  As a ubiquitous aspect of modern information technology, data compression has
a wide range of applications. Therefore, a quantum autoencoder which can
compress quantum information into a low-dimensional space is fundamentally
important to achieve automatic data compression in the field of quantum
information. Such a quantum autoencoder can be implemented through training the
parameters of a quantum device using classical optimization algorithms. In this
article, we analyze the condition of achieving a perfect quantum autoencoder
and theoretically prove that a quantum autoencoder can losslessly compress
high-dimensional quantum information into a low-dimensional space (also called
latent space) if the number of maximum linearly independent vectors from input
states is no more than the dimension of the latent space. Also, we
experimentally realize a universal two-qubit unitary gate and design a quantum
autoencoder device by applying machine learning method. Experimental results
demonstrate that our quantum autoencoder is able to compress two two-qubit
states into two one-qubit states. Besides compressing quantum information, the
quantum autoencoder is used to experimentally discriminate two groups of
nonorthogonal states.


  In this paper we prove that the universal cover of a smooth projective
variety with nilpotent fundamental group is holomorphically convex.


  Using 3D AMR simulations, linking the 50 kpc to the sub-pc scales over the
course of 40 Myr, we systematically relax the classic Bondi assumptions in a
typical galaxy hosting a SMBH. In the realistic scenario, where the hot gas is
cooling, while heated and stirred on large scales, the accretion rate is
boosted up to two orders of magnitude compared with the Bondi prediction. The
cause is the nonlinear growth of thermal instabilities, leading to the
condensation of cold clouds and filaments when t_cool/t_ff < 10. Subsonic
turbulence of just over 100 km/s (M > 0.2) induces the formation of thermal
instabilities, even in the absence of heating, while in the transonic regime
turbulent dissipation inhibits their growth (t_turb/t_cool < 1). When heating
restores global thermodynamic balance, the formation of the multiphase medium
is violent, and the mode of accretion is fully cold and chaotic. The recurrent
collisions and tidal forces between clouds, filaments and the central clumpy
torus promote angular momentum cancellation, hence boosting accretion. On
sub-pc scales the clouds are channelled to the very centre via a funnel. A good
approximation to the accretion rate is the cooling rate, which can be used as
subgrid model, physically reproducing the boost factor of 100 required by
cosmological simulations, while accounting for fluctuations. Chaotic cold
accretion may be common in many systems, such as hot galactic halos, groups,
and clusters, generating high-velocity clouds and strong variations of the AGN
luminosity and jet orientation. In this mode, the black hole can quickly react
to the state of the entire host galaxy, leading to efficient self-regulated AGN
feedback and the symbiotic Magorrian relation. During phases of overheating,
the hot mode becomes the single channel of accretion (with a different cuspy
temperature profile), though strongly suppressed by turbulence.


  Every encoding has priori information if the encoding represents any semantic
information of the unverse or object. Encoding means mapping from the unverse
to the string or strings of digits. The semantic here is used in the
model-theoretic sense or denotation of the object. If encoding or strings of
symbols is the adequate and true mapping of model or object, and the mapping is
recursive or computable, the distance between two strings (text) is mapping the
distance between models. We then are able to measure the distance by computing
the distance between the two strings. Otherwise, we may take a misleading
course. "Language tree" may not be a family tree in the sense of historical
linguistics. Rather it just means the similarity.


  Thickness (dF) and concentration (x) dependence of the Curie temperature of
NixCu100-x(dF) ferromagnetic alloy layers (x =0.55,0.65, dF =[3nm{\div}12nm])
being in contact with a vanadium layer was studied. The Curie temperature of
the ferromagnetic layers depends on the thickness when it is comparable with
the interface layer between the F and the vanadium layers, which is attributed
to the proximity coupling of the interface region with the rest of the F layer.
The present study provides valuable information for fabrication of samples with
controlled exchange coupling strength for studies of superconductor/ferromagnet
(S/F) proximity effects.


  Pulsars are remarkably precise "celestial clocks" that can be used to explore
many different aspects of physics and astrophysics. In this article I give a
brief summary of pulsar properties and describe some of the applications of
pulsar timing, including tests of theories of gravitation, efforts to detect
low-frequency gravitational waves using pulsar timing arrays and establishment
a "pulsar timescale".


  Using a simplified framework, we attempt to explain the recent DAMPE cosmic
$e^+ + e^-$ flux excess by leptophilic Dirac fermion dark matter (LDM). The
scalar ($\Phi_0$) and vector ($\Phi_1$) mediator fields connecting LDM and
Standard Model particles are discussed. Under constraints of DM relic density,
gamma-rays, cosmic-rays and Cosmic Microwave Background (CMB), we find that the
couplings $P \otimes S$, $P \otimes P$, $V \otimes A$ and $V \otimes V$ can
produce the right bump in $e^+ + e^-$ flux for a DM mass around 1.5 TeV with a
natural thermal annihilation cross-section $<\sigma v> \sim 3 \times 10^{-26}
cm^3/s$ today. Among them, $V \otimes V$ coupling is tightly constrained by
PandaX-II data (although LDM-nucleus scattering appears at one-loop level) and
the surviving samples appear in the resonant region, $m_{\Phi_1} \simeq
2m_{\chi}$. We also study the related collider signatures, such as dilepton
production $pp \to \Phi_1 \to \ell^+\ell^-$, and muon $g-2$ anomaly. Finally,
we present a possible $U(1)_X$ realization for such leptophilic dark matter.


  A reparametrization invariant model, introduced by Montesinos, Rovelli and
Thiemann, possessing an SL(2,R) gauge symmetry is treated along the guidelines
of an algebraic constraint quantization scheme that translates the vanishing of
the constraints into representation conditions for the algebra of observables.
The application of this algebraic scheme to the SL(2,R) model yields an
unambiguous identification of the physical representation of the algebra of
observables.


  We revisit the question of whether the strong law of large numbers (SLLN)
holds uniformly in a rich family of distributions, culminating in a
distribution-uniform generalization of the Marcinkiewicz-Zygmund SLLN. These
results can be viewed as extensions of Chung's distribution-uniform SLLN to
random variables with uniformly integrable $q^\text{th}$ absolute central
moments for $0 < q < 2;\ q \neq 1$. Furthermore, we show that uniform
integrability of the $q^\text{th}$ moment is both sufficient and necessary for
the SLLN to hold uniformly at the Marcinkiewicz-Zygmund rate of $n^{1/q - 1}$.
These proofs centrally rely on distribution-uniform analogues of some familiar
almost sure convergence results including the Khintchine-Kolmogorov convergence
theorem, Kolmogorov's three-series theorem, a stochastic generalization of
Kronecker's lemma, and the Borel-Cantelli lemmas. The non-identically
distributed case is also considered.


  Magnetic free energy powers solar flares and coronal mass ejections (CMEs),
and the buildup of magnetic helicity might play a role in the development of
unstable structures that subsequently erupt. To better understand the roles of
energy and helicity in large flares and eruptions, we have characterized the
evolution of magnetic energy and helicity associated with 21 X-class flares
from 2010 to 2017. Our sample includes both confined and eruptive events, with
6 and 15 in each category, respectively. Using HMI vector magnetic field
observations from several hours before to several hours after each event, we
employ (a) the Differential Affine Velocity Estimator for Vector Magnetograms
(DAVE4VM) to determine the photospheric fluxes of energy and helicity, and (b)
non-linear force-free field (NLFFF) extrapolations to estimate the coronal
content of energy and helicity in source-region fields. Using Superposed Epoch
analysis (SPE), we find, on average: (1) decreases in both magnetic energy and
helicity, in both photospheric fluxes and coronal content, that persist for a
few hours after eruptions, but no clear changes, notably in relative helicity,
for confined events; (2) significant increases in the twist of photospheric
fields in eruptive events, with twist uncertainties too large in confined
events to constrain twist changes (and lower overall twist in confined events);
and (3) on longer time scales (event time +12 hours), replenishment of free
magnetic energy and helicity content to near pre-event levels for eruptive
events. For eruptive events, magnetic helicity and free energy in coronal
models clearly decrease after flares, with the amounts of decrease proportional
to each region's pre-flare content.


  Protein-protein interactions are central mediators in many biological
processes. Accurately predicting the effects of mutations on interactions is
crucial for guiding the modulation of these interactions, thereby playing a
significant role in therapeutic development and drug discovery. Mutations
generally affect interactions hierarchically across three levels: mutated
residues exhibit different sidechain conformations, which lead to changes in
the backbone conformation, eventually affecting the binding affinity between
proteins. However, existing methods typically focus only on sidechain-level
interaction modeling, resulting in suboptimal predictions. In this work, we
propose a self-supervised multi-level pre-training framework, ProMIM, to fully
capture all three levels of interactions with well-designed pretraining
objectives. Experiments show ProMIM outperforms all the baselines on the
standard benchmark, especially on mutations where significant changes in
backbone conformations may occur. In addition, leading results from zero-shot
evaluations for SARS-CoV-2 mutational effect prediction and antibody
optimization underscore the potential of ProMIM as a powerful next-generation
tool for developing novel therapeutic approaches and new drugs.


  We perform a perturbative analysis of the Aharonov-Bohm problem to one loop
in a field-theoretic formulation, and show that contact interactions are
necessary for renormalizability. In general, the classical scale invariance of
this problem is broken quantum mechanically. There exists however a critical
point for which this anomaly disappears.


  The $^{25}$F($5/2^+) (-1p) ^{24}$O reaction was studied at the NSCL using the
S800 spectrometer. The experimental spectroscopic factor for the ground-state
to ground-state transition indicates a substantial depletion of the proton
$d_{5/2}$ strength compared to shell-model expectations. Our result supports
the findings reported by Tang \textit{et al.}, from their study of the $(p,2p)$
reaction at RIBF. The overlap between the $^{25}$F and $^{24}$O ground-states
is considerably less than anticipated if $^{24}$O acted as a robust and rigid
doubly-magic core in $^{25}$F. We interpret the results within the framework of
the Particle-Vibration Coupling (PVC) of a $d_{5/2}$ proton coupled to a
quadrupole phonon of an effective core. This approach provides a good
description of the experimental data by requiring an effective $^{24}$O* core
with a phonon energy of $\hbar\omega_2$= 3.2 MeV, and a $B(E2) ~ 2.7$ W.u.,
softer and more collective than a bare $^{24}$O. Both the Nilsson deformed mean
field and the PVC models appear to capture the properties of the effective core
of $^{25}$F, suggesting that the additional proton tends to polarize the free,
doubly magic $^{24}$O in such a way that it becomes either slightly deformed or
a quadrupole vibrator.


