  We analyze a phenomenon called ``image reflection'' on a type of
characterization graphs -- LLEE charts -- of 1-free regular expressions. Due to
the correspondence between 1-free regular expressions and the provable
solutions of LEE/LLEE charts, this observation naturally leads to a new proof
for the completeness of the proof system \MilIfree\ for 1-free regular
expressions modulo bisimulation equivalence. The critical part of the previous
proof is to show that bisimulation collapse, which plays the role in linking
the provable solutions of two LLEE charts, is still an LLEE chart. The
difference of our proof, compared to the previous one, is that we do not rely
on the graph transformations from LLEE charts into their bisimulation collapses
by merging two carefully-selected bisimilar nodes in each transformation step.
Instead, we directly show that the bisimulation collapse of an LLEE chart
possesses an LEE/LLEE structure based on its set of images mapped through the
bisimulation function from the LLEE chart, and the constrained relation between
the images and their so-called ``well-structured'' looping-back charts
pre-images on the LLEE chart. Our approach provides a novel angle to look at
this problem and related problems, and can also be used for simplifying the
graph transformations in the proof of the completeness problem of the proof
system \Mil\ for regular expressions modulo bisimulation equivalence, which had
remained open until very recently.


  A wind turbines' power curve is easily accessible damage sensitive data, and
as such is a key part of structural health monitoring in wind turbines. Power
curve models can be constructed in a number of ways, but the authors argue that
probabilistic methods carry inherent benefits in this use case, such as
uncertainty quantification and allowing uncertainty propagation analysis. Many
probabilistic power curve models have a key limitation in that they are not
physically meaningful - they return mean and uncertainty predictions outside of
what is physically possible (the maximum and minimum power outputs of the wind
turbine). This paper investigates the use of two bounded Gaussian Processes in
order to produce physically meaningful probabilistic power curve models. The
first model investigated was a warped heteroscedastic Gaussian process, and was
found to be ineffective due to specific shortcomings of the Gaussian Process in
relation to the warping function. The second model - an approximated Gaussian
Process with a Beta likelihood was highly successful and demonstrated that a
working bounded probabilistic model results in better predictive uncertainty
than a corresponding unbounded one without meaningful loss in predictive
accuracy. Such a bounded model thus offers increased accuracy for performance
monitoring and increased operator confidence in the model due to guaranteed
physical plausibility.


  Characterizing the delocalization transition in closed quantum systems with a
many-body localized phase is a key open question in the field of nonequilibrium
physics. We exploit that localization of particles as realized in Anderson and
standard many-body localization (MBL) implies Fock-space localization in
single-particle basis sets characterized by a real-space index. Using a
recently introduced quantitative measure for Fock-space localization computed
from the density distributions, the occupation distance, we systematically
study its scaling behavior across delocalozation transitions and identify
critical points from scaling collapses of numerical data. Excellent agreement
with literature results is found for the critical disorder strengths of
noninteracting fermions, such as the one-dimensional Aubry-Andr\'e and the
three-dimensional Anderson model. We observe a distinctively different scaling
behavior in the case of interacting fermions with random disorder consistent
with a Kosterlitz-Thouless transition. Finally, we use our measure to extract
the transition point as a function of filling for interacting fermions.


  Koopman operator is a composition operator defined for a dynamical system
described by nonlinear differential or difference equation. Although the
original system is nonlinear and evolves on a finite-dimensional state space,
the Koopman operator itself is linear but infinite-dimensional (evolves on a
function space). This linear operator captures the full information of the
dynamics described by the original nonlinear system. In particular, spectral
properties of the Koopman operator play a crucial role in analyzing the
original system. In the first part of this paper, we review the so-called
Koopman operator theory for nonlinear dynamical systems, with emphasis on modal
decomposition and computation that are direct to wide applications. Then, in
the second part, we present a series of applications of the Koopman operator
theory to power systems technology. The applications are established as
data-centric methods, namely, how to use massive quantities of data obtained
numerically and experimentally, through spectral analysis of the Koopman
operator: coherency identification of swings in coupled synchronous generators,
precursor diagnostic of instabilities in the coupled swing dynamics, and
stability assessment of power systems without any use of mathematical models.
Future problems of this research direction are identified in the last
concluding part of this paper.


  We study F-saturation games, first introduced by F\"uredi, Reimer and Seress
in 1991, and named as such by West. The main question is to determine the
length of the game whilst avoiding various classes of graph, playing on a large
complete graph. We show lower bounds on the length of path-avoiding games, and
more precise results for short paths. We show sharp results for the tree
avoiding game and the star avoiding game.


  Head generation with diverse identities is an important task in computer
vision and computer graphics, widely used in multimedia applications. However,
current full head generation methods require a large number of 3D scans or
multi-view images to train the model, resulting in expensive data acquisition
cost. To address this issue, we propose Head3D, a method to generate full 3D
heads with limited multi-view images. Specifically, our approach first extracts
facial priors represented by tri-planes learned in EG3D, a 3D-aware generative
model, and then proposes feature distillation to deliver the 3D frontal faces
into complete heads without compromising head integrity. To mitigate the domain
gap between the face and head models, we present dual-discriminators to guide
the frontal and back head generation, respectively. Our model achieves
cost-efficient and diverse complete head generation with photo-realistic
renderings and high-quality geometry representations. Extensive experiments
demonstrate the effectiveness of our proposed Head3D, both qualitatively and
quantitatively.


  Nonlinear optical frequency conversion, in which optical fields interact with
a nonlinear medium to produce new field frequencies, is ubiquitous in modern
photonic systems. However, the nonlinear electric susceptibilities that give
rise to such phenomena are often challenging to tune in a given material, and
so far, dynamical control of optical nonlinearities remains confined to
research labs as a spectroscopic tool. Here, we report a mechanism to
electrically control second-order optical nonlinearities in monolayer WSe2, an
atomically thin semiconductor. We show that the intensity of second-harmonic
generation at the A-exciton resonance is tunable by over an order of magnitude
at low temperature and nearly a factor of 4 at room temperature through
electrostatic doping in a field-effect transistor. Such tunability arises from
the strong exciton charging effects in monolayer semiconductors, which allow
for exceptional control over the oscillator strengths at the exciton and trion
resonances. The exciton-enhanced second-harmonic generation is
counter-circularly polarized to the excitation laser, arising from the
combination of the two-photon and one-photon valley selection rules that have
opposite helicity in the monolayer. Our study paves the way towards a new
platform for chip-scale, electrically tunable nonlinear optical devices based
on two-dimensional semiconductors.


  We demonstrate tuning of the Fermi contour anisotropy of two-dimensional (2D)
holes in a symmetric GaAs (001) quantum well via the application of in-plane
strain. The ballistic transport of high-mobility hole carriers allows us to
measure the Fermi wavevector of 2D holes via commensurability oscillations as a
function of strain. Our results show that a small amount of in-plane strain, on
the order of $10^{-4}$, can induce significant Fermi wavevector anisotropy as
large as 3.3, equivalent to a mass anisotropy of 11 in a parabolic band. Our
method to tune the anisotropy \textit{in situ} provides a platform to study the
role of anisotropy on phenomena such as the fractional quantum Hall effect and
composite fermions in interacting 2D systems.


  This study proposes a physics-informed convolutional neural network (CNN) for
identifying dynamical systems' time series near a fold bifurcation. The
peculiarity of this work is that the CNN is trained with a relatively small
amount of data and on a single, very simple system. In contrast, the CNN is
validated on much more complicated systems. A similar task requires significant
extrapolation capabilities, which are obtained by exploiting physics-based
information. Physics-based information is provided through a specific
pre-processing of the input data, consisting mostly of a transformation into
polar coordinates, normalization, transformation into the logarithmic scale,
and filtering through a moving mean. The results illustrate that such data
pre-processing enables the CNN to grasp the important features related to
approaching a fold bifurcation, namely, the trend of the oscillation amplitude,
and neglect other characteristics that are not particularly relevant, such as
the vibration frequency. The developed CNN was able to correctly classify
trajectories near a fold for a mass-on-moving-belt system, a van der
Pol-Duffing oscillator with an attached tuned mass damper, and a
pitch-and-plunge wing profile. The results obtained pave the way for the
development of similar CNNs effective in real-life applications.


  We present the formulation and implementation of the integral- and
intermediate-screened coupled-cluster method (ISSCC). The IISCC method gives a
simple and rigorous integral and intermediate screening (IIS) of the
coupled-cluster method and will significantly reduces the scaling for all
orders of the CC hierarchy exactly like seen for the integral-screened
configuration-interaction method (ISCI). The rigorous IIS in the IISCC gives a
robust and adjustable error control which should allow for the possibility of
converging the energy without any loss of accuracy while retaining low or
linear scaling at the same time. The derivation of the IISCC is performed in a
similar fashion as in the ISCI where we show that the tensor contractions for
the nested commutators are separable up to an overall sign and that this
separability can lead to a rigorous IIS. In the nested commutators the
integrals are screened in the first tensor contraction and the intermediates
are screened in all successive tensor contractions. The rigorous IIS will lead
to linear scaling for all nested commutators for large systems in a similar way
as seen for the ISCI. The reduced scaling can in this way be obtained without
any range dependent parameter for the interaction, unlike other low scaling
methods and is therefore also suitable for charge separated systems. It is
expected that the IISCC, just like the ISCI, can use dramatically larger
orbital spaces combined with large CC expansions as compared with traditional
CC methods. Due to the size extensive nature of the CC method the IISCC should
not only be applicable to few electron systems but also to large molecular
system unlike the ISCI. The IISCC can here either be used as a stand alone
method or combined with other linear scaling approaches like the fragmentation
method or other methods which introduces a range dependent interaction
screening.


  With the development of machine learning, a data-driven model has been widely
used in vibration signal fault diagnosis. Most data-driven machine learning
algorithms are built based on well-designed features, but feature extraction is
usually required to be completed in advance. In the deep learning era, feature
extraction and classifier learning are conducted simultaneously, which will
lead to an end-to-end learning system. This paper explores which one of the two
key factors, i.e., feature extraction and classification algorithm, is more
essential for a specific task of vibration signal diagnosis during a learning
system is generated. Feature extractions from vibration signal based on both
well-known Gaussian model and statistical characteristics are discussed,
respectively. And several classification algorithms are selected to
experimentally validate the comparative impact of both feature extraction and
classification algorithm on prediction performance.


