of the
interfacial AFM phase is 63 K, which is higher than that of typical magnetic
topological insulators [53]. Our study shows how industrial
CMOS-process-compatible sputtered TI/FM heterostructures can provide a novel
materials platform for exploring the emergence of interfacial topological
magnetic phases and high-temperature topological magnetic states.