  We categorify tensor products of the fundamental representation of quantum
$\mathfrak{sl}_2$ at prime roots of unity building upon earlier work where a
tensor product of two Weyl modules was categorified.


  Melting of two dimensional (2D) clusters of classical particles is studied
using Brownian dynamics and Langevin molecular dynamics simulations. The
particles are confined by a circular hard wall or a parabolic external
potential and interact through a dipole or a screened Coulomb potential. We
found that with decreasing strength of the inter--particle interaction clusters
with short-range inter-particle interaction which are confined by a hard wall
exhibit a re-entrant behavior in its orientational order.


  Tetrahedrite (copper antimony sulfosalt) is promising p-type themoeletric
material due to very low intrinsic thermal conductivity and moderately-high
power factor, with one of the limitations being lack of n-type variant to
create thermoelectric generator. In this paper, DFT calculations have been
carried out to study tetrahedrite doped with Li into structural voids,
LixCu12Sb4S13 (0 <= x <= 3). Enthalpies of formation shows that introduction of
Li into both 6b and 24g sites is energetically favorable. Dopants in those
positions differently affect rattling Cu(12e) behaviour, as well as vary in
magnitude of induced local disorder. Topological analysis of charge density
classifies tetrahedrite as closed-shell, ionic system of interactions with some
degree of covalency. Addition of Li increases bond strain and decreases
structure stability. Electronic band structure shows that for x>2.0, material
becomes n-type, however results are not precisely conclusive on whether
structure will be synthesizable, which should be determined experimentally.


  From a census of forty copies, we can distinguish three different editions of
von Staudt's Geometrie der Lage: the first of 1847 and two undated ones from
the 1870's.


  Let $\phi$ be an automorphism of a free group $F_n$ of rank $n$, and let
$M_{\phi}=F_n \rtimes_{\phi} \mathbb{Z}$ be the corresponding mapping torus of
$\phi$. We study the group $Out(M_{\phi})$ under certain technical conditions
on $\phi$. Moreover, in the case of rank 2, we classify the cases when this
group is finite or virtually cyclic, depending on the conjugacy class of the
image of $\phi$ in $GL_2(\mathbb{Z})$.


  In this work we are interested in the central configurations of the spatial
seven-body problem where six of them are at vertices of two congruents
equilateral triangles belong to parallel planes and one triangle is a rotation
by the angle $\pi/3$ from the other one. We show a existence and uniqueness of
a class of central configuration with this shape, namely six bodies with equal
masses at the vertice of a regular octahedron with the seventh body in its
center. There is not restriction to the mass of the seventh body.


  This collection bundles the following memos dedicated to Fast-speed (100
Mb/s) and Original-speed (10 Mb/s) Ethernet protocols, including upgradeable
from Manchester (ME/DME) into Like-a-Manchester (LaM) encoding schemes: [1]
"Data Coding Means and Event Coding Means Multiplexed Over the 100BASE-T1 PMA
Sublayer" (extends the IEEE 802.3bw protocol, uses a non-LaM encoding, present
at pp. 1-4); [2] "Data Coding Means and Event Coding Means Multiplexed Over a
10BASE-T/Te MAU-like Entity" (IEEE 802.3i/az, LaM-based, pp. 5-8); [3] "Data
Coding Means and Event Coding Means Multiplexed Over a 10BASE-T1S PMA-like
Entity" (IEEE 802.3cg's Clause 147, LaM-based, pp. 9-12); and [4] "Data Coding
Means and Event Coding Means Multiplexed Over the 10BASE-T1L PMA Sublayer"
(IEEE 802.3cg's Clause 146, non-LaM, pp. 13-16).


  We describe the links between group theory and psychology, in particular
through the works of Piaget. We show that groups appear universally in his
description of children's intelligence, and that the notion of groupoid, which
was little considered in psychology, may be fundamental. We study in particular
the applicability of group theory concepts to the development of educative
games.


  We study models that produce a Higgs boson plus photon ($h^0 \gamma$)
resonance at the LHC. When the resonance is a $Z'$ boson, decays to $h^0
\gamma$ occur at one loop. If the $Z'$ boson couples at tree-level to quarks,
then the $h^0 \gamma$ branching fraction is typically of order $10^{-5}$ or
smaller. Nevertheless, there are models that would allow the observation of $Z'
\to h^0 \gamma$ at $\sqrt{s} = 13$ TeV with a cross section times branching
fraction larger than 1 fb for a $Z'$ mass in the 200--450 GeV range, and larger
than 0.1 fb for a mass up to 800 GeV. The 1-loop decay of the $Z'$ into lepton
pairs competes with $h^0 \gamma$, even if the $Z'$ couplings to leptons vanish
at tree level. We also present a model in which a $Z'$ boson decays into a
Higgs boson and a pair of collimated photons, mimicking an $h^0 \gamma$
resonance. In this model, the $h^0 \gamma$ resonance search would be the
discovery mode for a $Z'$ as heavy as 2 TeV. When the resonance is a scalar,
although decay to $h^0 \gamma$ is forbidden by angular momentum conservation,
the $h^0$ plus collimated photons channel is allowed. We comment on prospects
of observing an $h^0 \gamma$ resonance through different Higgs decays, on
constraints from related searches, and on models where $h^0$ is replaced by a
nonstandard Higgs boson.


  We develop a coarse grained (CG) approach for efficiently simulating calcium
dynamics in the endoplasmic reticulum membrane based on a fine stochastic
lattice gas model. By grouping neighboring microscopic sites together into CG
cells and deriving CG reaction rates using local mean field approximation, we
perform CG kinetic Monte Carlo (kMC) simulations and find the results of CG-kMC
simulations are in excellent agreement with that of the microscopic ones.
Strikingly, there is an appropriate range of coarse proportion $m$,
corresponding to the minimal deviation of the phase transition point compared
to the microscopic one. For fixed $m$, the critical point increases
monotonously as the system size increases, especially, there exists scaling law
between the deviations of the phase transition point and the system size.
Moreover, the CG approach provides significantly faster Monte Carlo simulations
which are easy to implement and are directly related to the microscopics, so
that one can study the system size effects at the cost of reasonable
computational time.


  We show that for nice enough $\mathbb{N}$-graded $\mathbb{E}_2$-algebras, a
diagonal vanishing line in $\mathbb{E}_1$-homology of gives rise to slope $1$
homological stability. This is an integral version of a result by
Kupers-Miller-Patzt.


  After the completion of the gallium solar neutrino experiments at the
Laboratori Nazionali del Gran Sasso (GALLEX}: 1991-1997; GNO: 1998-2003) we
have retrospectively updated the GALLEX results with the help of new technical
data that were impossible to acquire for principle reasons before the
completion of the low rate measurement phase (that is, before the end of the
GNO solar runs). Subsequent high rate experiments have allowed the calibration
of absolute internal counter efficiencies and of an advanced pulse shape
analysis for counter background discrimination. The updated overall result for
GALLEX (only) is (73.4 +7.1 -7.3) SNU. This is 5.3% below the old value of
(77.5 + 7.5 -7.8) SNU (PLB 447 (1999) 127-133) with a substantially reduced
error. A similar reduction is obtained from the reanalysis of the 51Cr neutrino
source experiments of 1994/1995.


  Laser-based angle-resolved photoemission spectroscopy (ARPES) and two-photon
photoemission spectroscopy (2PPES) are employed to study the valence electronic
structure of the Weyl semimetal candidate Td-WTe$_2$ along two high symmetry
directions and for binding energies between $\approx$ -1 eV and 5 eV. The
experimental data show a good agreement with band structure calculations.
Polarization dependent measurements provide furthermore information on initial
and intermediate state symmetry properties with respect to the mirror plane of
the Td structure of WTe$_2$.


  We study the ground-state structure of nuclei in the vicinity of the
one-neutron dripline within the latest version of the quark-meson coupling
(QMC) model with a particular emphasis on 23O. For this nucleus the model
predicts a [22O(0+) + n (2s_{1/2})] configuration for its ground state, with a
one neutron separation energy in close agreement with the corresponding
experimental value. The wave function describing the valence neutron-core
relative motion was then used to calculate the Coulomb dissociation of 23O on a
lead target at a beam energy of 422 MeV/nucleon. The experimental neutron-core
relative energy spectrum and the total one-neutron removal cross sections are
well described by the calculations. The widths of the longitudinal momentum
distributions of the 22O fragment are found to be broad, which do not support
the formation of a neutron halo in this nucleus.


  We propose a robust method for constructing conditionally valid prediction
intervals based on models for conditional distributions such as quantile and
distribution regression. Our approach can be applied to important prediction
problems including cross-sectional prediction, k-step-ahead forecasts,
synthetic controls and counterfactual prediction, and individual treatment
effects prediction. Our method exploits the probability integral transform and
relies on permuting estimated ranks. Unlike regression residuals, ranks are
independent of the predictors, allowing us to construct conditionally valid
prediction intervals under heteroskedasticity. We establish approximate
conditional validity under consistent estimation and provide approximate
unconditional validity under model misspecification, overfitting, and with time
series data. We also propose a simple "shape" adjustment of our baseline method
that yields optimal prediction intervals.


  Classical-particle trajectories are calculated for the static Einstein
universe without requiring that the 3-space be closed and curved. Freely-moving
test particles are found to return to their starting positions because of
strong gravitational-field effects. Possible implications for the underlying
(quantum) theory of gravity are briefly discussed.


  A knotted surface in the 4-sphere may be described by means of a hyperbolic
diagram that captures the 0-section of a special Morse function, called a
hyperbolic decomposition. We show that every hyperbolic decomposition of a
knotted surface K defines a projection of K onto a 2-sphere, whose set of
critical values is the hyperbolic diagram of K. We apply such projections,
called flattenings, to define three invariants of knotted surfaces: the
layering, the trunk and the partition number. The basic properties of
flattenings and their derived invariants are obtained. Our construction is used
to study flattenings of satellite 2-knots.