  Recently, much research has been dedicated to understanding topological
superconductivity and Majorana zero modes induced by a magnetic field in hybrid
proximity structures. This paper proposes a realization of topological
superconductivity in a short Josephson junction at an edge of a 2D topological
insulator subject to a perpendicular magnetic field. The magnetic field effect
is entirely orbital, coming from a gradient of the order parameter phase at the
edge, which results in a soliton defect at the junction with a pair of gapless
Andreev bound states. The latter are reducible to Majorana zero modes by a
unitary rotation and protected by a chiral symmetry. Furthermore, both ground
state and excitations are quasiperiodic in the magnetic flux enclosed in the
junction, with the period equal to the double flux quantum $2\Phi_0 = h/e$.
This behaviour follows from the gauge invariance of the $4\pi$ - phase
periodicity of the Majorana states and manifests itself as $2\Phi_0$ - spaced
magnetic oscillations of the critical current. Another proposed observable is a
persistent current occurring in the absence of an external phase bias. Beside
the oscillations, it shows a sign reversal prompted by the neutral Majorana
zero modes. These findings offer the possibility to access topological
superconductivity through low-field dc magnetotransport measurements.


  Shannon and Khinchin showed that assuming four information theoretic axioms
the entropy must be of Boltzmann-Gibbs type, $S=-\sum_i p_i \log p_i$. Here we
note that in physical systems one of these axioms may be violated. For
non-ergodic systems the so called separation axiom (Shannon-Khinchin axiom 4)
will in general not be valid. We show that when this axiom is violated the
entropy takes a more general form, $S_{c,d}\propto \sum_i ^W \Gamma(d+1, 1- c
\log p_i)$, where $c$ and $d$ are scaling exponents and $\Gamma(a,b)$ is the
incomplete gamma function. The exponents $(c,d)$ define equivalence classes for
all interacting and non interacting systems and unambiguously characterize any
statistical system in its thermodynamic limit. The proof is possible because of
two newly discovered scaling laws which any entropic form has to fulfill, if
the first three Shannon-Khinchin axioms hold. $(c,d)$ can be used to define
equivalence classes of statistical systems. A series of known entropies can be
classified in terms of these equivalence classes. We show that the
corresponding distribution functions are special forms of Lambert-${\cal W}$
exponentials containing -- as special cases -- Boltzmann, stretched exponential
and Tsallis distributions (power-laws). In the derivation we assume trace form
entropies, $S=\sum_i g(p_i)$, with $g$ some function, however more general
entropic forms can be classified along the same scaling analysis.


  Self-testing was originally introduced as a device-independent method of
certification of entangled quantum states and local measurements performed on
them. Recently, in [F. Baccari \textit{et al.}, arXiv:2003.02285] the notion of
state self-testing has been generalized to entangled subspaces and the first
self-testing strategies for exemplary genuinely entangled subspaces have been
given. The main aim of our work is to pursue this line of research and to
address the question how "large" (in terms of dimension) are genuinely
entangled subspaces that can be self-tested, concentrating on the multiqubit
stabilizer formalism. To this end, we first introduce a framework allowing to
efficiently check whether a given stabilizer subspace is genuinely entangled.
Building on it, we then determine the maximal dimension of genuinely entangled
subspaces that can be constructed within the stabilizer subspaces and provide
an exemplary construction of such maximally-dimensional subspaces for any
number of qubits. Third, we construct Bell inequalities that are maximally
violated by any entangled state from those subspaces and thus also any mixed
states supported on them, and we show these inequalities to be useful for
self-testing. Interestingly, our Bell inequalities allow for identification of
higher-dimensional face structures in the boundaries of the sets of quantum
correlations in the simplest multipartite Bell scenarios in which every
observer performs two dichotomic measurements.


  We have studied how parton distributions based on the inclusion of nonlinear
scale evolution and constraints from HERA data affect charm production in $pp$
collisions at center-of-mass energies of 5.5, 8.8 and 14 TeV. We find that,
while the resulting enhancement can be substantial, it is very sensitive to the
charm quark mass and the scale entering the parton densities and the strong
coupling constant.


  In this article, the results of investigation of processes occurring during
the molecular-beam deposition of germanium layers on Si$_3$N$_4$ dielectric
substrates within a wide range of the Ge film growth temperatures (30 to
600{\deg}C) are presented. The intensity of the IR absorption bands related to
the vibrations of the N$-$H and Si$-$N bonds are established to decrease with
the increase of the Ge deposition temperature. It appears that this phenomenon
cannot be explained only as a thermally activated process. Simultaneously, the
peak corresponding to the Ge$-$N vibration bonds emerges in the X-ray
photoelectron spectra. We suppose that the deposition of germanium layers on
Si3N4 dielectric substrates containing hydrogen atoms causes the diffusion of
hydrogen atoms from the dielectric layer into the growing film. The
experimental results may be interpreted in terms of a model, according to which
the migration of hydrogen atoms from the Si$_3$N$_4$ layer into the growing
germanium film is due to the difference in chemical potentials of hydrogen
atoms in the dielectric layer and the germanium film. This process initiates
the diffusion of germanium atoms in the opposite direction, into the
Si$_3$N$_4$ layer, where they connect to free bonds of nitrogen atoms arising
due to the escape of hydrogen atoms. The analogous processes occur during the
deposition of silicon layers on Si$_3$N$_4$ substrates.


  Jing Run Chen proved in 1966 that $p+2$ has at most two prime factors for
infinitely many primes $p$. However, due to the parity problem we do not know
whether $p+2$ has an odd (or even) number of prime factors infinitely often. In
the present work it is proved that $p+d$ has an odd number of prime factors for
at least one value of d=2,4,...16.


  We explicitly construct a strongly aperiodic subshift of finite type for the
discrete Heisenberg group. Our example builds on the classical aperiodic
tilings of the plane due to Raphael Robinson. Extending those tilings to the
Heisenberg group by exploiting the group's structure and posing additional
local rules to prune out remaining periodic behavior we maintain a rich
projective subdynamics on $\mathbb Z^2$ cosets. In addition the obtained
subshift factors onto a strongly aperiodic, minimal sofic shift via a map that
is invertible on a dense set of configurations.


  In the first part we discuss how the BEC picture for magnons is modified by
anisotropies induced by spin-orbit coupling. In particular we focus on the
effects of antisymmetric spin interactions and/or a staggered component of the
$g$ (gyromagnetic) tensor. Such terms lead to a gapped quasiparticle spectrum
and a nonzero condensate density for all temperatures so that no phase
transition occurs. We contrast this to the effect of crystal field anisotropies
which are also induced by spin-orbit coupling. In the second part we study the
field-induced magnetic ordering in TlCuCl$_3$ on a quantitative level. We show
that the usual BEC picture does not allow for a good description of the
experimental magnetisation data and argue that antisymmetric spin interactions
and/or a staggered $g$ tensor component are still crucial, although both are
expected to be tiny in this compound due to crystal symmetries. Including this
type of interaction we obtain excellent agreement with experimental data.


  An exotic narrow state in the $D^0D^0\pi^+$ mass spectrum just below the
$D^{*+}D^0$ mass threshold is studied using a data set corresponding to an
integrated luminosity of 9 fb$^{-1}$ acquired with the LHCb detector in
proton-proton collisions at centre-of-mass energies of 7, 8 and 13 TeV. The
state is consistent with the ground isoscalar $T^+_{cc}$ tetraquark with a
quark content of $cc\bar{u}\bar{d}$ and spin-parity quantum numbers
$\mathrm{J}^{\mathrm{P}}=1^+$. Study of the $DD$ mass spectra disfavours
interpretation of the resonance as the isovector state. The decay structure via
intermediate off-shell $D^{*+}$ mesons is confirmed by the $D^0\pi^+$ mass
distribution. The mass of the resonance and its coupling to the $D^{*}D$ system
are analysed. Resonance parameters including the pole position, scattering
length, effective range and compositeness are measured to reveal important
information about the nature of the $T^+_{cc}$ state. In addition, an
unexpected dependence of the production rate on track multiplicity is observed.


  In Bayesian Network Structure Learning (BNSL), one is given a variable set
and parent scores for each variable and aims to compute a DAG, called Bayesian
network, that maximizes the sum of parent scores, possibly under some
structural constraints. Even very restricted special cases of BNSL are
computationally hard, and, thus, in practice heuristics such as local search
are used. A natural approach for a local search algorithm is a hill climbing
strategy, where one replaces a given BNSL solution by a better solution within
some pre-defined neighborhood as long as this is possible. We study
ordering-based local search, where a solution is described via a topological
ordering of the variables. We show that given such a topological ordering, one
can compute an optimal DAG whose ordering is within inversion distance $r$ in
subexponential FPT time; the parameter $r$ allows to balance between solution
quality and running time of the local search algorithm. This running time bound
can be achieved for BNSL without structural constraints and for all structural
constraints that can be expressed via a sum of weights that are associated with
each parent set. We also introduce a related distance called `window inversions
distance' and show that the corresponding local search problem can also be
solved in subexponential FPT time for the parameter $r$. For two further
natural modification operations on the variable orderings, we show that
algorithms with an FPT time for $r$ are unlikely. We also outline the limits of
ordering-based local search by showing that it cannot be used for common
structural constraints on the moralized graph of the network.


  We explore the effect of stacking fault defects on the transmission of forces
in three-dimensional face-centered-cubic granular crystals. An external force
is applied to a small area at the top surface of a crystalline packing of
granular beads containing one or two stacking faults at various depths. The
response forces at the bottom surface are measured and found to correspond to
predictions based on vector force balance within the geometry of the defects.
We identify the elementary stacking fault as a boundary between two pure
face-centered-cubic crystals with different stacking orders. Other stacking
faults produce response force patterns that can be viewed as resulting from
repetitions of this basic defect. As the number of stacking faults increases,
the intensity pattern evolves toward that of an hexagonal-close-packed crystal.
This leads to the conclusion that the force pattern of that crystal structure
crystal can be viewed as the extreme limit of a face-centered-cubic crystal
with a stacking fault at every layer.