  Gradient inversion attack enables recovery of training samples from model
gradients in federated learning (FL), and constitutes a serious threat to data
privacy. To mitigate this vulnerability, prior work proposed both principled
defenses based on differential privacy, as well as heuristic defenses based on
gradient compression as countermeasures. These defenses have so far been very
effective, in particular those based on gradient compression that allow the
model to maintain high accuracy while greatly reducing the effectiveness of
attacks. In this work, we argue that such findings underestimate the privacy
risk in FL. As a counterexample, we show that existing defenses can be broken
by a simple adaptive attack, where a model trained on auxiliary data is able to
invert gradients on both vision and language tasks.


  The rapid growth of news dissemination and user engagement on social media
has raised concerns about the influence and societal impact of biased and
unreliable information. As a response to these concerns, a substantial body of
research has been dedicated to understanding how users interact with different
news. However, this research has primarily analyzed publicly shared posts. With
a significant portion of engagement taking place within Facebook's private
sphere, it is therefore important to also consider the private posts. In this
paper, we present the first comprehensive comparison of the interaction
patterns and depth of engagement between public and private posts of different
types of news content shared on Facebook. To compare these patterns, we
gathered and analyzed two complementary datasets: the first includes
interaction data for all Facebook posts (private + public) referencing a
manually labeled collection of over 19K news articles, while the second
contains only interaction data for public posts tracked by CrowdTangle. As part
of our methodology, we introduce several carefully designed data processing
steps that address some critical aspects missed by prior works but that
(through our iterative discussions and feedback with the CrowdTangle team)
emerged as important to ensure fairness for this type of study. Our findings
highlight significant disparities in interaction patterns across various news
classes and spheres. For example, our statistical analysis demonstrates that
users engage significantly more deeply with news in the private sphere compared
to the public one, underscoring the pivotal role of considering both the public
and private spheres of Facebook in future research. Beyond its scholarly
impact, the findings of this study can benefit Facebook content moderators,
regulators, and policymakers, contributing to a healthier online discourse.


  This report presents our SmartSpace event handling framework for managing
smart-grids and renewable energy installations. SmartSpace provides decision
support for human stakeholders. Based on different datasources that feed into
our framework, a variety of analysis and decision steps are supported. These
decision steps are ultimately used to provide adequate information to human
stakeholders. The paper discusses potential data sources for decisions around
smart energy systems and introduces a spatio-temporal modeling technique for
the involved data. Operations to reason about the formalized data are provided.
Our spatio-temporal models help to provide a semantic context for the data.
Customized rules allow the specification of conditions under which information
is provided to stakeholders. We exemplify our ideas and present our
demonstrators including visualization capabilities.


  We show that the abundance and redshift distribution ($dN/dz$) of galaxy
clusters in future high--yield cluster surveys, combined with the spatial power
spectrum ($P_c(k)$) of the same clusters, can place significant constraints on
the evolution of the dark energy equation of state, $w=w(a)$. We evaluate the
expected errors on $w_a=-dw/da$ and other cosmological parameters using a
Fisher matrix approach, and simultaneously including cluster structure
evolution parameters in our analysis. We study three different types of
forthcoming surveys that will identify clusters based on their X-ray emission
(such as DUO, the Dark Universe Observatory), their Sunyaev--Zel'dovich (SZ)
decrement (such as SPT, the South Pole Telescope), or their weak lensing (WL)
shear (such as LSST, the Large Synoptic Survey Telescope). We find that
combining the cluster abundance and power spectrum significantly enhances
constraints from either method alone. We show that the weak-lensing survey can
deliver a constraint as tight as $\Delta w_a \sim 0.1$ on the evolution of the
dark energy equation of state, and that the X-ray and SZ surveys each yield
$\Delta w_a \sim 0.4$ separately, or $\Delta w_a \sim 0.2$ when these two
surveys are combined. For the X-ray and SZ surveys, constraints on dark energy
parameters are improved by a factor of two by combining the cluster data with
cosmic microwave background (CMB) anisotropy measurements by Planck, but
degrade by a factor of two if the survey is required to solve simultaneously
for cosmological and cluster structure evolution parameters. The constraint on
$w_a$ from the weak lensing survey is improved by $\sim 25$% with the addition
of Planck data.


  The needs to assess robust performances for complex systems and to answer
tighter regulatory processes (security, safety, environmental control, and
health impacts, etc.) have led to the emergence of a new industrial simulation
challenge: to take uncertainties into account when dealing with complex
numerical simulation frameworks. Therefore, a generic methodology has emerged
from the joint effort of several industrial companies and academic
institutions. EDF R&D, Airbus Group and Phimeca Engineering started a
collaboration at the beginning of 2005, joined by IMACS in 2014, for the
development of an Open Source software platform dedicated to uncertainty
propagation by probabilistic methods, named OpenTURNS for Open source Treatment
of Uncertainty, Risk 'N Statistics. OpenTURNS addresses the specific industrial
challenges attached to uncertainties, which are transparency, genericity,
modularity and multi-accessibility. This paper focuses on OpenTURNS and
presents its main features: openTURNS is an open source software under the LGPL
license, that presents itself as a C++ library and a Python TUI, and which
works under Linux and Windows environment. All the methodological tools are
described in the different sections of this paper: uncertainty quantification,
uncertainty propagation, sensitivity analysis and metamodeling. A section also
explains the generic wrappers way to link openTURNS to any external code. The
paper illustrates as much as possible the methodological tools on an
educational example that simulates the height of a river and compares it to the
height of a dyke that protects industrial facilities. At last, it gives an
overview of the main developments planned for the next few years.


  Artificial Intelligence (AI) has been adopted in a wide range of domains.
This shows the imperative need to develop means to endow common people with a
minimum understanding of what AI means. Combining visual programming and WiSARD
weightless artificial neural networks, this article presents a new methodology,
AI from concrete to abstract (AIcon2abs), to enable general people (including
children) to achieve this goal. The main strategy adopted by is to promote a
demystification of artificial intelligence via practical activities related to
the development of learning machines, as well as through the observation of
their learning process. Thus, it is possible to provide subjects with skills
that contributes to making them insightful actors in debates and decisions
involving the adoption of artificial intelligence mechanisms. Currently,
existing approaches to the teaching of basic AI concepts through programming
treat machine intelligence as an external element/module. After being trained,
that external module is coupled to the main application being developed by the
learners. In the methodology herein presented, both training and classification
tasks are blocks that compose the main program, just as the other programming
constructs. As a beneficial side effect of AIcon2abs, the difference between a
program capable of learning from data and a conventional computer program
becomes more evident. In addition, the simplicity of the WiSARD weightless
artificial neural network model enables easy visualization and understanding of
training and classification tasks internal realization.


  Recently, the deviation of the ratios $R(D)$, $R(D^{*})$ and $R(J/\psi)$ have
been found between experimental data and the Standard Model predictions, which
may be the hint of New Physics. In this work, we calculate these ratios within
the Standard Model by using the improved instantaneous Bethe-Salpeter method.
The emphasis is pad to the relativistic correction of the form factors. The
results are $R(D)=0.312 ^{+0.006}_{-0.007}$, $R(D^*)= 0.249^{+0.001}_{-0.002}$,
$R(D_s)=0.320 ^{+0.009}_{-0.009}$, $R(D^*_s)=0.251 ^{+0.002}_{-0.003}$,
$R(\eta_c)=0.384 ^{+0.032}_{-0.042}$, and $R(J/\psi)=0.267 ^{+0.009}_{-0.011}$,
which are consistent with predictions of other models and the experimental
data. The semileptonic decay rates and corresponding form factors at zero
recoil are also given.


  Open Inflation has recently been suggested as a possible way out of the age
crisis caused by observations of a large rate of expansion of the universe, in
conflict with the existence of very old globular clusters. It proposes that our
local patch of the universe originated in a quantum tunneling event, with the
formation of a single bubble within which our universe inflated to almost
flatness. I review the different models proposed together with their
predictions for the amplitude of temperature anisotropies in the cosmic
microwave background.


  Binary neutron star (BNS) mergers are the leading model to explain the
phenomenology of short gamma-ray bursts (SGRBs), which are among the most
luminous explosions in the universe. Recent observations of long-lasting X-ray
afterglows of SGRBs challenge standard paradigms and indicate that in a large
fraction of events a long-lived neutron star (NS) may be formed rather than a
black hole. Understanding the mechanisms underlying these afterglows is
necessary in order to address the open questions concerning the nature of SGRB
central engines. However, recent theoretical progress has been hampered by the
fact that the timescales of interest for the afterglow emission are
inaccessible to numerical relativity simulations. Here we present a detailed
model to bridge the gap between numerical simulations of the merger process and
the relevant timescales for the afterglows, assuming that the merger results in
a long-lived NS. This model is formulated in terms of a set of coupled
differential equations that follow the evolution of the post-merger system and
predict its electromagnetic (EM) emission in a self-consistent way, starting
from initial data that can be extracted from BNS merger simulations and taking
into account the most relevant radiative processes. Moreover, the model can
accomodate the collapse of the remnant NS at any time during the evolution as
well as different scenarios for the prompt SGRB emission. A second major reason
of interest for BNS mergers is that they are considered the most promising
source of gravitational waves (GWs) for detection with the advanced
ground-based detector network LIGO/Virgo coming online this year.
Multimessenger astronomy with joint EM and GW observations of the merger and
post-merger phase can greatly enhance the scientific output of either type of
observation. However, the actual benefit depends on ...


  The use of graphene for antennas and other electromagnetic passives could
bring significant benefit such as extreme miniaturization, monolithic
integration with graphene RF nanoelectronics, efficient dynamic tuning, and
even transparency and mechanical flexibility. Though recently different related
theoretical works have been presented, relatively few applications have been
proposed and realistically assessed. In this invited talk we will briefly
review the main properties of graphene and the state of the art in its
theoretical and experimental characterization. Then, we will discuss a number
of potential antenna applications from microwave to THz, providing in each case
a critical assessment of the benefits, limitations, and remaining issues
towards actual real-life implementations. Here we provide a brief overview of
different devices and associated developments in our group discussed in the
talk, including graphene antennas and reflectarrays at microwave and THz,
plasmonic switches, isotropic and anisotropic meta-surfaces, or graphene
RF-NEMS.


  The paper is centered around a new proof of the infinitesimal rigidity of
smooth closed surfaces with everywhere positive Gauss curvature. We use a
reformulation that replaces deformation of an embedding by deformation of the
metric inside the body bounded by the surface. The proof is obtained by
studying derivatives of the Hilbert-Einstein functional with boundary term.
This approach is in a sense dual to proving the Gauss infinitesimal rigidity,
that is rigidity with respect to the Gauss curvature parametrized by the Gauss
map, by studying derivatives of the volume bounded by the surface. We recall
that Blaschke's classical proof of the infinitesimal rigidity is also related
to the Gauss infinitesimal rigidity, but in a different way: while Blaschke
uses Gauss rigidity of the same surface, we use the Gauss rigidity of the polar
dual. In the spherical and in the hyperbolic-de Sitter space, there is a
perfect duality between the Hilbert-Einstein functional and the volume, as well
as between both kinds of rigidity. We also indicate directions for future
research, including the infinitesimal rigidity of convex cores of hyperbolic
3--manifolds.


  The actual knowledge of the structure and future evolution of our universe is
based on the use of cosmological models, which can be tested through the
so-called 'probes', namely astrophysical phenomena, objects or structures with
peculiar properties that can help to discriminate among different cosmological
models. Among all the existing probes, of particular importance are the
Supernovae Ia (SNe Ia) and the Gamma Ray Bursts (GRBs): the former are
considered among the best standard candles so far discovered but suffer from
the fact that can be observed until redshift $z=2.26$, while the latter are
promising standardizable candles which have been observed up to $z=9.4$,
surpassing even the farthest quasar known to date, which is at $z=7.64$. The
standard candles can be used to test the cosmological models and to give the
expected values of cosmological parameters, in particular the Hubble constant
value. The Hubble constant is affected by the so-called \say{Hubble constant
tension}, a discrepancy in more than 4 $\sigma$ between its value measured with
local probes and its value measured through the cosmological probes. The
increase in the number of observed SNe Ia, as well as the future
standardization of GRBs through their correlations, will surely be of help in
alleviating the Hubble constant tension and in explaining the structure of the
universe at higher redshifts. A promising class of GRBs for future
standardization is represented by the GRBs associated with Supernovae Ib/c,
since these present features similar to the SNe Ia class and obey a tight
correlation between their luminosity at the end of the plateau emission in
X-rays and the time at the end of the plateau in the rest-frame.


  We deposit droplets of nanorods dispersed in solvents on substrate surfaces
and let the solvent evaporate. We find that strong contact line pinning leads
to dense nanorod deposition inside coffee stain fringes, where we observe
large-scale lateral ordering of the nanorods with the long axis of the rods
oriented parallel to the contact line. We observe birefringence of these coffee
stain fringes by polarized microscopy and we find the direction of the
extraordinary refractive index parallel to the long axis of the nanorods.


  For satellite images, the presence of clouds presents a problem as clouds
obscure more than half to two-thirds of the ground information. This problem
causes many issues for reliability in a noise-free environment to communicate
data and other applications that need seamless monitoring. Removing the clouds
from the images while keeping the background pixels intact can help address the
mentioned issues. Recently, deep learning methods have become popular for
researching cloud removal by demonstrating promising results, among which
Generative Adversarial Networks (GAN) have shown considerably better
performance. In this project, we aim to address cloud removal from satellite
images using AttentionGAN and then compare our results by reproducing the
results obtained using traditional GANs and auto-encoders. We use RICE dataset.
The outcome of this project can be used to develop applications that require
cloud-free satellite images. Moreover, our results could be helpful for making
further research improvements.


  The fitness landscape encodes the mapping of genotypes to fitness and
provides a succinct representation of possible trajectories followed by an
evolving population. Evolutionary accessibility is quantified by the existence
of fitness-monotonic paths connecting far away genotypes. Studies of
accessibility percolation use probabilistic fitness landscape models to explore
the emergence of such paths as a function of the initial fitness, the
parameters of the landscape or the structure of the genotype graph. This
chapter reviews these studies and discusses their implications for the
predictability of evolutionary processes.


  Soil as a complex multi-phase porous material typical exhibits several
distributed relaxation processes in the frequency range from 1 MHz to
approximately 10 GHz of interest in applications. To relate physico-chemical
material parameters to the dielectric relaxation behavior, measured dielectric
relaxation spectra have to be parameterized. In this context, a broadband
numerical 3D FEM study was carried out to analyze the possibilities and
limitations in the characterization of the relaxation processes in complex
systems.


  Pair production of W bosons constitutes an important background to Higgs
boson and new physics searches at the Large Hadron Collider LHC. We have
calculated the loop-induced gluon-fusion process gg -> W*W* -> leptons,
including intermediate light and heavy quarks and allowing for arbitrary
invariant masses of the W bosons. While formally of next-to-next-to-leading
order, the gg -> W*W* -> leptons process is enhanced by the large gluon flux at
the LHC and by experimental Higgs search cuts, and increases the
next-to-leading order WW background estimate for Higgs searches by about 30%.
We have extended our previous calculation to include the contribution from the
intermediate top-bottom massive quark loop and the Higgs signal process. We
provide updated results for cross sections and differential distributions and
study the interference between the different gluon scattering contributions. We
describe important analytical and numerical aspects of our calculation and
present the public GG2WW event generator.


  Newton law arising due to the gravity localized on the general singular brane
embedded in $AdS_5$ bulk is examined in the absence or presence of the 4d
induced Einstein term. For the RS brane, apart from the subleading correction,
Newton potential obeys 4d-type and $5d$-type gravitational law at long- and
short-ranges if it were not for the induced Einstein term. The 4d induced
Einstein term generates an intermediate range at short distance, in which the
$5d$ Newton potential $1/r^2$ emerges. For Neumann brane the long-range
behavior of Newton potential is exponentially suppressed regardless of the
existence of the induced Einstein term. For Dirichlet brane the expression of
Newton potential is dependent on the renormalized coupling constant $v^{ren}$.
At particular value of $v^{ren}$ Newton potential on Dirichlet brane exhibits a
similar behavior to that on RS brane. For other values the long-range behavior
of Newton potential is exponentially suppressed as that in Neumann brane.


  We develop a simple formalism of biased tracers that we dub $\mathit{Monkey\
bias}$. In this formalism, a biased tracer field is constructed directly in
terms of the linear matter fluctuation field and the set of derivative
operators acting on it. Such bias expansion is first organized based on the
general structure of non-linear dynamical equations for the biased tracers.
Further physical conditions, like the equivalence principle, are imposed on
tree-level correlators utilising the consistency relations. We obtain the bias
expansion up to the third-order in linear matter fluctuation in the generalized
$\Lambda$CDM background, which reproduces the previous results in the limit of
the EdS universe. This algorithmic construction of our bias operator basis is
well suited for extensions towards higher-order bias fields. Moreover, this
formalism reveals that biased tracer dynamics in generalized $\Lambda$CDM
background is not entirely degenerate with the rest of bias parameters, thus
opening a possibility of testing the background cosmology through the
observations of biased tracers.


  Quarks of other flavours than up and down, i.e. $s$, $c$, and $b$ quarks,
have been long recognized as effective probes of the structure of hot QCD
matter. In this talk, I review some of the motivations for their investigation
and discuss the salient results obtained so far, with a focus on the results
from the Relativistic Heavy Ion Collider (RHIC). Some ideas for future studies
are also mentioned.


  Data is a critical aspect of the world we live in. With systems producing and
consuming vast amounts of data, it is essential for businesses to digitally
transform and be equipped to derive the most value out of data. Data analytics
techniques can be used to augment strategic decision-making. While this overall
objective of data analytics remains fairly constant, the data itself can be
available in numerous forms and can be categorized under various contexts. In
this paper, we aim to research terms such as 'small' and 'big' data, understand
their attributes, and look at ways in which they can add value. Specifically,
the paper probes into the question "If we didn't solve small data in the past,
how can we solve Big Data today?". Based on the research, it can be inferred
that, regardless of how small data might have been used, organizations can
still leverage big data with the right technology and business vision.


  We analyze the Stern-Gerlach experiment in phase space with the help of the
matrix Wigner function, which includes the spin degree of freedom. Such
analysis allows for an intuitive visualization of the quantum dynamics of the
apparatus. We include the interaction with the environment, as described by the
Caldeira-Leggett model. The diagonal terms of the matrix provide us with
information about the two components of the state, that arise from interaction
with the magnetic field gradient. In particular, from the marginals of these
components, we obtain an analytical formula for the position and momentum
probability distributions in presence of decoherence, that show a diffusive
behavior for large values of the decoherence parameter. These features limit
the dynamics of the present model. We also observe the decay of the
non-diagonal terms with time, and use this fact to quantify the amount of
decoherence, from the norm of those terms in phase space. From here, we can
define a decoherence time scale, which differs from previous results that make
use of the same model.


  Persistent activity in neuronal populations has been shown to represent the
spatial position of remembered stimuli. Networks that support bump attractors
are often used to model such persistent activity. Such models usually exhibit
translational symmetry. Thus activity bumps are neutrally stable, and
perturbations in position do not decay away. We extend previous work on bump
attractors by constructing model networks capable of encoding the certainty or
salience of a stimulus stored in memory. Such networks support bumps that are
not only neutrally stable to perturbations in position, but also perturbations
in amplitude. Possible bump solutions then lie on a two-dimensional attractor,
determined by a continuum of positions and amplitudes. Such an attractor
requires precisely balancing the strength of recurrent synaptic connections.
The amplitude of activity bumps represents certainty, and is determined by the
initial input to the system. Moreover, bumps with larger amplitudes are more
robust to noise, and over time provide a more faithful representation of the
stored stimulus. In networks with separate excitatory and inhibitory
populations, generating bumps with a continuum of possible amplitudes, requires
tuning the strength of inhibition to precisely cancel background excitation.


  While the helical character of the edge channels responsible for charge
transport in the quantum spin Hall regime of a two-dimensional topological
insulator is by now well established, an experimental confirmation that the
transport in the edge channels is spin-polarized is still outstanding. We
report experiments on nanostructures fabricated from HgTe quantum wells with an
inverted band structure, in which a split gate technique allows us to combine
both quantum spin Hall and metallic spin Hall transport in a single device. In
these devices, the quantum spin Hall effect can be used as a spin current
injector and detector for the metallic spin Hall effect, and vice versa,
allowing for an all-electrical detection of spin polarization.