  In the correspondence between spectral problems and topological strings, it
is natural to consider complex values for the string theory moduli. In the
spectral theory side, this corresponds to non-Hermitian quantum curves with
complex spectra and resonances, and in some cases, to PT-symmetric spectral
problems. The correspondence leads to precise predictions about the spectral
properties of these non-Hermitian operators. In this paper we develop
techniques to compute the complex spectra of these quantum curves, providing in
this way precision tests of these predictions. In addition, we analyze quantum
Seiberg-Witten curves with PT symmetry, which provide interesting and exactly
solvable examples of spontaneous PT-symmetry breaking.


  By numerically calculating the time-evolved Wigner functions, we investigate
the dynamics of a few-photon superposed (e.g., up to two ones) state in a
dissipating cavity. It is shown that, the negativity of the Wigner function of
the photonic state unquestionably vanishes with the cavity's dissipation. As a
consequence, the nonclassical effects related to the negativity of the Wigner
function should be weakened gradually. However, it is found that the value of
the second-order correlation function $g^{(2)}(0)$ (which serves usually as the
standard criterion of a typical nonclassical effect, i.e., $g^{(2)}(0)<1$
implies that the photon is anti-bunching) is a dynamical invariant during the
dissipative process of the cavity. This feature is also proven analytically and
suggests that $g^{(2)}(0)$ might not be a good physical parameter to describe
the photonic decays. Alternatively, we find that the anti-normal-order
correlation function $g^{(2A)}(0)$ changes with the cavity's dissipation and
thus is more suitable to describe the dissipative-dependent cavity. Finally, we
propose an experimental approach to test the above arguments with a
practically-existing cavity QED system.


  We present a method to parallelize the stochastic cutoff (SCO) method, which
is a Monte-Carlo method for long-range interacting systems. After interactions
are eliminated by the SCO method, we subdivide the lattice into non-interacting
interpenetrating sublattices. This subdivision enables us to parallelize
Monte-Carlo calculation in the SCO method. Such subdivision is found by
numerically solving the vertex coloring of a graph created by the SCO method.
We use an algorithm proposed by Kuhn and Wattenhofer to solve the vertex
coloring by parallel computation. The present method was applied to a
two-dimensional magnetic dipolar system on an $L\times L$ square lattice to
examine its parallelization efficiency. The result showed that, in the case of
L=2304, the speed of computation increased about 102 times by parallel
computation with 288 processors.


  Effective placement of charging stations plays a key role in Electric Vehicle
(EV) adoption. In the placement problem, given a set of candidate sites, an
optimal subset needs to be selected with respect to the concerns of both (a)
the charging station service provider, such as the demand at the candidate
sites and the budget for deployment, and (b) the EV user, such as charging
station reachability and short waiting times at the station. This work
addresses these concerns, making the following three novel contributions: (i) a
supervised multi-view learning framework using Canonical Correlation Analysis
(CCA) for demand prediction at candidate sites, using multiple datasets such as
points of interest information, traffic density, and the historical usage at
existing charging stations; (ii) a mixed-packing-and- covering optimization
framework that models competing concerns of the service provider and EV users;
(iii) an iterative heuristic to solve these problems by alternately invoking
knapsack and set cover algorithms. The performance of the demand prediction
model and the placement optimization heuristic are evaluated using real world
data.


  We prove the following results: (1) for any nonsingular projective $3$-folds
$X$ of general type with $\chi(\mathcal{O}_X)\neq 2,3$, the canonical volume
$\text{Vol}(X)$ has the optimal lower bound $\frac{1}{420}$; (2) for
nonsingular projective $3$-folds (resp. $4$-folds) $X$ of general type with
$h^{2, 0}(X)\geq 108\cdot 42^3+4$ (resp. with sufficiently large $h^{2,
0}(X)$), the $3$-canonical map (resp. $5$-canonical map) is stably birational;
(3) for any nonsingular projective $n$-fold $X$ of general type with
$q(X)>n\geq 4$, the canonical stability index $r_s(X)$ is upper bounded by the
$(n-1)$-th canonical stability index $r_{n-1}$.


  The primary alcohol $n$-propanol (i.e., $normal$-propanol or propan-1-ol;
C$_3$H$_7$OH) occurs in five different conformers: $Ga$, $Gg$, $Gg'$, $Aa$, and
$Ag$. All rotational spectra of the three conformers of the $G$ family are well
described, making astronomical search of their spectroscopic signatures
possible, as opposed to those of the $Aa$ and $Ag$ conformers. Our goal is to
facilitate the astronomical detection of $Aa$ and $Ag$ conformers of
$n$-propanol by characterizing their rotational spectra. We recorded the
rotational spectra of $n$-propanol in the frequency domain of
18$-$505\,GHz.Additional double-modulation double-resonance (DM-DR)
measurements were performed, more specifically with the goal to unambiguously
assign weak transitions of the $Aa$ conformer and to verify assignments of the
$Ag$ conformer. We derived a spectroscopic quantum mechanical model with
experimental accuracy (with $J_\textrm{max}=70$ and $K_{a,\textrm{max}}=6$) for
$Aa$ $n$-propanol. Furthermore, we unambiguously assigned transitions (with
$J_\textrm{max}=69$ and $K_{a,\textrm{max}}=9$) of $Ag$ $n$-propanol; in doing
so, we prove the existence of two tunneling states, $Ag^+$ and $Ag^-$. The
astronomical search of all five conformers of $n$-propanol is now possible via
their rotational signatures. These are applied in a companion article on the
detection of $n$-propanol toward the hot molecular core Sgr B2(N2).


  We investigate the sensing performance of a single-qubit quantum thermometer
within a non-Markovian dynamical framework. By employing an exactly numerical
hierarchical equations of the motion method, we go beyond traditional paradigms
of the Born-Markov theory, the pure dephasing mechanism, and the weak-coupling
approximation, which were commonly used in many previous studies of quantum
thermometry. We find (i) the non-Markovian characteristics may boost the
estimation efficiency, (ii) the sensitivity of quantum thermometry can be
effectively optimized by engineering the proportions of different coupling
operators in the whole sensor-reservoir interaction Hamiltonian, and (iii) a
threshold, above which the strong sensor-reservoir coupling can significantly
enhance the sensing precision in the long-encoding-time regime. Our results may
have certain applications for high-resolution quantum thermometry.


  Recent research in computational linguistics has developed algorithms which
associate matrices with adjectives and verbs, based on the distribution of
words in a corpus of text. These matrices are linear operators on a vector
space of context words. They are used to construct the meaning of composite
expressions from that of the elementary constituents, forming part of a
compositional distributional approach to semantics. We propose a Matrix Theory
approach to this data, based on permutation symmetry along with Gaussian
weights and their perturbations. A simple Gaussian model is tested against word
matrices created from a large corpus of text. We characterize the cubic and
quartic departures from the model, which we propose, alongside the Gaussian
parameters, as signatures for comparison of linguistic corpora. We propose that
perturbed Gaussian models with permutation symmetry provide a promising
framework for characterizing the nature of universality in the statistical
properties of word matrices. The matrix theory framework developed here
exploits the view of statistics as zero dimensional perturbative quantum field
theory. It perceives language as a physical system realizing a universality
class of matrix statistics characterized by permutation symmetry.


  This review concentrates on the specific properties and characteristics of
damage structures generated with high-energy ions in the electronic energy loss
regime. Irradiation experiments with so-called swift heavy ions (SHI) find
applications in many different fields, with examples presented in ion-track
nanotechnology, radiation hardness analysis of functional materials, and
laboratory tests of cosmic radiation. The basics of the SHI-solid interaction
are described with special attention to processes in the electronic subsystem.
The broad spectrum of damage phenomena is exemplified for various materials and
material classes, along with a description of typical characterization
techniques. The review also presents state-of-the-art modeling efforts that try
to account for the complexity of the coupled processes of the electronic and
atomic subsystems. Finally, the relevance of SHI phenomena for effects induced
by fission fragments in nuclear fuels and how this knowledge can be applied to
better estimate damage risks in nuclear materials is discussed.


  Aims: We observe the nearby, weakly-active single giant, Pollux, in order to
directly study and infer the nature of its magnetic field. Methods: We used the
new generation spectropolarimeters ESPaDOnS and NARVAL to observe and detect
circular polarization within the photospheric absorption lines of Pollux. Our
observations span 18 months from 2007-2009. We treated the spectropolarimetric
data using the Least-Squares Deconvolution method to create high
signal-to-noise ratio mean Stokes V profiles. We also measured the classical
activity indicator S-index for the Ca H&K lines, and the stellar radial
velocity (RV). Results: We have unambiguously detected a weak Stokes V signal
in the spectral lines of Pollux, and measured the related surface-averaged
longitudinal magnetic field Bl. The longitudinal field averaged over the span
of the observations is below one gauss. Our data suggest variations of the
longitudinal magnetic field, but no significant variation of the S-index. We
observe variations of RV which are qualitatively consistent with the published
ephemeris for a proposed exoplanet orbiting Pollux. The observed variations of
Bl appear to mimic those of RV, but additional data for this relationship to be
established. Using evolutionary models including the effects of rotation, we
derive the mass of Pollux and we discuss its evolutionary status and the origin
of its magnetic field. Conclusions: This work presents the first direct
detection of the magnetic field of Pollux, and demonstrates that ESPaDOnS and
NARVAL are capable of obtaining sub-G measurements of the surface-averaged
longitudinal magnetic field of giant stars, and of directly studying the
relationships between magnetic activity, stellar evolution and planet hosting
of these stars.


  We study the effective interactions induced by loops of extra-dimensional
gravitons and show the special role of a specific dimension-6 four-fermion
operator, product of two flavour-universal axial currents. By introducing an
ultraviolet cut-off, we compare the present constraints on low-scale quantum
gravity from various processes involving real-graviton emission and
virtual-graviton exchange. The LEP2 limits on dimension-6 four-fermion
interactions give one of the strongest constraint on the theory, in particular
excluding the case of strongly-interacting gravity at the weak scale.


  This paper proposes a novel and interpretable recurrent neural-network
structure using the echo-state network (ESN) paradigm for time-series
prediction. While the traditional ESNs perform well for dynamical systems
prediction, it needs a large dynamic reservoir with increased computational
complexity. It also lacks interpretability to discern contributions from
different input combinations to the output. Here, a systematic reservoir
architecture is developed using smaller parallel reservoirs driven by different
input combinations, known as features, and then they are nonlinearly combined
to produce the output. The resultant feature-based ESN (Feat-ESN) outperforms
the traditional single-reservoir ESN with less reservoir nodes. The predictive
capability of the proposed architecture is demonstrated on three systems: two
synthetic datasets from chaotic dynamical systems and a set of real-time
traffic data.