  A word $u$ is a scattered factor of $w$ if $u$ can be obtained from $w$ by
deleting some of its letters. That is, there exist the (potentially empty)
words $u_1,u_2,..., u_n$, and $v_0,v_1,..,v_n$ such that $u = u_1u_2...u_n$ and
$w = v_0u_1v_1u_2v_2...u_nv_n$. We consider the set of length-$k$ scattered
factors of a given word w, called here $k$-spectrum and denoted
$\ScatFact_k(w)$. We prove a series of properties of the sets $\ScatFact_k(w)$
for binary strictly balanced and, respectively, $c$-balanced words $w$, i.e.,
words over a two-letter alphabet where the number of occurrences of each letter
is the same, or, respectively, one letter has $c$-more occurrences than the
other. In particular, we consider the question which cardinalities $n=
|\ScatFact_k(w)|$ are obtainable, for a positive integer $k$, when $w$ is
either a strictly balanced binary word of length $2k$, or a $c$-balanced binary
word of length $2k-c$. We also consider the problem of reconstructing words
from their $k$-spectra.


  It is well established that late-type main-sequence stars display a
relationship between X-ray activity and the Rossby number, $Ro$, the ratio of
rotation period to the convective turnover time. This manifests itself as a
saturated regime (where X-ray activity is constant) and an unsaturated regime
(where X-ray activity anti-correlates with the Rossby number). However, this
relationship breaks down for the fastest rotators. We cross-correlated
SuperWASP visually classified photometric light curves and ASAS-SN
automatically classified photometric light curves with XMM-Newton X-ray
observations to identify 3,178 stars displaying a photometrically defined
rotational modulation in their light curve and corresponding X-ray
observations. We fitted a power-law to characterise the rotation-activity
relation of 900 main-sequence stars. We identified that automatically
classified rotationally modulated light curves are not as reliable as visually
classified light curves for this work. We found a power-law index in the
unsaturated regime of G- to M-type stars of $\beta=-1.84\pm0.18$ for the
SuperWASP catalogue, in line with the canonical value of $\beta=-2$. We find
evidence of supersaturation in the fastest rotating K-type stars, with a
power-law index of $\beta_{s}=1.42\pm0.26$.


  We report the discovery of a fifth image in the large separation lensed
quasar system SDSS J1004+4112. A faint point source located 0.2'' from the
center of the brightest galaxy in the lensing cluster is detected in images
taken with the Advanced Camera for Surveys (ACS) and the Near Infrared Camera
and Multi-Object Spectrometer (NICMOS) on the Hubble Space Telescope. The flux
ratio between the point source and the brightest lensed component in the ACS
image is similar to that in the NICMOS image. The location and brightness of
the point source are consistent with lens model predictions for a lensed image.
We therefore conclude that the point source is likely to be a fifth image of
the source quasar. In addition, the NICMOS image reveals the lensed host galaxy
of the source quasar, which can strongly constrain the structure of the lensing
critical curves and thereby the mass distribution of the lensing cluster.


  Bayesian optimization is a widely used technique for optimizing black-box
functions, with Expected Improvement (EI) being the most commonly utilized
acquisition function in this domain. While EI is often viewed as distinct from
other information-theoretic acquisition functions, such as entropy search (ES)
and max-value entropy search (MES), our work reveals that EI can be considered
a special case of MES when approached through variational inference (VI). In
this context, we have developed the Variational Entropy Search (VES)
methodology and the VES-Gamma algorithm, which adapts EI by incorporating
principles from information-theoretic concepts. The efficacy of VES-Gamma is
demonstrated across a variety of test functions and read datasets, highlighting
its theoretical and practical utilities in Bayesian optimization scenarios.


  This article is meant to give a lucid and widely accessible, self-contained
account of a novel way of performing arithmetic operations on fuzzy intervals.
Based on two formulae of generalized inversion (the first in close analogy to
the inversion of cumulative distribution functions in probability and
statistics, and subsequent re-inversion which in this form seems to be new in
the literature) the technique could prove to be of some importance for the
practical handling of fuzzy intervals whose characterizing functions are
discontinuous and/or not strictly monotonic, e.g. piecewise constant.
Notwithstanding its innovative nature, the article is written in the style of
an introductory textbook featuring a multitude of illustrated examples.


  In this paper, we study the parallel and the space complexity of the graph
isomorphism problem (\GI{}) for several parameterizations. Let
$\mathcal{H}=\{H_1,H_2,\cdots,H_l\}$ be a finite set of graphs where
$|V(H_i)|\leq d$ for all $i$ and for some constant $d$. Let $\mathcal{G}$ be an
$\mathcal{H}$-free graph class i.e., none of the graphs $G\in \mathcal{G}$
contain any $H \in \mathcal{H}$ as an induced subgraph. We show that \GI{}
parameterized by vertex deletion distance to $\mathcal{G}$ is in a
parameterized version of $\AC^1$, denoted $\PL$-$\AC^1$, provided the colored
graph isomorphism problem for graphs in $\mathcal{G}$ is in $\AC^1$. From this,
we deduce that \GI{} parameterized by the vertex deletion distance to cographs
is in $\PL$-$\AC^1$.
  The parallel parameterized complexity of \GI{} parameterized by the size of a
feedback vertex set remains an open problem. Towards this direction we show
that the graph isomorphism problem is in $\PL$-$\TC^0$ when parameterized by
vertex cover or by twin-cover.
  Let $\mathcal{G}'$ be a graph class such that recognizing graphs from
$\mathcal{G}'$ and the colored version of \GI{} for $\mathcal{G}'$ is in
logspace ($\L$). We show that \GI{} for bounded vertex deletion distance to
$\mathcal{G}'$ is in $\L$. From this, we obtain logspace algorithms for \GI{}
for graphs with bounded vertex deletion distance to interval graphs and graphs
with bounded vertex deletion distance to cographs.


  Many models of one-dimensional local random growth are expected to lie in the
Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface
profile at advanced time may be viewed in scaled coordinates specified via
characteristic KPZ scaling exponents of one-third and two-thirds. When the long
time limit of this scaled interface is taken, it is expected -- and proved for
a few integrable models -- that, up to a parabolic shift, the Airy$_2$ process
$\mathcal{A}:\mathbb{R} \to \mathbb{R}$ is obtained. This process may be
embedded via the Robinson-Schensted-Knuth correspondence as the uppermost curve
in an $\mathbb{N}$-indexed system of random continuous curves, the Airy line
ensemble.
  Among our principal results is the assertion that the Airy$_2$ process enjoys
a very strong similarity to Brownian motion $B$ (of rate two) on unit-order
intervals; as a consequence, the Radon-Nikodym derivative of the law of
$\mathcal{A}$ on say $[-1,1]$, with respect to the law of $B$ on this interval,
lies in every $L^p$ space for $p \in (1,\infty)$.
  Our technique of proof harnesses a probabilistic resampling or {\em Brownian
Gibbs} property satisfied by the Airy line ensemble after parabolic shift, and
this article develops Brownian Gibbs analysis of this ensemble begun in [CH14]
and pursued in [Ham19a]. Our Brownian comparison for scaled interface profiles
is an element in the ongoing programme of studying KPZ universality via
probabilistic and geometric methods of proof, aided by limited but essential
use of integrable inputs. Indeed, the comparison result is a useful tool for
studying this universality class. We present and prove several applications,
concerning for example the structure of near ground states in Brownian last
passage percolation, or Brownian structure in scaled interface profiles that
arise from evolution from any element in a very general class of initial data.


  I present results from the first global hydrodynamical simulations of the
elliptical instability in a tidally deformed gaseous planet (or star) with a
free surface. The elliptical instability is potentially important for tidal
evolution of the shortest-period hot Jupiters. I model the planet as a
spin-orbit aligned or anti-aligned, and non-synchronously rotating, tidally
deformed, homogeneous fluid body. A companion paper presented an analysis of
the global modes and instabilities of such a planet. Here I focus on the
nonlinear evolution of the elliptical instability. This is observed to produce
bursts of turbulence that drive the planet towards synchronism with its orbit
in an erratic manner. If the planetary spin is initially anti-aligned, the
elliptical instability also drives spin-orbit alignment on a similar timescale
as the spin synchronisation. The instability generates differential rotation
inside the planet in the form of zonal flows, which play an important role in
the saturation of the instability, and in producing the observed burstiness.
These results are broadly consistent with the picture obtained using a local
Cartesian model (where columnar vortices played the role of zonal flows). I
also simulate the instability in a container that is rigid (but stress-free)
rather than free, finding broad quantitative agreement. The dissipation
resulting from the elliptical instability could explain why the shortest-period
hot Jupiters tend to have circular orbits inside about 2-3 days, and predicts
spin-synchronisation (and spin-orbit alignment) out to about 10-15 days.
However, other mechanisms must be invoked to explain tidal circularisation for
longer orbital periods.


  A new algorithm for solving the solution of the linear-quadratic optimization
problem (LQP) with unseparated boundary conditions in the continuous case is
given. Using the properties of symmetry of the corresponding Hamiltonian
matrix, the Euler-Lagrange equations, it is shown that linear algebraic
equations for determining the missing initial data of the system being solved
have a symmetric principal matrix. The results are illustrated by the example
of LQP optimization (stationary case) with minimal control actions.


  In this paper we investigate dynamics of the modified loop quantum cosmology
models using dynamical systems methods. Modifications considered come from the
choice of the different field strength operator $\hat{F}$ and result in
different forms of the effective Hamiltonian. Such an ambiguity of the choice
of this expression from some class of functions is allowed in the framework of
loop quantisation. Our main goal is to show how such modifications can
influence the bouncing universe scenario in the loop quantum cosmology. In
effective models considered we classify all evolutional paths for all
admissible initial conditions. The dynamics is reduced to the form of a
dynamical system of the Newtonian type on a 2-dimensional phase plane. These
models are equivalent dynamically to the FRW models with the decaying effective
cosmological term parametrised by the canonical variable $p$ (or by the scale
factor $a$). We find that for the positive cosmological constant there is a
class of oscillating models without the initial and final singularities. The
new phenomenon is the appearance of curvature singularities for the finite
values of the scale factor, but we find that for the positive cosmological
constant these singularities can be avoided. For the positive cosmological
constant the evolution begins at the asymptotic state in the past represented
by the deSitter contracting (deS$_{-}$) spacetime or the static Einstein
universe H=0 or $H=-\infty$ state and reaches the deSitter expanding state
(deS$_{+}$), the state H=0 or $H=+\infty$ state. In the case of the negative
cosmological constant we obtain the past and future asymptotic states as the
Einstein static universes.