  The discovery of multiple electronic orders in kagome superconductors AV3Sb5
(A = K, Rb, Cs) provides a promising platform for exploring unprecedented
emergent physics. Under moderate pressure (< 2.2 GPa), the triple-Q charge
density wave (CDW) order is monotonically suppressed by pressure, while the
superconductivity displays a two-dome-like behavior, suggesting an unusual
interplay between superconductivity and CDW order. Given that time-reversal
symmetry breaking and electronic nematicity have been revealed inside the
triple-Q CDW phase, understanding this CDW order and its interplay with
superconductivity becomes one of the core questions in AV3Sb5. Here, we report
the evolution of CDW and superconductivity with pressure in CsV3Sb5 by 51V
nuclear magnetic resonance measurements. An emergent CDW phase, ascribed to a
possible stripe-like CDW order with a unidirectional 4a0 modulation, is
observed between Pc1 ~ 0.58 GPa and Pc2 ~ 2.0 GPa, which explains the
two-dome-like superconducting behavior under pressure. Furthermore, the nuclear
spin-lattice relaxation measurement reveals evidence for pressure-independent
charge fluctuations above the CDW transition temperature and unconventional
superconducting pairing above Pc2. Our results not only shed new light on the
interplay of superconductivity and CDW but also reveal novel electronic
correlation effects in kagome superconductors AV3Sb5.


  We investigate the role which clouds could play in resolving the Faint Young
Sun Paradox (FYSP). Lower solar luminosity in the past means that less energy
was absorbed on Earth (a forcing of -50 Wm-2 during the late Archean), but
geological evidence points to the Earth being at least as warm as it is today,
with only very occasional glaciations. We perform radiative calculations on a
single global mean atmospheric column. We select a nominal set of three
layered, randomly overlapping clouds, which are both consistent with observed
cloud climatologies and reproduce the observed global mean energy budget of
Earth. By varying the fraction, thickness, height and particle size of these
clouds we conduct a wide exploration of how changed clouds could affect
climate, thus constraining how clouds could contribute to resolving the FYSP.
Low clouds reflect sunlight but have little greenhouse effect. Removing them
entirely gives a~forcing of +25 Wm-2 whilst more modest reduction in their
efficacy gives a forcing of +10 to +15 Wm-2. For high clouds, the greenhouse
effect dominates. It is possible to generate +50 Wm-2 forcing from enhancing
these, but this requires making them 3.5 times thicker and 14 K colder than the
standard high cloud in our nominal set and expanding their coverage to 100% of
the sky. Such changes are not credible. More plausible changes would generate
no more that +15 Wm-2 forcing. Thus neither fewer low clouds nor more high
clouds can provide enough forcing to resolve the FYSP. Decreased surface albedo
can contribute no more than +5 Wm-2 forcing. Some models which have been
applied to the FYSP do not include clouds at all. These overestimate the
forcing due to increased CO2 by 20 to 25% when CO2 is 0.01 to 0.1 bar.


  A thorough analysis of stochastically stabilised hermitian one matrix models
for two dimensional quantum gravity at all its $(2,2k-1)$ multicritical points
is made. It is stressed that only the zero fermion sector of the supersymmetric
hamiltonian, i.e., the forward Fokker-Planck hamiltonian, is relevant for the
analysis of bosonic matter coupled to two dimensional gravity. Therefore,
supersymmetry breaking is not the physical mechanism that creates non
perturbative effects in the case of points of even multicriticality $k$. Non
perturbative effects in the string coupling constant $g_{str}$ result in a loss
of any explicit relation to the KdV hierarchy equations in the latter case,
while maintaining the perturbative genus expansion. As a by-product of our
analysis it is explicitly proved that polynomials orthogonal relative to an
arbitrary weight $\exp (-\beta V(x))$ along the whole real line obey an
Hartree-Fock equation.


  An excess in the electronic recoil data was observed in the XENON1T detector.
One of plausible explanations for the excess is absorption of a vector bosonic
particle with the mass of $2-3\,{\rm keV}$. For this, the kinetic mixing
$\kappa\!\sim\!10^{-15}$ of the dark photon with the photon is required if the
dark photon explains the current DM abundance. We recently proposed a model
where the main component DM today is a decaying warm dark matter (WDM) with the
life time comparable to the age of the current universe. The WDM decays to a
massless fermion and a massive dark photon. This model was originally designed
for addressing both the small scale problems which $\Lambda$CDM suffers from
and the $H_{0}$ tension. In this letter, we show that the massive dark photon
produced by the WDM decay can be identified with the vector boson inducing the
anomalous excess in the XENON1T experiment. Depending on a lifetime of the
parent decaying WDM, the dark photon could be either the main component or the
sub-component of DM population today.


  We study a unique behavioral network data set (based on periodic surveys and
on electronic logs of dyadic contact via smartphones) collected at the
University of Notre Dame.The participants are a sample of members of the
entering class of freshmen in the fall of 2011 whose opinions on a wide variety
of political and social issues and activities on campus were regularly recorded
- at the beginning and end of each semester - for the first three years of
their residence on campus. We create a communication activity network implied
by call and text data, and a friendship network based on surveys. Both networks
are limited to students participating in the NetSense surveys. We aim at
finding student traits and activities on which agreements correlate well with
formation and persistence of links while disagreements are highly correlated
with non-existence or dissolution of links in the two social networks that we
created. Using statistical analysis and machine learning, we observe several
traits and activities displaying such correlations, thus being of potential use
to predict social network evolution.


  I describe how gravitational entropy is intimately connected with the concept
of gravitational heat, expressed as the difference between the total and free
energies of a given gravitational system. From this perspective one can compute
these thermodyanmic quantities in settings that go considerably beyond
Bekenstein's original insight that the area of a black hole event horizon can
be identified with thermodynamic entropy. The settings include the outsides of
cosmological horizons and spacetimes with NUT charge. However the
interpretation of gravitational entropy in these broader contexts remains to be
understood.


  Let $X$ be a set, $\ka$ be a cardinal number and let $\iH$ be a family of
subsets of $X$ which covers each $x\in X$ at least $\ka$ times. What
assumptions can ensure that $\iH$ can be decomposed into $\kappa$ many disjoint
subcovers?
  We examine this problem under various assumptions on the set $X$ and on the
cover $\iH$: among other situations, we consider covers of topological spaces
by closed sets, interval covers of linearly ordered sets and covers of
$\real^{n}$ by polyhedra and by arbitrary convex sets. We focus on these
problems mainly for infinite $\kappa$. Besides numerous positive and negative
results, many questions turn out to be independent of the usual axioms of set
theory.


  Unequal technology access for Black and Latine communities has been a
persistent economic, social justice, and human rights issue despite increased
technology accessibility due to advancements in consumer electronics like
phones, tablets, and computers. We contextualize socio-technical access
inequalities for Black and Latine urban communities and find that many students
are hesitant to engage with available technologies due to a lack of engaging
support systems. We present a holistic student-led STEM engagement model
through AVELA - A Vision for Engineering Literacy and Access leveraging
culturally responsive lessons, mentor embodied community representation, and
service learning. To evaluate the model's impact after 4 years of mentoring
200+ university student instructors in teaching to 2,500+ secondary school
students in 100+ classrooms, we conducted 24 semi-structured interviews with
college AnonymizedOrganization members. We identify access barriers and provide
principled recommendations for designing future STEM education programs.


  Traditional multi-agent reinforcement learning algorithms are difficultly
applied in a large-scale multi-agent environment. The introduction of mean
field theory has enhanced the scalability of multi-agent reinforcement learning
in recent years. This paper considers partially observable multi-agent
reinforcement learning (MARL), where each agent can only observe other agents
within a fixed range. This partial observability affects the agent's ability to
assess the quality of the actions of surrounding agents. This paper focuses on
developing a method to capture more effective information from local
observations in order to select more effective actions. Previous work in this
field employs probability distributions or weighted mean field to update the
average actions of neighborhood agents, but it does not fully consider the
feature information of surrounding neighbors and leads to a local optimum. In
this paper, we propose a novel multi-agent reinforcement learning algorithm,
Partially Observable Mean Field Multi-Agent Reinforcement Learning based on
Graph--Attention (GAMFQ) to remedy this flaw. GAMFQ uses a graph attention
module and a mean field module to describe how an agent is influenced by the
actions of other agents at each time step. This graph attention module consists
of a graph attention encoder and a differentiable attention mechanism, and this
mechanism outputs a dynamic graph to represent the effectiveness of
neighborhood agents against central agents. The mean--field module approximates
the effect of a neighborhood agent on a central agent as the average effect of
effective neighborhood agents. We evaluate GAMFQ on three challenging tasks in
the MAgents framework. Experiments show that GAMFQ outperforms baselines
including the state-of-the-art partially observable mean-field reinforcement
learning algorithms.


  By using femtosecond laser pulses at a wavelength range from 720 to 780 nm,
we have observed absorptive and refractive nonlinearities in a film of
multi-walled carbon nanotubes grown mainly along the direction perpendicular to
the surface of quartz substrate. The Z-scans show that both absorptive and
refractive nonlinearities are of negative and cubic nature in the laser
irradiance range from a few to 300 GW/cm^2. The magnitude of the third-order
nonlinear susceptibility,chi-(3), is of an order of 10^-11 esu. The degenerate
pump-probe measurement reveals a relaxation time of 2 ps.


  This paper has been withdrawn by the authors due to the too limited range of
the current version of the model (the dark energy fraction is constant, but it
has to be a function of the scale factor). We will resubmit the paper after
extension.


  A class of spiking neuronal models with threshold 2 is considered. It is
defined by a set of conditions typical for basic threshold-type models, such as
the leaky integrate-and-fire (LIF) or the binding neuron model and also for
some artificial neurons. A neuron is stimulated with a Poisson stream of
excitatory impulses. Each output impulse is conveyed through the feedback line
to the neuron input after finite delay $\Delta$. This impulse is identical to
those delivered from the input stream. We have obtained a general relation
allowing calculating exactly the probability density function (PDF) $p(t)$ for
distribution of the first passage time of crossing the threshold, which is the
distribution of output interspike intervals (ISI) values for this neuron. The
calculation is based on known PDF $p^0(t)$ for that same neuron without
feedback, intensity of the input stream $\lambda$ and properties of the
feedback line. Also, we derive exact relation for calculating the moments of
$p(t)$ based on known moments of $p^0(t)$.
  The obtained general expression for $p(t)$ is checked numerically using Monte
Carlo simulation for the case of LIF model. The course of $p(t)$ has a
$\delta$-function type peculiarity. This fact contributes to the discussion
about the possibility to model neuronal activity with Poisson process,
supporting the "no" answer.


  In this work, we study controllability in the set of all density matrices for
a two-level open quantum system driven by coherent and incoherent controls. In
[A. Pechen, Phys. Rev. A 84, 042106 (2011)] an approximate controllability,
i.e., controllability with some precision, was shown for generic $N$-level open
quantum systems driven by coherent and incoherent controls. However, the
explicit formulation of this property, including the behavior of this precision
as a function of transition frequencies and decoherence rates of the system,
was not known. The present work provides a rigorous analytical study of
reachable sets for two-level open quantum systems. First, it is shown that for
$N=2$ the presence of incoherent control does not affect the reachable set
(while incoherent control may affect the time necessary to reach particular
state). Second, the reachable set in the Bloch ball is described and it is
shown that already just for one coherent control any point in the Bloch ball
can be achieved with precision $\delta\sim \gamma/\omega$, where $\gamma$ is
the decoherence rate and $\omega$ is the transition frequency. Typical values
are $\delta\lesssim10^{-3}$ that implies high accuracy of achieving any density
matrix. Moreover, we show that most points in the Bloch ball can be exactly
reached, except of two lacunae of size $\sim\delta$. For two coherent controls,
the system is shown to be completely controllable in the set of all density
matrices. Third, the reachable set as a function of the final time is found and
shown to exhibit a non-trivial structure.


  The application of quadrupole-devices with high field gradients and small
apertures requires precise control over higher order multipole field
components. We present a new scheme for performance control and tuning, which
allows the illumination of most of the quadrupole-device aperture because of
the reduction of higher order field components. Consequently, the size of the
aperture can be minimized to match the beam size achieving field gradients of
up to 500 T/m at good imaging quality. The characterization method based on a
Hall probe measurement and a Fourier analysis was confirmed using the high
quality electron beam at the Mainz Microtron MAMI.


  Prior knowledge can improve the performance of spectrum sensing. Instead of
using universal features as prior knowledge, we propose to blindly learn the
localized feature at the secondary user. Motivated by pattern recognition in
machine learning, we define signal feature as the leading eigenvector of the
signal's sample covariance matrix. Feature learning algorithm (FLA) for blind
feature learning and feature template matching algorithm (FTM) for spectrum
sensing are proposed. Furthermore, we implement the FLA and FTM in hardware.
Simulations and hardware experiments show that signal feature can be learned
blindly. In addition, by using signal feature as prior knowledge, the detection
performance can be improved by about 2 dB. Motivated by experimental results,
we derive several GLRT based spectrum sensing algorithms under rank-1
assumption, considering signal feature, signal power and noise power as the
available parameters. The performance of our proposed algorithms is tested on
both synthesized rank-1 signal and captured DTV data, and compared to other
state-of-the-art covariance matrix based spectrum sensing algorithms. In
general, our GLRT based algorithms have better detection performance. In
addition, algorithms with signal feature as prior knowledge are about 2 dB
better than algorithms without prior knowledge.


  A recent paper of Shekhar compares the ranks of elliptic curves $E_1$ and
$E_2$ for which there is an isomorphism $E_1[p] \simeq E_2[p]$ as
$\mathrm{Gal}(\bar{\mathbf{Q}}/\mathbf{Q})$-modules, where $p$ is a prime of
good ordinary reduction for both curves. In this paper we prove an analogous
result in the case where $p$ is a prime of good supersingular reduction.


  The dynamics of shower development for a jet traveling through the QGP
involves a variety of scales, one of them being the heavy quark mass. Even
though the mass of the heavy quarks plays a subdominant role during the high
virtuality portion of the jet evolution, it does affect longitudinal drag and
diffusion, stimulating additional radiation from heavy quarks. These emissions
partially compensate the reduction in radiation from the dead cone effect. In
the lower virtuality part of the shower, when the mass is comparable to the
transverse momenta of the partons, scattering and radiation processes off heavy
quarks differ from those off light quarks. All these factors result in a
different nuclear modification factor for heavy versus light flavors and thus
for heavy-flavor tagged jets.
  In this study, the heavy quark shower evolution and the fluid dynamical
medium are modeled on an event by event basis using the JETSCAPE Framework. We
present a multi-stage calculation that explores the differences between various
heavy quark energy-loss mechanisms within a realistically expanding quark-gluon
plasma (QGP). Inside the QGP, the highly virtual and energetic portion of the
shower is modeled using the MATTER generator, while the LBT generator models
the showers induced by energetic and close-to-on-shell heavy quarks.
Energy-momentum exchange with the medium, essential for the study of jet
modification, proceeds using a weak coupling recoil approach. The JETSCAPE
framework allows for transitions, on the level of individual partons, from one
energy-loss prescription to the other depending on the parton's energy and
virtuality and the local density. This allows us to explore the effect and
interplay between the different regimes of energy loss on the propagation and
radiation from hard heavy quarks in a dense medium.


  Augmented listening devices, such as hearing aids and augmented reality
headsets, enhance human perception by changing the sounds that we hear.
Microphone arrays can improve the performance of listening systems in noisy
environments, but most array-based listening systems are designed to isolate a
single sound source from a mixture. This work considers a source-remixing
filter that alters the relative level of each source independently. Remixing
rather than separating sounds can help to improve perceptual transparency: it
causes less distortion to the signal spectrum and especially to the interaural
cues that humans use to localize sounds in space.


  The unitary group U(N) acts by conjugations on the space H(N) of NxN
Hermitian matrices, and every orbit of this action carries a unique invariant
probability measure called an orbital measure. Consider the projection of the
space H(N) onto the real line assigning to an Hermitian matrix its (1,1)-entry.
Under this projection, the density of the pushforward of a generic orbital
measure is a spline function with N knots. This fact was pointed out by Andrei
Okounkov in 1996, and the goal of the paper is to propose a multidimensional
generalization. Namely, it turns out that if instead of the (1,1)-entry we cut
out the upper left matrix corner of arbitrary size KxK, where K=2,...,N-1, then
the pushforward of a generic orbital measure is still computable: its density
is given by a KxK determinant composed from one-dimensional splines. The result
can also be reformulated in terms of projections of the Gelfand-Tsetlin
polytopes.


  We studied the shock propagation and its stability with the causal
dissipative hydrodynamics in 1+1 dimensional systems. We show that the presence
of the usual viscosity is not enough to stabilize the solution. This problem is
solved by introducing an additional viscosity which is related to the
coarse-graining scale of the theory.


  We introduce a class of probabilistic theories where the dynamics of each
system is limited to the minimal set of operations consistent with the set of
states and allowing for conditional tests. We show that almost all minimal
theories with conditioning satisfy two quantum no-go theorems: no-information
without disturbance and no-broadcasting. As a relevant example, we construct a
minimal toy-theory with conditioning where all systems are classical. The
theory does not have incompatible measurements nor preparation uncertainty
relations, and it is Kochen-Specker noncontextual, and at the same time it
exhibits irreversibility of measurement disturbance, no-information without
disturbance and no-broadcasting. This proves that the latter three properties
cannot be understood $per se$ as signatures of non-classicality.


  The Budd-Vannimenus theorem is modified to apply to superconductors in the
Meissner state. The obtained identity links the surface value of the
electrostatic potential to the density of free energy at the surface which
allows one to evaluate the electrostatic potential observed via the capacitive
pickup without the explicit solution of the charge profile.


  We study the focusing nonlinear Schr\"odinger equation in the
$L^2$-supercritical regime with finite energy and finite variance initial data.
We investigate solutions above the energy (or mass-energy) threshold. In our
first result, we extend the known scattering versus blow-up dichotomy above
that threshold for finite variance solutions in the energy-subcritical and
energy-critical regimes, obtaining scattering and blow-up criteria for
solutions with arbitrarily large mass and energy. As a consequence, we
characterize the behavior of the ground state initial data modulated by a
quadratic phase. Our second result gives two blow up criteria, which are also
applicable in the energy-supercritical NLS setting. We finish with various
examples illustrating our results.


  A super-massive black hole (SMBH) binary in the core of the blazar OJ 287 has
been invoked in previous works to explain its observed optical flare
quasi-periodicity. Following this picture, we investigate a hadronic origin for
the X-ray and $\gamma$-ray counterparts of the November 2015 major optical
flare of this source. An impact outflow must result after the lighter SMBH (the
secondary) crosses the accretion disc of the heavier one (the primary). We then
consider acceleration of cosmic-ray (CR) protons in the shock driven by the
impact outflow as it expands and collides with the active galactic nucleus
(AGN) wind of the primary SMBH. We show that the emission of these CRs can
reproduce the X-ray and $\gamma$-ray flare data self-consistently with the
optical component of the November 2015 major flare. The derived emission models
are consistent with a magnetic field $B \sim 5$ G in the emission region and a
power-law index of $q\sim2.2$ for the energy distribution of the emitting CRs.
The mechanical luminosity of the AGN wind represents $\lesssim 50\%$ of the
mass accretion power of the primary SMBH in all the derived emission profiles.


  The classical alternating current optimal power flow problem is highly
nonconvex and generally hard to solve. Convex relaxations, in particular
semidefinite, second-order cone, convex quadratic, and linear relaxations, have
recently attracted significant interest. The semidefinite relaxation is the
strongest among them and is exact for many cases. However, the computational
efficiency for solving large-scale semidefinite optimization is lower than for
second-order cone optimization. We propose a conic relaxation obtained by
combining semidefinite optimization with the reformulation-linearization
technique, commonly known as RLT. The proposed relaxation is stronger than the
second-order cone relaxation and nearly as tight as the standard semidefinite
relaxation. Computational experiments using standard test cases with up to 6515
buses show that the time to solve the new conic relaxation is up to one order
of magnitude lower than for the chordal relaxation, a semidefinite relaxation
technique that exploits the sparsity of power networks.