  Short time spectral features such as mel frequency cepstral
coefficients(MFCCs) have been previously deployed in state of the art speaker
recognition systems, however lesser heed has been paid to short term spectral
features that can be learned by generative learning models from speech signals.
Higher dimensional encoders such as deep belief networks (DBNs) could improve
performance in speaker recognition tasks by better modelling the statistical
structure of sound waves. In this paper, we use short term spectral features
learnt from the DBN augmented with MFCC features to perform the task of speaker
recognition. Using our features, we achieved a recognition accuracy of 0.95 as
compared to 0.90 when using standalone MFCC features on the ELSDSR dataset.


  The Riesz transform of $u$ : $\mathcal{S}(\mathbb{R}^n) \rightarrow
\mathcal{S'}(\mathbb{R}^n)$ is defined as a convolution by a singular kernel,
and can be conveniently expressed using the Fourier Transform and a simple
multiplier. We extend this analysis to higher order Riesz transforms, i.e. some
type of singular integrals that contain tensorial polyadic kernels and define
an integral transform for functions $\mathcal{S}(\mathbb{R}^n) \rightarrow
\mathcal{S'}(\mathbb{R}^{ n \times n \times \dots n})$. We show that the
transformed kernel is also a polyadic tensor, and propose a general method to
compute explicitely the Fourier mutliplier. Analytical results are given, as
well as a recursive algorithm, to compute the coefficients of the transformed
kernel. We compare the result to direct numerical evaluation, and discuss the
case $n=2$, with application to image analysis.


  The design of electron multiplying CCD cameras require a very different
approach from that appropriate for slow scan CCD operation. This paper
describes the main problems in using electron multiplying CCDs for high-speed,
photon counting applications in astronomy and how these may be substantially
overcome. With careful design it is possible to operate the E2V Technologies
L3CCDs at rates well in excess of that claimed by the manufacturer, and that
levels of clock induced charge dramatically lower than those experienced with
commercial cameras that need to operate at unity gain. Measurements of the
performance of the E2V Technologies CCD201 operating at 26 MHz will be
presented together with a guide to the effective reduction of clock induced
charge levels. Examples of astronomical results obtained with our cameras are
presented.


  It is shown, by DFT calculations, that the uniform functionalization of upper
layer of graphite by hydrogen or fluorine does not change essentially its
bonding energy with the underlying layers, whereas the functionalization by
phenyl groups decreases the bonding energy by a factor of approximately ten.
This means that the functionalized monolayer in the latter case can be easily
separated by mild sonication. According to our computational results, such
layers can be cleaned up to pure graphene, as well as functionalized further up
to 25% coverage, without essential difficulties. The energy gap within the
interval from 0.5 to 3 eV can be obtained by such one-side funtionalization
using different chemical species.


  Quantum chromodynamics (QCD) is the theory of subnuclear physics, aiming at
mod- eling the strong nuclear force, which is responsible for the interactions
of nuclear particles. Lattice QCD (LQCD) is the corresponding discrete
formulation, widely used for simula- tions. The computational demand for the
LQCD is tremendous. It has played a role in the history of supercomputers, and
has also helped defining their future. Designing efficient LQCD codes that
scale well on large (probably hybrid) supercomputers requires to express many
levels of parallelism, and then to explore different algorithmic solutions.
While al- gorithmic exploration is the key for efficient parallel codes, the
process is hampered by the necessary coding effort. We present in this paper a
domain-specific language, QIRAL, for a high level expression of parallel
algorithms in LQCD. Parallelism is expressed through the mathematical struc-
ture of the sparse matrices defining the problem. We show that from these
expressions and from algorithmic and preconditioning formulations, a parallel
code can be automatically generated. This separates algorithms and mathematical
formulations for LQCD (that be- long to the field of physics) from the
effective orchestration of parallelism, mainly related to compilation and
optimization for parallel architectures.


  We give a mathematical foundation for, and numerical demonstration of, the
existence of mean curvature 1 surfaces of genus 1 with either two elliptic ends
or two hyperbolic ends in de Sitter 3-space. An end of a mean curvature 1
surface is an ``elliptic end'' (resp. a ``hyperbolic end'') if the monodromy
matrix at the end is diagonalizable with eigenvalues in the unit circle (resp.
in the reals). Although the existence of the surfaces is numerical, the types
of ends are mathematically determined.


  In this letter we propose a new and model-independent cosmological test for
the distance-duality (DD) relation, \eta=D_{L}(z)(1+z)^{-2}/D_{A}(z)=1, where
D_{L} and D_{A} are, respectively, the luminosity and angular diameter
distances. For $D_L$ we consider two sub-samples of SNe type Ia taken from
Constitution data (2009) whereas $D_A$ distances are provided by two samples of
galaxy clusters compiled by De Fillipis et al. (2005) and Bonamente et al.
(2006) by combining Sunyaev-Zeldovich effect (SZE) and X-ray surface
brightness. The SNe Ia redshifts of each sub-sample were carefully chosen to
coincide with the ones of the associated galaxy cluster sample (\Delta z<0.005)
thereby allowing a direct test of DD relation. Since for very low redshifts,
D_{A}(z) \approxeq D_{L}(z), we have tested the DD relation by assuming that
$\eta$ is a function of the redshift parametrized by two different expressions:
\eta(z) = 1 + \eta_{0}z and \eta(z) = 1 + \eta_{0}z/(1+z), where \eta_0 is a
constant parameter quantifying a possible departure from the strict validity of
the reciprocity relation (\eta_0=0). In the best scenario (linear
parametrization) we obtain \eta_{0} = -0.28^{+ 0.44}_{- 0.44} (2\sigma$,
statistical + systematic errors) for de Fillipis et al. sample (eliptical
geometry), a result only marginally compatible with the DD relation. However,
for Bonamente et al. sample (spherical geometry) the constraint is \eta_{0} =
-0.42^{+ 0.34}_{- 0.34} (3\sigma$, statistical + systematic errors) which is
clearly incompatible with the duality-distance relation.


  The evolution of communication networks shows a clear shift of focus from
just improving the communications aspects to enabling new important services,
from Industry 4.0 to automated driving, virtual/augmented reality, Internet of
Things (IoT), and so on. This trend is evident in the roadmap planned for the
deployment of the fifth generation (5G) communication networks. This ambitious
goal requires a paradigm shift towards a vision that looks at communication,
computation and caching (3C) resources as three components of a single holistic
system. The further step is to bring these 3C resources closer to the mobile
user, at the edge of the network, to enable very low latency and high
reliability services. The scope of this chapter is to show that signal
processing techniques can play a key role in this new vision. In particular, we
motivate the joint optimization of 3C resources. Then we show how graph-based
representations can play a key role in building effective learning methods and
devising innovative resource allocation techniques.


  We construct quantum effective action in spacetime with branes/boundaries.
This construction is based on the reduction of the underlying Neumann type
boundary value problem for the propagator of the theory to that of the much
more manageable Dirichlet problem. In its turn, this reduction follows from the
recently suggested Neumann-Dirichlet duality which we extend beyond the tree
level approximation. In the one-loop approximation this duality suggests that
the functional determinant of the differential operator subject to Neumann
boundary conditions in the bulk factorizes into the product of its Dirichlet
counterpart and the functional determinant of a special operator on the brane
-- the inverse of the brane-to-brane propagator. As a byproduct of this
relation we suggest a new method for surface terms of the heat kernel
expansion. This method allows one to circumvent well-known difficulties in heat
kernel theory on manifolds with boundaries for a wide class of generalized
Neumann boundary conditions. In particular, we easily recover several lowest
order surface terms in the case of Robin and oblique boundary conditions. We
briefly discuss multi-loop applications of the suggested Dirichlet reduction
and the prospects of constructing the universal background field method for
systems with branes/boundaries, analogous to the Schwinger-DeWitt technique.


  We study the preorder $\le_p$ on the family of subsets of an algebraically
closed field of characteristic $0$ defined by letting $A\le_pB $ if there
exists a polynomial $P$ such that $A=P^{-1}(B)$.


  The mathematical structure of the widely popular Sudoku puzzles is akin to
typical hard constraint satisfaction problems that lie at the heart of many
applications, including protein folding and the general problem of finding the
ground state of a glassy spin system. Via an exact mapping of Sudoku into a
deterministic, continuous-time dynamical system, here we show that the
difficulty of Sudoku translates into transient chaotic behavior exhibited by
the dynamical system. In particular, we show that the escape rate $\kappa$, an
invariant characteristic of transient chaos, provides a single scalar measure
of the puzzle's hardness, which correlates well with human difficulty level
ratings. Accordingly, $\eta = -\log_{10}{\kappa}$ can be used to define a
"Richter"-type scale for puzzle hardness, with easy puzzles falling in the
range $0 < \eta \leq 1$, medium ones within $1 < \eta \leq 2$, hard in $2 <
\eta \leq 3$ and ultra-hard with $\eta > 3$. To our best knowledge, there are
no known puzzles with $\eta > 4$.


  This paper introduces a simple formalism for dealing with deterministic, non-
deterministic and stochastic cellular automata in an unified and composable
manner. This formalism allows for local probabilistic correlations, a feature
which is not present in usual definitions. We show that this feature allows for
strictly more behaviors (for instance, number conserving stochastic cellular
automata require these local probabilistic correlations). We also show that
several problems which are deceptively simple in the usual definitions, become
undecidable when we allow for local probabilistic correlations, even in
dimension one. Armed with this formalism, we extend the notion of intrinsic
simulation between deterministic cellular automata, to the non-deterministic
and stochas- tic settings. Although the intrinsic simulation relation is shown
to become undecidable in dimension two and higher, we provide explicit tools to
prove or disprove the existence of such a simulation between any two given
stochastic cellular automata. Those tools rely upon a characterization of
equality of stochastic global maps, shown to be equivalent to the existence of
a stochastic coupling between the random sources. We apply them to prove that
there is no universal stochastic cellular automaton. Yet we provide stochastic
cellular automata achieving optimal partial universality, as well as a
universal non-deterministic cellular automaton.