  Many newly discovered excited states are interpreted as bound states of
hadrons. Can these hadrons also form resonant states? In this paper, we extend
the complex scaling method (CSM) to calculate the bound state and resonant
state consistently for the $\Lambda_c D(\bar D)$ and $\Lambda_c \Lambda_c (\bar
\Lambda_c)$ systems. For these systems, the $\pi, \eta, \rho$ meson exchange
contributions are suppressed, the contributions of intermediate- and
short-range forces from $\sigma/\omega$ exchange are dominant. Our results
indicate that $\Lambda_c D$ system can not form bound state and resonant state.
There exist resonant states in a wide range of parameters for $\Lambda_c \bar
D$ and $\Lambda_c \Lambda_c (\bar \Lambda_c)$ systems. For these systems, the
larger bound state energy, the easier to form resonant states. Among all the
resonant states, the energies and widths of the P wave resonant states are
smaller and more stable, which is possible to be observed in the experiments.
The energies of D and F wave resonant states can reach dozens of MeV and the
widths can reach hundreds of MeV.


  Human evaluation of modern high-quality machine translation systems is a
difficult problem, and there is increasing evidence that inadequate evaluation
procedures can lead to erroneous conclusions. While there has been considerable
research on human evaluation, the field still lacks a commonly-accepted
standard procedure. As a step toward this goal, we propose an evaluation
methodology grounded in explicit error analysis, based on the Multidimensional
Quality Metrics (MQM) framework. We carry out the largest MQM research study to
date, scoring the outputs of top systems from the WMT 2020 shared task in two
language pairs using annotations provided by professional translators with
access to full document context. We analyze the resulting data extensively,
finding among other results a substantially different ranking of evaluated
systems from the one established by the WMT crowd workers, exhibiting a clear
preference for human over machine output. Surprisingly, we also find that
automatic metrics based on pre-trained embeddings can outperform human crowd
workers. We make our corpus publicly available for further research.


  We examine the scaling behavior of the entanglement entropy for the 2D
quantum dimer model (QDM) at criticality and derive the universal finite
sub-leading correction $\gamma_{QCP}$. We compute the value of $\gamma_{QCP}$
without approximation working directly with the wave function of a generalized
2D QDM at the Rokhsar-Kivelson QCP in the continuum limit. Using the replica
approach, we construct the conformal boundary state corresponding to the cyclic
identification of $n$-copies along the boundary of the observed region. We find
that the universal finite term is $\gamma_{QCP}=\ln R-1/2$ where $R$ is the
compactification radius of the bose field theory quantum Lifshitz model, the
effective field theory of the 2D QDM at quantum criticality. We also
demonstrated that the entanglement spectrum of the critical wave function on a
large but finite region is described by the characters of the underlying
conformal field theory. It is shown that this is formally related to the
problems of quantum Brownian motion on $n$-dimensional lattices or equivalently
a system of strings interacting with a brane containing a background
electromagnetic field and can be written as an expectation value of a vertex
operator.


  This paper proposes a novel propensity score weighting analysis. We define
two sufficient and necessary conditions for a function of the covariates to be
the propensity score. The first is "local balance", which ensures the
conditional independence of covariates and treatment assignment across a dense
grid of propensity score values. The second condition, "local calibration",
guarantees that a balancing score is a propensity score. Using three-layer
feed-forward neural networks, we develop a nonparametric propensity score model
that satisfies these conditions, effectively circumventing the issue of model
misspecification and optimizing covariate balance to minimize bias and
stabilize the inverse probability weights. Our proposed method performed
substantially better than existing methods in extensive numerical studies of
both real and simulated benchmark datasets.


  We provide a natural canonical decomposition of postcritically finite
rational maps with non-empty Fatou sets based on the topological structure of
their Julia sets. The building blocks of this decomposition are maps where all
Fatou components are Jordan disks with disjoint closures (Sierpi\'{n}ski maps),
as well as those where any two Fatou components can be connected through a
countable chain of Fatou components with common boundary points (crochet or
Newton-like maps). We provide several alternative characterizations for our
decomposition, as well as an algorithm for its effective computation. We also
show that postcritically finite rational maps have dynamically natural
quotients in which all crochet maps are collapsed to points, while all
Sierpi\'{n}ski maps become small spheres; the quotient is a maximal expanding
cactoid. The constructions work in the more general setup of B\"{o}ttcher
expanding maps, which are metric models of postcritically finite rational maps.


  This paper presents the work of restoring punctuation for ASR transcripts
generated by multilingual ASR systems. The focus languages are English,
Mandarin, and Malay which are three of the most popular languages in Singapore.
To the best of our knowledge, this is the first system that can tackle
punctuation restoration for these three languages simultaneously. Traditional
approaches usually treat the task as a sequential labeling task, however, this
work adopts a slot-filling approach that predicts the presence and type of
punctuation marks at each word boundary. The approach is similar to the
Masked-Language Model approach employed during the pre-training stages of BERT,
but instead of predicting the masked word, our model predicts masked
punctuation. Additionally, we find that using Jieba1 instead of only using the
built-in SentencePiece tokenizer of XLM-R can significantly improve the
performance of punctuating Mandarin transcripts. Experimental results on
English and Mandarin IWSLT2022 datasets and Malay News show that the proposed
approach achieved state-of-the-art results for Mandarin with 73.8% F1-score
while maintaining a reasonable F1-score for English and Malay, i.e. 74.7% and
78% respectively. Our source code that allows reproducing the results and
building a simple web-based application for demonstration purposes is available
on Github.


  The dynamics of electronic tunneling through a disordered 1D chain of finite
length is considered. We calculate distributions of the transmission
coefficient T, Wigner delay time and, $\tau_\phi$ and the transport time,
$\tau_t=T\tau_\phi$. The central bodies of these distributions have a power-law
form, what can be understood in terms of the resonant tunneling through
localised states.


  To ascertain whether photometric decompositions of galaxies into bulges and
disks are astrophysically meaningful, we have developed a new technique to
decompose spectral data cubes into separate bulge and disk components, subject
only to the constraint that they reproduce the conventional photometric
decomposition. These decompositions allow us to study the kinematic and stellar
population properties of the individual components and how they vary with
position, in order to assess their plausibility as discrete elements, and to
start to reconstruct their distinct formation histories. An initial application
of this method to CALIFA integral field unit observations of three isolated S0
galaxies confirms that in regions where both bulge and disc contribute
significantly to the flux they can be physically and robustly decomposed into a
rotating dispersion-dominated bulge component, and a rotating low-dispersion
disc component. Analysis of the resulting stellar populations shows that the
bulges of these galaxies have a range of ages relative to their discs,
indicating that a variety of processes are necessary to describe their
evolution. This simple test case indicates the broad potential for extracting
from spectral data cubes the full spectral data of a wide variety of individual
galaxy components, and for using such decompositions to understand the
interplay between these various structures, and hence how such systems formed.


  Recent advances show that deep neural networks are not robust to deliberately
crafted adversarial examples which many are generated by adding human
imperceptible perturbation to clear input. Consider $l_2$ norms attacks,
Project Gradient Descent (PGD) and the Carlini and Wagner (C\&W) attacks are
the two main methods, where PGD control max perturbation for adversarial
examples while C\&W approach treats perturbation as a regularization term
optimized it with loss function together. If we carefully set parameters for
any individual input, both methods become similar. In general, PGD attacks
perform faster but obtains larger perturbation to find adversarial examples
than the C\&W when fixing the parameters for all inputs. In this report, we
propose an efficient modified PGD method for attacking ensemble models by
automatically changing ensemble weights and step size per iteration per input.
This method generates smaller perturbation adversarial examples than PGD method
while remains efficient as compared to C\&W method. Our method won the first
place in IJCAI19 Targeted Adversarial Attack competition.


  Recently, Sieber and Richter calculated semiclassically a first off-diagonal
contribution to the orthogonal form factor for a billiard on a surface of
constant negative curvature by considering orbit pairs having almost the same
action. For a generalization of this derivation to systems invariant under
non-conventional time reversal symmetry, which also belong to the orthogonal
symmetry class, we show in this paper that it is necessary to redefine the
configuration space in an appropriate way.


  Several challenging problem in clustering, partitioning and imaging have
traditionally been solved using the "spectral technique". These problems
include the normalized cut problem, the graph expander ratio problem, the
Cheeger constant problem and the conductance problem. These problems share
several common features: all seek a bipartition of a set of elements; the
problems are formulated as a form of ratio cut; the formulation as discrete
optimization is shown here to be equivalent to a quadratic ratio, sometimes
referred to as the Raleigh ratio, on discrete variables and a single sum
constraint which we call the balance or orthogonality constraint; when the
discrete nature of the variables is disregarded, the continuous relaxation is
solved by the spectral method. Indeed the spectral relaxation technique is a
dominant method providing an approximate solution to these problems.
  We propose an algorithm for these problems which involves a relaxation of the
orthogonality constraint only. This relaxation is shown here to be solved
optimally, and in strongly polynomial time, in O(mn log((n^2) / m) for a graph
on $n$ nodes and $m$ edges. The algorithm, using HPF (Hochbaum's Pseudo-Flow)
as subroutine, is efficient enough to be used to solve these bi-partitioning
problems on millions of elements and more than 300 million edges within less
than 10 minutes. It is also demonstrated, via a preliminary experimental study,
that the results of the combinatorial algorithm proposed often improve
dramatically on the quality of the results of the spectral method.


  Let $A$ be a commutative Banach algebra with non-empty character space
$\Delta(A)$. In this paper, we change the concepts of convergence and
boundedness in the classical notion of bounded approximate identity. This work
give us a new kind of approximate identity between bounded approximate identity
and bounded weak approximate identity. More precisely, a net $\{e_{\alpha}\}$
in $A$ is a \emph{c-w approximate identity} if for each $a\in A$, the Gel'fand
transform of $e_{\alpha}a$ tends to the Gel'fand transform of $a$ in the
compact-open topology and we say $\{e_{\alpha}\}$ is \emph{weakly bounded} if
the image of $\{e_{\alpha}\}$ under the Gel'fand transform is bounded in
$C_{0}(\Delta(A))$.


  We characterize the indecomposable injective objects in the category of
finitely presented representations of an interval finite quiver.


  Alongside superfluidity, itinerant (Stoner) ferromagnetism remains one of the
most well-characterized phases of correlated Fermi systems. A recent experiment
has reported the first evidence for novel phase behavior on the repulsive side
of the Feshbach resonance in a two-component ultracold Fermi gas. By adapting
recent theoretical studies to the atomic trap geometry, we show that an
adiabatic ferromagnetic transition would take place at a weaker interaction
strength than is observed in experiment. This discrepancy motivates a simple
non-equilibrium theory that takes account of the dynamics of magnetic defects
and three-body losses. The formalism developed displays good quantitative
agreement with experiment.


  Large amount of electronic data is generated in Cloud computing every day.
Efficient maintenance of this data requires proper services. Hence a method to
collect data securely, by protecting and developing backups is mentioned. The
Objective is to provide Auto Response Server, better solutions for data backup
and restoring using Cloud. Data can be collected and sent to a centralized
repository in a platform independent format without any network consideration.
This data can then be used according to the requirement. The purpose of this
particular Remote Backup Server is to collect information from any remote
location even if network connectivity is not available at that point of time
and provide proper services as well as to recover data in case of loss.


  We prove an Erd\H{o}s-Kac type of theorem for the set $S(x,y)=\{n\leq x: p|n
\Rightarrow p\leq y \}$. If $\omega (n)$ is the number of prime factors of $n$,
we prove that the distribution of $\omega(n)$ for $n \in S(x,y)$ is Gaussian
for a certain range of $y$ using method of moments. The advantage of the
present approach is that it recovers classical results for the range $u=o(\log
\log x )$ where $u=\frac{\log x}{\log y}$, with a much simpler proof.


  CONTEXT. The exquisite precision of the space-based photometric surveys and
the unavoidable presence of instrumental systematics and intrinsic stellar
variability call for the development of sophisticated methods that separate
these signal components from those caused by planetary transits. AIMS. Here we
introduce tran_k2 a stand-alone Fortran code to search for planetary transits
under the colored noise of stellar variability and instrumental effects. With
this code we perform a survey for new candidates. METHODS. Stellar variability
is represented by a Fourier series, and, if needed, by an autoregressive model
to avoid excessive Gibbs overshoots at the edges. For the treatment of
systematics, cotrending and external parameter decorrelation are employed by
using cotrending stars with low stellar variability, the chip position and the
background flux level at the target. The filtering is made within the framework
of the standard weighted least squares, where the weights are determined
iteratively, to allow robust fit and separate the transit signal from stellar
variability and systematics. Once the periods of the transit components are
determined from the filtered data by the box-fitting least squares method, we
reconstruct the full signal and determine the transit parameters with a higher
accuracy. This step greatly reduces the excessive attenuation of the transit
depths and minimizes shape deformation. RESULTS. The code was tested on the
field of Campaign 5 of the K2 mission. We detected 98% of the systems with all
their candidate planets reported earlier by other authors, surveyed the whole
field and discovered 15 new systems. Additional 3 planets were found in 3
multiplanetary systems and 2 more planets were found in a previously known
single planet system.


  A new coronavirus disease, called COVID-19, appeared in the Chinese region of
Wuhan at the end of last year; since then the virus spread to other countries,
including most of Europe. We propose a differential equation governing the
evolution of the COVID-19. This dynamic equation also describes the evolution
of the number of infected people for 13 common respiratory viruses (including
the SARS-CoV-2). We validate our theoretical predictions with experimental data
for Italy, Belgium and Luxembourg, and compare them with the predictions of the
logistic model. We find that our predictions are in good agreement with the
real world since the beginning of the appearance of the COVID-19; this is not
the case for the logistic model that only applies to the first days. The second
part of the work is devoted to modelling the descending phase, i.e. the
decrease of the number of people tested positive for COVID-19. Also in this
case, we propose a new set of dynamic differential equations that we solved
numerically. We use our differential equations parametrised with experimental
data to make several predictions, such as the date when Italy, Belgium, and
Luxembourg will reach a peak number of SARS-CoV-2 infected people. The
descending curves provide valuable information such as the duration of the
COVID-19 epidemic in a given Country and therefore when it will be possible to
return to normal life. The study of the the dynamics of COVID-19 when the
population have been subject to less restrictive measures is beyond the scope
of this work and it will be matter of future works.


  In this work we present a novel item recommendation approach that aims at
improving Collaborative Filtering (CF) in social tagging systems using the
information about tags and time. Our algorithm follows a two-step approach,
where in the first step a potentially interesting candidate item-set is found
using user-based CF and in the second step this candidate item-set is ranked
using item-based CF. Within this ranking step we integrate the information of
tag usage and time using the Base-Level Learning (BLL) equation coming from
human memory theory that is used to determine the reuse-probability of words
and tags using a power-law forgetting function.
  As the results of our extensive evaluation conducted on data-sets gathered
from three social tagging systems (BibSonomy, CiteULike and MovieLens) show,
the usage of tag-based and time information via the BLL equation also helps to
improve the ranking and recommendation process of items and thus, can be used
to realize an effective item recommender that outperforms two alternative
algorithms which also exploit time and tag-based information.


  A quantum anharmonic oscillator is defined by the Hamiltonian ${\cal H}=
-\frac{ {\rm d^{2}}}{{\rm d}x^{2}} + V(x)$, where the potential is given by
$V(x) = \sum_{i=1}^{m} c_{i} x^{2i}$ with $c_{m}>0$. Using the Sinc collocation
method combined with the double exponential transformation, we develop a method
to efficiently compute highly accurate approximations of energy eigenvalues for
anharmonic oscillators. Convergence properties of the proposed method are
presented. Using the principle of minimal sensitivity, we introduce an
alternate expression for the mesh size for the Sinc collocation method which
improves considerably the accuracy in computing eigenvalues for potentials with
multiple wells.
  We apply our method to a number of potentials including potentials with
multiple wells. The numerical results section clearly illustrates the high
efficiency and accuracy of the proposed method. All our codes are written using
the programming language Julia and are available upon request.


  The colored Jones function of a knot is a sequence of Laurent polynomials
that encodes the Jones polynomial of a knot and its parallels. It has been
understood in terms of representations of quantum groups and Witten gave an
intrinsic quantum field theory interpretation of the colored Jones function as
the expectation value of Wilson loops of a 3-dimensional gauge theory, the
Chern-Simons theory. We present the colored Jones function as an evaluation of
the inverse of a non-commutative fermionic partition function. This result is
in the form familiar in quantum field theory, namely the inverse of a
generalized determinant.
  Our formula also reveals a direct relation between the Alexander polynomial
and the colored Jones function of a knot and immediately implies the
extensively studied Melvin-Morton-Rozansky conjecture, first proved by
Bar-Natan and the first author about ten years ago.


  We investigate the avalanche dynamics of the abelian sandpile model on
arbitrarily large balls of the expanded cactus graph (the Cayley graph of the
free product $\mathbb{Z}_3 * \mathbb{Z}_2$). We follow the approach of Dhar and
Majumdar (1990) to enumerate the number of recurrent configurations. We also
propose the filling method of enumerating all the recurrent configurations in
which adding a grain to a designated origin vertex (far enough away from the
boundary vertices) causes topplings to occur in a specific cluster (a connected
subgraph that is the union of cells, or copies of the 3-cycle) within the first
wave of an avalanche. This filling method lends itself to combinatorial
evaluation of the number of positions in which a certain number of cells topple
in an avalanche starting at the origin, which are amenable to analysis using
well-known recurrences and corresponding generating functions. We show that,
when counting cells that topple in the avalanche, the cell-wise first-wave
critical exponent of the Abelian sandpile model on the expanded cactus is 3/2.


  We describe a nonsmooth notion of globally hyperbolic, regular length metric
spacetimes $(\mathrm{M},l)$. It is based on ideas of Kunzinger-S\"amann, but
does not require Lipschitz continuity of causal curves. We study geodesics on
$\mathrm{M}$ and the space of probability measures over $\mathrm{M}$ in detail.
  Furthermore, for such a spacetime endowed with a reference measure
$\mathfrak{m}$, a lower semicontinuous function $k\colon \mathrm{M} \to
\textbf{R}$, and constants $0<p<1$ and $N\geq 1$, we introduce and study the
entropic timelike curvature dimension condition $\smash{\mathrm{TCD}_p^e(k,N)}$
with variable Ricci curvature bound $k$. This provides a unified synthetic
approach to general relativistic energy conditions, including
  $\bullet$ the Hawking-Penrose strong energy condition $\mathrm{Ric}\geq 0$,
or more generally $\mathrm{Ric}\geq K$ for constant $K\in\textbf{R}$, in all
timelike directions,
  $\bullet$ the weak energy condition $\mathrm{Ric} \geq \mathrm{scal} -
\Lambda$ in all timelike directions, and
  $\bullet$ the null energy condition $\smash{\mathrm{Ric} \geq 0}$ in all null
directions.
  Our approach also allows for the synthetic quantification of asymptotic
conditions or integral controls on the timelike Ricci curvature. For example,
we give a nonsmooth generalization of a timelike diameter estimate of
Frankel-Galloway (and Schneider), and of a Hawking-type singularity theorem
which requires only that the negative Ricci curvature have small enough
integral relative to the maximal mean curvature of an achronal slice.
  As further applications, we discuss the stability of our notion and provide
timelike geometric inequalities. To obtain sharp constants in the latter, we
develop the localization paradigm in the variable $k$ framework.


  The exponentially weighted moving average (EMWA) could be labeled as a
competitive volatility estimator, where its main strength relies on computation
simplicity, especially in a multi-asset scenario, due to dependency only on the
decay parameter, $\lambda$. But, what is the best election for $\lambda$ in the
EMWA volatility model? Through a large time-series data set of historical
returns of the top US large-cap companies; we test empirically the forecasting
performance of the EWMA approach, under different time horizons and varying the
decay parameter. Using a rolling window scheme, the out-of-sample performance
of the variance-covariance matrix is computed following two approaches. First,
if we look for a fixed decay parameter for the full sample, the results are in
agreement with the RiskMetrics suggestion for 1-month forecasting. In addition,
we provide the full-sample optimal decay parameter for the weekly and bi-weekly
forecasting horizon cases, confirming two facts: i) the optimal value is as a
function of the forecasting horizon, and ii) for lower forecasting horizons the
short-term memory gains importance. In a second way, we also evaluate the
forecasting performance of EWMA, but this time using the optimal time-varying
decay parameter which minimizes the in-sample variance-covariance estimator,
arriving at better accuracy than the use of a fixed-full-sample optimal
parameter.