  The application of ultrathin two-dimensional (2D) perovskites in
near-infrared and visible-range optoelectronics has been limited owing to their
inherent wide bandgaps, large excitonic binding energies and low optical
absorption at higher wavelengths. Here, we show that by tailoring interfacial
band alignments via conjugation with low-dimensional materials like monolayer
transition metal dichalcogenides (TMD), the functionalities of 2D perovskites
can be extended to diverse, visible-range photophysical applications. Based on
the choice of individual constituents in the 2D perovskite/TMD
heterostructures, our first principles calculations demonstrate widely tunable
type-II band gaps, carrier effective masses and band offsets to enable an
effective separation of photogenerated excitons for enhanced photodetection and
photovoltaic applications. In addition, we show the possibilities of achieving
a type-I band alignment for recombination based light emitters as well as a
type-III configuration for tunnelling devices. Further, we evaluate the effect
of strain on the electronic properties of the heterostructures to show a
significant strain tolerance, making them prospective candidates in flexible
photosensors.


  Using $\Delta\chi^2$ which is defined by the difference of the number of
events with the CP phase $\delta$ and the hypothetical one with $\delta=0$, we
discuss correlations of errors of the CP phase and other oscillation parameters
as well as the matter effect in measurements at neutrino factories. By varying
the oscillation parameters and the normalization of the matter effect, we
evaluated the data size required to reject a hypothesis with $\delta=0$ at
3$\sigma$CL. The optimum muon energy and the baseline depends on the magnitude
of $\theta_{13}$, the background fraction, the uncertainty of the normalization
of the matter effect, but in general lie in the ranges 20GeV $\lesssim
E_\mu\lesssim$ 50GeV, 1000km$\lesssim L\lesssim$3000km. If we assume that the
uncertainty of the matter effect is as large as 20% then the optimum values may
be modified to $E_\mu\lesssim$ 10GeV, $L\lesssim$1000km due to the strong
correlation of $\delta$ and the matter effect. We show analytically that
sensitivity to CP violation is lost for $E_\mu\ll$ 10GeV or for $E_\mu\gg$
50GeV. We also discuss the possibility of measuring CP violation at the
upgraded JHF experiment by taking all the error correlations into account, and
show that it is possible to demonstrate $\delta\ne0$ at 3$\sigma$CL for
$\theta_{13}\gtrsim 3^\circ$.


  In this article, we study geometric aspects of semi-arithmetic Riemann
surfaces by means of number theory and hyperbolic geometry. First, we show the
existence of infinitely many semi-arithmetic Riemann surfaces of various shapes
and prove that their systoles are dense in the positive real numbers.
Furthermore, this leads to a construction, for each genus $g \geq 2,$ of
infinite families of semi-arithmetic surfaces with pairwise distinct invariant
trace fields, giving a negative answer to a conjecture of B. Jeon. Finally, for
any semi-arithmetic surface we find a sequence of congruence coverings with
logarithmic systolic growth and, for the special case of surfaces admitting
modular embedding, we are able to exhibit explicit constants.


  In this work a detailed spectral analysis for periodicity search of the time
series of the 8B solar neutrino flux released by the SNO Collaboration is
presented. The data have been publicly released with truncation of the event
times to the unit of day (1 day binning); they are thus suited to undergo the
traditional Lomb-Scargle analysis for periodicity investigation, as well as an
extension of such a method based on a likelihood approach. The results of the
analysis presented here confirm the absence of modulation signatures in the SNO
data. For completeness, a more refined "1 day binned" likelihood is also
illustrated, which approximates the unbinned likelihood methodology, based upon
the availability of the full time information, adopted by the SNO
collaboration. Finally, this work is completed with two different joint
analyses of the SNO and Super-Kamiokande data, respectively, over the common
and the entire data taking periods. While both analyses reinforce the case of
the constancy of the neutrino flux, the latter in addition provides evidence of
the detection at the 99.7% confidence level of the annual modulation spectral
line due to the Earth's orbit eccentricity around the Sun


  Networks arise in many applications, such as in the analysis of text
documents, social interactions and brain activity. We develop a general
framework for extrinsic statistical analysis of samples of networks, motivated
by networks representing text documents in corpus linguistics. We identify
networks with their graph Laplacian matrices, for which we define metrics,
embeddings, tangent spaces, and a projection from Euclidean space to the space
of graph Laplacians. This framework provides a way of computing means,
performing principal component analysis and regression, and carrying out
hypothesis tests, such as for testing for equality of means between two samples
of networks. We apply the methodology to the set of novels by Jane Austen and
Charles Dickens.


  We study the visual semantic embedding problem for image-text matching. Most
existing work utilizes a tailored cross-attention mechanism to perform local
alignment across the two image and text modalities. This is computationally
expensive, even though it is more powerful than the unimodal dual-encoder
approach. This work introduces a dual-encoder image-text matching model,
leveraging a scene graph to represent captions with nodes for objects and
attributes interconnected by relational edges. Utilizing a graph attention
network, our model efficiently encodes object-attribute and object-object
semantic relations, resulting in a robust and fast-performing system.
Representing caption as a scene graph offers the ability to utilize the strong
relational inductive bias of graph neural networks to learn object-attribute
and object-object relations effectively. To train the model, we propose losses
that align the image and caption both at the holistic level (image-caption) and
the local level (image-object entity), which we show is key to the success of
the model. Our model is termed Composition model for Object Relations and
Attributes, CORA. Experimental results on two prominent image-text retrieval
benchmarks, Flickr30K and MSCOCO, demonstrate that CORA outperforms existing
state-of-the-art computationally expensive cross-attention methods regarding
recall score while achieving fast computation speed of the dual encoder.


  The low-temperature states of bosonic fluids exhibit fundamental quantum
effects at the macroscopic scale: the best-known examples are Bose-Einstein
condensation (BEC) and superfluidity, which have been tested experimentally in
a variety of different systems. When bosons are interacting, disorder can
destroy condensation leading to a so-called Bose glass. This phase has been
very elusive to experiments due to the absence of any broken symmetry and of a
finite energy gap in the spectrum. Here we report the observation of a Bose
glass of field-induced magnetic quasiparticles in a doped quantum magnet
(Br-doped dichloro-tetrakis-thiourea-Nickel, DTN). The physics of DTN in a
magnetic field is equivalent to that of a lattice gas of bosons in the
grand-canonical ensemble; Br-doping introduces disorder in the hoppings and
interaction strengths, leading to localization of the bosons into a Bose glass
down to zero field, where it acquires the nature of an incompressible Mott
glass. The transition from the Bose glass (corresponding to a gapless spin
liquid) to the BEC (corresponding to a magnetically ordered phase) is marked by
a novel, universal exponent governing the scaling on the critical temperature
with the applied field, in excellent agreement with theoretical predictions.
Our study represents the first, quantitative account of the universal features
of disordered bosons in the grand-canonical ensemble.


  Moment-angle manifolds provide a wide class of examples of non-Kaehler
compact complex manifolds. A complex moment-angle manifold Z is constructed via
certain combinatorial data, called a complete simplicial fan. In the case of
rational fans, the manifold Z is the total space of a holomorphic bundle over a
toric variety with fibres compact complex tori. In general, a complex
moment-angle manifold Z is equipped with a canonical holomorphic foliation F
which is equivariant with respect to the (C*)^m-action. Examples of
moment-angle manifolds include Hopf manifolds of Vaisman type, Calabi-Eckmann
manifolds, and their deformations.
  We construct transversely Kaehler metrics on moment-angle manifolds, under
some restriction on the combinatorial data. We prove that any Kaehler
submanifold (or, more generally, a Fujiki class C subvariety) in such a
moment-angle manifold is contained in a leaf of the foliation F. For a generic
moment-angle manifold Z in its combinatorial class, we prove that all
subvarieties are moment-angle manifolds of smaller dimension. This implies, in
particular, that the algebraic dimension of Z is zero.


  A proof is one of the most important concepts of mathematics. However, there
is a striking difference between how a proof is defined in theory and how it is
used in practice. This puts the unique status of mathematics as exact science
into peril. Now may be the time to reconcile theory and practice, i.e.
precision and intuition, through the advent of computer proof assistants. For
the most time this has been a topic for experts in specialized communities.
However, mathematical proofs have become increasingly sophisticated, stretching
the boundaries of what is humanly comprehensible, so that leading
mathematicians have asked for formal verification of their proofs. At the same
time, major theorems in mathematics have recently been computer-verified by
people from outside of these communities, even by beginning students. This
article investigates the gap between the different definitions of a proof and
possibilities to build bridges. It is written as a polemic or a collage by
different members of the communities in mathematics and computer science at
different stages of their careers, challenging well-known preconceptions and
exploring new perspectives.


  Perturbation theory is an important technique for reducing computational cost
and providing physical insights in simulating quantum systems with classical
computers. Here, we provide a quantum algorithm to obtain perturbative energies
on quantum computers. The benefit of using quantum computers is that we can
start the perturbation from a Hamiltonian that is classically hard to solve.
The proposed algorithm uses quantum signal processing (QSP) to achieve this
goal. Along with the perturbation theory, we construct a technique for ground
state preparation with detailed computational cost analysis, which can be of
independent interest. We also estimate a rough computational cost of the
algorithm for simple chemical systems such as water clusters and polyacene
molecules. To the best of our knowledge, this is the first of such estimates
for practical applications of QSP. Unfortunately, we find that the proposed
algorithm, at least in its current form, does not exhibit practical numbers
despite of the efficiency of QSP compared to conventional quantum algorithms.
However, perturbation theory itself is an attractive direction to explore
because of its physical interpretability; it provides us insights about what
interaction gives an important contribution to the properties of systems. This
is in sharp contrast to the conventional approaches based on the quantum phase
estimation algorithm, where we can only obtain values of energy. From this
aspect, this work is a first step towards ``explainable'' quantum simulation on
fault-tolerant quantum computers.


  In this paper, we present a method to utilize 2D-2D point matches between
images taken during different image conditions to train a convolutional neural
network for semantic segmentation. Enforcing label consistency across the
matches makes the final segmentation algorithm robust to seasonal changes. We
describe how these 2D-2D matches can be generated with little human interaction
by geometrically matching points from 3D models built from images. Two
cross-season correspondence datasets are created providing 2D-2D matches across
seasonal changes as well as from day to night. The datasets are made publicly
available to facilitate further research. We show that adding the
correspondences as extra supervision during training improves the segmentation
performance of the convolutional neural network, making it more robust to
seasonal changes and weather conditions.