  In this article we calculate the five-loop anomalous dimension of twist-two
operators in the planar N=4 SYM theory. Firstly, using reciprocity, we derive
the contribution of the asymptotic Bethe ansatz. Subsequently, we employ the
first finite-size correction for the AdS5xS5 sigma model to determine the
wrapping correction. The anomalous dimension found in this way passes all known
tests provided by the NLO BFKL equation and double-logarithmic constraints.
This result thus furnishes an infinite number of experimental data for testing
the veracity of the recently proposed spectral equations for planar AdS/CFT
correspondence.


  The last decade has seen an unprecedented growth in artificial intelligence
and photonic technologies, both of which drive the limits of modern-day
computing devices. In line with these recent developments, this work brings
together the state of the art of both fields within the framework of
reinforcement learning. We present the blueprint for a photonic implementation
of an active learning machine incorporating contemporary algorithms such as
SARSA, Q-learning, and projective simulation. We numerically investigate its
performance within typical reinforcement learning environments, showing that
realistic levels of experimental noise can be tolerated or even be beneficial
for the learning process. Remarkably, the architecture itself enables
mechanisms of abstraction and generalization, two features which are often
considered key ingredients for artificial intelligence. The proposed
architecture, based on single-photon evolution on a mesh of tunable
beamsplitters, is simple, scalable, and a first integration in portable systems
appears to be within the reach of near-term technology.


  We work out a theory of shot noise in a special case. This is a noise of the
Coulomb drag current excited under the ballistic transport regime in a
one-dimensional nanowire by a ballistic non-Ohmic current in a nearby parallel
nanowire. We predict sharp oscillation of the noise power as a function of gate
voltage or the chemical potential of electrons. We also study dependence of the
noise on the voltage V across the driving wire. For relatively large values of
V the noise power is proportional to V^2.


  The force field by Lenosky and coworkers is the latest force field for
silicon which is one of the most studied materials. It has turned out to be
highly accurate in a large range of test cases. The optimization and
parallelization of this force field using OpenMp and Fortan90 is described
here. The optimized program allows us to handle a very large number of silicon
atoms in large scale simulations. Since all the parallelization is hidden in a
single subroutine that returns the total energies and forces, this subroutine
can be called from within a serial program in an user friendly way.


  Cyclic codes have efficient encoding and decoding algorithms over finite
fields, so that they have practical applications in communication systems,
consumer electronics and data storage systems. The objective of this paper is
to give eight new classes of optimal ternary cyclic codes with parameters
$[3^m-1,3^m-1-2m,4]$, according to a result on the non-existence of solutions
to a certain equation over $F_{3^m}$. It is worth noticing that some recent
conclusions on such optimal ternary cyclic codes are some special cases of our
work. More importantly, three of the nine open problems proposed by Ding and
Helleseth in [8] are solved completely. In addition, another one among the nine
open problems is also promoted.


  We consider the Sasa-Satsuma (SS) and Nonlinear Schr\"odinger (NLS) equations
posed along the line, in 1+1 dimensions. Both equations are canonical
integrable $U(1)$ models, with solitons, multi-solitons and breather solutions,
see Yang for instance. For these two equations, we recognize four distinct
localized breather modes: the Sasa-Satsuma for SS, and for NLS the
Satsuma-Yajima, Kuznetsov-Ma and Peregrine breathers. Very little is known
about the stability of these solutions, mainly because of their complex
structure, which does not fit into the classical soliton behavior by
Grillakis-Shatah-Strauss. In this paper we find the natural $H^2$ variational
characterization for each of them, and prove that Sasa-Satsuma breathers are
$H^2$ nonlinearly stable, improving the linear stability property previously
proved by Pelinovsky and Yang. Moreover, in the SS case, we provide an
alternative understanding of the SS solution as a breather, and not only as an
embedded soliton. The method of proof is based in the use of a $H^2$ based
Lyapunov functional, in the spirit of the first and third authors, extended
this time to the vector-valued case. We also provide another rigorous
justification of the instability of the remaining three nonlinear modes
(Satsuma-Yajima, Peregrine y Kuznetsov-Ma), based in the study of their
corresponding linear variational structure (as critical points of a suitable
Lyapunov functional), and complementing the instability results recently proved
e.g. in a paper by the third author.


  We consider the random continued fraction S(t) := 1/(s_1 + t/(s_2 + t/(s_3 +
>...))) where the s_n are independent random variables with the same gamma
distribution. For every realisation of the sequence, S(t) defines a Stieltjes
function. We study the convergence of the finite truncations of the continued
fraction or, equivalently, of the diagonal Pade approximants of the function
S(t). By using the Dyson--Schmidt method for an equivalent one-dimensional
disordered system, and the results of Marklof et al. (2005), we obtain explicit
formulae (in terms of modified Bessel functions) for the almost-sure rate of
convergence of these approximants, and for the almost-sure distribution of
their poles.


  Elaborating on our joint work with Abramsky in quant-ph/0402130 we further
unravel the linear structure of Hilbert spaces into several constituents. Some
prove to be very crucial for particular features of quantum theory while others
obstruct the passage to a formalism which is not saturated with physically
insignificant global phases.
  First we show that the bulk of the required linear structure is purely
multiplicative, and arises from the strongly compact closed tensor which,
besides providing a variety of notions such as scalars, trace, unitarity,
self-adjointness and bipartite projectors, also provides Hilbert-Schmidt norm,
Hilbert-Schmidt inner-product, and in particular, the preparation-state
agreement axiom which enables the passage from a formalism of the vector space
kind to a rather projective one, as it was intended in the (in)famous Birkhoff
& von Neumann paper.
  Next we consider additive types which distribute over the tensor, from which
measurements can be build, and the correctness proofs of the protocols
discussed in quant-ph/0402130 carry over to the resulting weaker setting. A
full probabilistic calculus is obtained when the trace is moreover linear and
satisfies the \em diagonal axiom, which brings us to a second main result,
characterization of the necessary and sufficient additive structure of a both
qualitatively and quantitatively effective categorical quantum formalism
without redundant global phases. Along the way we show that if in a category a
(additive) monoidal tensor distributes over a strongly compact closed tensor,
then this category is always enriched in commutative monoids.


  Studies of open-charm hadron production in pp and \pPb collisions are
performed by the ALICE Collaboration at the LHC to investigate charm-quark
hadronization mechanisms. Recent measurements of charm meson (${\rm D^0}$,
${\rm D^+}$, ${\rm D^+_{\rm s}}$, and ${\rm D^{*+}}$) and baryon
($\Lambda^+_{\rm c}$, $\Xi^{0,+}_{\rm c}$, $\Sigma^{0,++}_{\rm c}$, and
$\Omega^0_{\rm c}$) production in pp collisions at $\sqrt{s}$ = 5.02 TeV and
$\sqrt{s}$ = 13 TeV allow the determination of the charm cross section and the
fragmentation fractions at $\sqrt{s}$ = 5.02 TeV with unprecedented precision.
The measurements show that the fragmentation fractions significantly differ
from the ones measured in ${\rm e^+e^-}$ and \ep collisions. This highlights
possible differences in the hadronization process between electron induced
collisions and pp collisions at the LHC. \\ Furthermore, the first measurement
of the baryon-to-meson yield ratio $\Lambda^+_{\rm c}/{\rm D^0}$, down to
$p_{\rm T}=0$ in pp and \pPb collisions will be discussed. In p--Pb collisions
a modification of the hadronization mechanisms could be present due to cold
nuclear matter effects and collective phenomena. A systematic comparison
between data and model calculations will help to understand charm quark
hadronization in pp and p--Pb collisions.


  One of the most intriguing features of Earth's axial magnetic dipole field,
well-known from the geological record, is its occasional and unpredictable
reversal of polarity. Understanding the phenomenon is rendered very difficult
by the highly non-linear nature of the underlying magnetohydrodynamic problem.
Numerical simulations of the liquid outer core, where regeneration occurs, are
only able to model conditions that are far from Earth-like. On the analytical
front, the situation is not much better; basic calculations, such as relating
the average rate of reversals to various core parameters, have apparently been
intractable. Here, we present a framework for solving such problems. Starting
with the magnetic induction equation, we show that by considering its sources
to be stochastic processes with fairly general properties, we can derive a
differential equation for the joint probability distribution of the dominant
toroidal and poloidal modes. This can be simplified to a Fokker-Planck equation
and, with the help of an adiabatic approximation, reduced even further to an
equation for the dipole amplitude alone. From these equations various
quantities related to the magnetic field, including the average reversal rate,
field strength, and time to complete a reversal, can be computed as functions
of a small number of numerical parameters. These parameters in turn can be
computed from physical considerations or constrained by paleomagnetic,
numerical, and experimental data.


  Machine learning techniques have shown remarkable accuracy in localization
tasks, but their dependency on vast amounts of labeled data, particularly
Channel State Information (CSI) and corresponding coordinates, remains a
bottleneck. Self-supervised learning techniques alleviate the need for labeled
data, a potential that remains largely untapped and underexplored in existing
research. Addressing this gap, we propose a pioneering approach that leverages
self-supervised pretraining on unlabeled data to boost the performance of
supervised learning for user localization based on CSI. We introduce two
pretraining Auto Encoder (AE) models employing Multi Layer Perceptrons (MLPs)
and Convolutional Neural Networks (CNNs) to glean representations from
unlabeled data via self-supervised learning. Following this, we utilize the
encoder portion of the AE models to extract relevant features from labeled
data, and finetune an MLP-based Position Estimation Model to accurately deduce
user locations. Our experimentation on the CTW-2020 dataset, which features a
substantial volume of unlabeled data but limited labeled samples, demonstrates
the viability of our approach. Notably, the dataset covers a vast area spanning
over 646x943x41 meters, and our approach demonstrates promising results even
for such expansive localization tasks.


  We examine several types of symmetries which are relevant to quantum phase
transitions in nuclei. These include: critical-point, quasidynamical, and
partial dynamical symmetries.