  Magnetism in carbon nanostructures is of high scientific interest, which
could lead to novel magnetic materials. The magnetic properties of symmetrical
and asymmetrical sized small fullerene dimers have been investigated using spin
polarized density functional theory. The interaction energies depict that small
fullerene cages form stable dimer structures and symmetrical sized fullerene
dimers are found more stable than asymmetrical sized dimers. The dimerization
of fullerene cages in different modes leads to change in their magnetic
properties. The non-magnetic fullerene cages become magnetic after formation of
dimer (C20-C20, C24-C24, C32-C32, C40-C40, C20-C24, C40-C44 and
C44-C50),whereas the magnetism of magnetic fullerenes is enhanced or lowered
after dimerization (C28-C28 C36-C36, C24-C28, C28-C32, C32-C36 and C36-C40).
The individual cages of dimer structures show ferromagnetic interactions
amongst them and resultant magnetic moment strongly depends on the type of
inter-connecting bonds. The magnetism may also be explained based on distortion
of carbon cages and change in the density of states (DOS) in dimer
configuration. The calculations presented show strong possibility of
experimental synthesis of small fullerene based magnetic dimers.


  The positive operator valued localizations (POL) of a massive scalar boson
are constructed and a characterization and structural analyses of their kernels
are obtained. In the focus of this article are the causal features of the POL.
There is the well-known causal time evolution (CT). Recently a POL by Terno and
Moretti, which is a kinematical deformation of the Newton-Wigner localization
(NWL) and belongs to the here fully analyzed class of finite POL, is shown by
V.Moretti to comply with CT. A further POL with CT treated here, which is in
the same class, is the only one being the trace of a projection valued
localization (like NWL) with CT. - Causality imposes a condition CC, which
implies CT but is more restrictive than CT. Extending Moretti's method it is
shown rigorously that the POL of the class introduced by Petzold et al. satisfy
CC. Their kernels are called causal kernels, of which a rather detailed
description is achieved. One the way there the case of one spatial dimension is
solved completely. This case is instructive. In particular it directed Petzold
et al. and subsequently Henning, Wolf to find their basic one-parameter family
$K_r$ of causal kernels. The causal kernels are, up to a fixed energy factor,
normalized positive definite Lorentz invariant kernels. A full characterization
of the latter is attained due to their close relation to the zonal spherical
functions on the Lorentz group. Finally these considerations discharge into the
main result that $K_{3/2}$ is the absolute maximum, viz. $|K|\le K_{3/2}$ for
all causal kernels $K$.


  The restoration of spin connection clarifies the long known local Lorentz
invariance problem in telelparallel gravities. It is considered now that any
tetrad together with the associated spin connection can be equally utilized.
Among the tetrads there is a particular one, namely proper tetrad, in which all
the spurious inertial effects are removed and the spin connection vanishes. A
specific tetrad was proposed in the literature for spherically symmetric cases,
which has been used in regularizing the action, as well as in searching
solutions in various scenarios. We show in this paper that the this tetrad is
not the unique choice for the proper tetrad. We construct a new tetrad that can
be considered as the proper one, and it will lead to different behaviors of the
field equation and results in different solutions. With this proper tetrad, it
is possible to find solutions to teleparallel gravities in the strong field
regime, which may have physical applications. In the flat spacetime limit, the
new tetrad coincides with the aforementioned one.


  Point defect qubits in semiconductors have demonstrated their outstanding
high spatial resolution sensing capabilities of broad multidisciplinary
interest. Two-dimensional (2D) semiconductors hosting such sensors have
recently opened up new horizons for sensing in the subnanometer scales in 2D
heterostructures. However, controlled creation of quantum sensor in a single
layer 2D materials with high sensitivity has been elusive so far. Here, we
report on a novel 2D quantum sensor, the VB2 centre in hexagonal boron nitride
(hBN), with superior sensing capabilities. The centre's inherently low symmetry
configuration gives rise to unique electronic and spin properties that
implement a qubit in a 2D material with unprecedented sensitivity. The qubit is
decoupled from its dense spin environment at low magnetic fields that gives
rise to the reduction of the spin resonance linewidth and elongation of the
coherence time. The VB2 centre is also equipped with a classical memory that
can be utilized in storing population information. Using scanning transmission
electron microscopy imaging, we confirm the presence of the point defect
structure in free standing monolayer hBN created by electron beam irradiation.
Our results provide a new material solution towards atomic-scale sensing in low
dimensions.


  We solve the quantum Hall problem exactly in a limit and show that the ground
states can be organized in a fractal pattern consistent with the
Haldane-Halperin hierarchy, and with the global phase diagram. We present wave
functions for a large family of states, including those of Laughlin and Jain
and also for states recently observed by Pan {\it et. al.}, and show that they
coincide with the exact ones in the solvable limit. We submit that they
establish an adiabatic continuation of our exact results to the experimentally
accessible regime, thus providing a unified approach to the hierarchy states.


  This article gives an exposition of the deformation theory for pairs $(X,
E)$, where $X$ is a compact complex manifold and $E$ is a holomorphic vector
bundle over $X$, adapting an analytic viewpoint \`{a} la Kodaira-Spencer. By
introducing and exploiting an auxiliary differential operator, we derive the
Maurer--Cartan equation and differential graded Lie algebra (DGLA) governing
the deformation problem, and express them in terms of differential-geometric
notions such as the connection and curvature of $E$, obtaining a chain level
refinement of the classical results that the tangent space and obstruction
space of the moduli problem are respectively given by the first and second
cohomology groups of the Atiyah extension of $E$ over $X$. As an application,
we give examples where deformations of pairs are unobstructed.


  Multi-user diversity is considered when the number of users in the system is
random. The complete monotonicity of the error rate as a function of the
(deterministic) number of users is established and it is proved that
randomization of the number of users always leads to deterioration of average
system performance at any average SNR. Further, using stochastic ordering
theory, a framework for comparison of system performance for different user
distributions is provided. For Poisson distributed users, the difference in
error rate of the random and deterministic number of users cases is shown to
asymptotically approach zero as the average number of users goes to infinity
for any fixed average SNR. In contrast, for a finite average number of users
and high SNR, it is found that randomization of the number of users
deteriorates performance significantly, and the diversity order under fading is
dominated by the smallest possible number of users. For Poisson distributed
users communicating over Rayleigh faded channels, further closed-form results
are provided for average error rate, and the asymptotic scaling law for ergodic
capacity is also provided. Simulation results are provided to corroborate our
analytical findings.


  Light-matter interactions are an established field that is experiencing a
renaissance in recent years due to the introduction of exotic coupling regimes.
These include the ultrastrong and deep strong coupling regimes, where the
coupling constant is smaller and of the order of the frequency of the light
mode, or larger than this frequency, respectively. In the past few years,
quantum simulations of light-matter interactions in all possible coupling
regimes have been proposed and experimentally realized, in quantum platforms
such as trapped ions, superconducting circuits, cold atoms, and quantum
photonics. We review this fledgling field, illustrating the benefits and
challenges of the quantum simulations of light-matter interactions with quantum
technologies.


  We report the serendipitous discovery of a heavily reddened Wolf-Rayet star
that we name WR142b. While photometrically monitoring a cataclysmic variable,
we detected weak variability in a nearby field star. Low-resolution
spectroscopy revealed a strong emission line at 7100 Ang., suggesting an
unusual object and prompting further study. A spectrum taken with the
Hobby-Eberly Telescope confirms strong HeII emission and a NIV 7112 Ang. line
consistent with a nitrogen-rich Wolf-Rayet star of spectral class WN6. Analysis
of the HeII line strengths reveals no detectable hydrogen in WR142b. A
blue-sensitive spectrum obtained with the Large Binocular Telescope shows no
evidence for a hot companion star. The continuum shape and emission line ratios
imply a reddening of E(B-V)=2.2 to 2.5 mag. If not for the dust extinction,
this new Wolf-Rayet star could be visible to the naked eye.


  We report experimental investigations of spin-to-charge current conversion
and charge transfer dynamics (CT) at the interface of graphene/WS$_2$ van der
Waals heterostructure. Pure spin current was produced by the spin precession in
the microwave-driven ferromagnetic resonance of a permalloy film
(Py-Ni$_{81}$Fe$_{19}$) and injected into the graphene/WS$_2$ heterostructure
through the spin pumping process. The observed spin-to-charge current
conversion in the heterostructure is attributed to inverse Rashba-Edelstein
effect (IREE) at the graphene/WS$_2$ interface. Interfacial CT dynamics in this
heterostructure was investigated based on the framework of core-hole-clock
(CHC) approach. The results obtained from spin pumping and CHC studies show
that the spin-to-charge current conversion and charge transfer process are more
efficient in the graphene/WS$_2$ heterostructure compared to isolated WS2 and
graphene films. The results show that the presence of WS$_2$ flakes improves
the current conversion efficiency. These experimental results are corroborated
by density functional theory (DFT) calculations, which reveal (i) Rashba
spin-orbit splitting of graphene orbitals and (ii) electronic coupling between
graphene and WS$_2$ orbitals. This study provides valuable insights for
optimizing the design and performance of spintronic devices.


  We present the explicit form for all the four dimensional, static,
spherically symmetric solutions in $(4+n)$-d Abelian Kaluza-Klein theory by
performing a subset of $SO(2,n)$ transformations corresponding to four
$SO(1,1)$ boosts on the Schwarzschild solution, supplemented by $SO(n)/SO(n-2)$
transformations. The solutions are parameterized by the mass $M$, Taub-Nut
charge $a$, $n$ electric $\vec{\cal Q}$ and $n$ magnetic $\vec{\cal P}$
charges. Non-extreme black holes (with zero Taub-NUT charge) have either the
Reissner-Nordstr\" om or Schwarzschild global space-time. Supersymmetric
extreme black holes have a null or naked singularity, while non-supersymmetric
extreme ones have a global space-time of extreme Reissner-Nordstr\" om black
holes.


  This paper proposes a novel method for distributed controller synthesis of
homogeneous interconnected systems consisting of identical subsystems. The
objective of the designed controller is to minimize the L2-gain of the
performance channel. The proposed method is an extended formulation of the Full
Block S-Procedure (FBSP) where we introduce an additional set of variables.
This allows relaxing the block-diagonal structural assumptions on the Lyapunov
and multiplier matrices required for distributed control design, which reduces
conservatism w.r.t most existing approaches. We show how to decompose the
proposed extended FBSP into small synthesis conditions, of the size of one
individual subsystem.