  We develop techniques for computing the integer valued SU(3) Casson
invariant. Our method involves resolving the singularities in the flat moduli
space using a twisting perturbation and analyzing its effect on the topology of
the perturbed flat moduli space. These techniques, together with Bott-Morse
theory and the splitting principle for spectral flow, are applied to calculate
the invariant for all Brieskorn homology spheres.


  The forgotten topological index of a graph $G$, denoted by $F(G)$, is defined
as the sum of weights $d(u)^{2}+d(v)^{2}$ over all edges $uv$ of $G$ , where
$d(u)$ denotes the degree of a vertex $u$. In this paper, we give sharp upper
bounds of the F-index (forgotten topological index) over bicyclic graphs, in
terms of the order and maximum degree.


  We present the properties of magnetic fields (B-fields) in two clumps (clump
1 and clump 2), located at the waist of the bipolar H II region Sh2-201, based
on JCMT SCUBA-2/POL-2 observations of 850 $\mu$m polarized dust emission. We
find that B-fields in the direction of the clumps are bent and compressed,
showing bow-like morphologies, which we attribute to the feedback effect of the
H II region on the surface of the clumps. Using the modified
Davis-Chandrasekhar-Fermi method we estimate B-fields strengths of 266 $\mu$G
and 65 $\mu$G for clump 1 and clump 2, respectively. From virial analyses and
critical mass ratio estimates, we argue that clump 1 is gravitationally bound
and could be undergoing collapse, whereas clump 2 is unbound and stable. We
hypothesize that the interplay between thermal pressure imparted by the H II
region, B-field morphologies, and the various internal pressures of the clumps
(such as magnetic, turbulent, and gas thermal pressure), has the following
consequences: (a) formation of clumps at the waist of the H II region; (b)
progressive compression and enhancement of the B-fields in the clumps; (c)
stronger B-fields will shield the clumps from erosion by the H II region and
cause pressure equilibrium between the clumps and the H II region, thereby
allowing expanding I-fronts to blow away from the filament ridge, forming
bipolar H II regions; and (d) stronger B-fields and turbulence will be able to
stabilize the clumps. A study of a larger sample of bipolar H II regions would
help to determine whether our hypotheses are widely applicable.


  Lepton flavor violation (LFV) represents a clear new physics (NP) signal
beyond the standard model (SM). In this paper, we study LFV decays
$Z\rightarrow l^{\pm}_{i}l^{\mp}_{j}$ in the B-L Supersymmetric Standard
Model(B-LSSM). We calculate these processes separately in the mass eigenstate
basis and the electroweak interaction basis, and the latter adopt the mass
insertion approximation (MIA) method. The MIA clearly shows the effect of
parameters on the LFV decays $Z\rightarrow l^{\pm}_{i}l^{\mp}_{j}$ in the
analytic level, which provides a new way for us to analyze the LFV processes.
At the same time, the corresponding constraints from the LFV decays $l^{-}_{j}
\rightarrow l^{-}_{i} \gamma$ and $(g-2)_{\mu}$ are considered to analyze the
numerical results.


  We present the numbers of ice model and eight-vertex model configurations
(with Boltzmann factors equal to one), I(n) and E(n) respectively, on the
two-dimensional Sierpinski gasket SG(n) at stage $n$. For the eight-vertex
model, the number of configurations is $E(n)=2^{3(3^n+1)/2}$ and the entropy
per site, defined as $\lim_{v \to \infty} \ln E(n)/v$ where $v$ is the number
of vertices on SG(n), is exactly equal to $\ln 2$. For the ice model, the upper
and lower bounds for the entropy per site $\lim_{v \to \infty} \ln I(n)/v$ are
derived in terms of the results at a certain stage. As the difference between
these bounds converges quickly to zero as the calculated stage increases, the
numerical value of the entropy can be evaluated with more than a hundred
significant figures accurate. The corresponding result of ice model on the
generalized two-dimensional Sierpinski gasket SG_b(n) with $b=3$ is also
obtained. For the generalized vertex model on SG_3(n), the number of
configurations is $2^{(8 \times 6^n +7)/5}$ and the entropy per site is equal
to $\frac87 \ln 2$. The general upper and lower bounds for the entropy per site
for arbitrary $b$ are conjectured.


  The security of public-key cryptosystems relies on computationally hard
problems, that are classically analyzed by number theoretic methods. In this
paper, we introduce a new perspective on cryptosystems by interpreting the
Diffie-Hellman key exchange as a nonlinear dynamical system. Employing Koopman
theory, we transfer this dynamical system into a higher-dimensional space to
analytically derive a purely linear system that equivalently describes the
underlying cryptosystem. In this form, analytic tools for linear systems allow
us to reconstruct the secret integers of the key exchange by simple
manipulations. Moreover, we provide an upper bound on the minimal required
lifting dimension to obtain perfect accuracy. To demonstrate the potential of
our method, we relate our findings to existing results on algorithmic
complexity. Finally, we transfer this approach to a data-driven setting where
the Koopman representation is learned from data samples of the cryptosystem.


  Modeling languages in software engineering (e.g., UML) evolved from software
systems modeling where denotational and operational kinds of semantics are the
traditional subjects of research and practice. According to some authors,
although a large portion of the static semantics (e.g., UML) seems to have
reached a consensus, the dynamic semantics of activities, interactions, and
state machines poses a major challenge. Central to semantics is the
relationship between a sentence and the (actual) world. Carefully examining
semantics-related issues in the modeling languages field to avoid problems that
may affect practical applicability is important. One effort in this direction
is OMG s release of a 2020 draft specification for Foundational UML (fUML),
with the base semantics specifying executions that are executable in the same
sense as a program in a traditional programming language. Additionally, efforts
within academia have sought to develop an alternative approach to modeling
languages using formal semantics (e.g., using Russell s theory of types and
Tarski s declarative semantics). This paper aims at a similar exploratory
venture of developing semantics, only for a much more modest diagrammatic
modeling language, called the thinging machine model. The model promotes a deep
understanding of the scrutinized modeling language and leads to considerably
fruitful questions. Constructing the thinging machine model seems to facilitate
progress in this direction, and the initial results in this paper indicate the
viability of the approach.


  We study the thermalization of an ensemble of $N$ elementary,
arbitrarily-complex, quantum systems, mutually noninteracting but coupled as
electric or magnetic dipoles to a blackbody radiation. The elementary systems
can be all the same or belong to different species, distinguishable or
indistinguishable, located at fixed positions or having translational degrees
of freedom. Even if the energy spectra of the constituent systems are
nondegenerate, as we suppose, the ensemble unavoidably presents degeneracies of
the energy levels and/or of the energy gaps. We show that, due to these
degeneracies, a thermalization analysis performed by the popular quantum
optical master equation reveals a number of serious pathologies, possibly
including a lack of ergodicity. On the other hand, a consistent thermalization
scenario is obtained by introducing a Lindblad-based approach, in which the
Lindblad operators, instead of being derived from a microscopic calculation,
are established as the elements of an operatorial basis with squared amplitudes
fixed by imposing a detailed balance condition and requiring their
correspondence with the dipole transition rates evaluated under the first-order
perturbation theory. Due to the above-mentioned degeneracies, this procedure
suffers a basis arbitrariness which, however, can be removed by exploiting the
fact that the thermalization of an ensemble of noninteracting systems cannot
depend on the ensemble size. As a result, we provide a clear-cut partitioning
of the thermalization time into dissipation and decoherence times, for which we
derive formulas giving the dependence on the energy levels of the elementary
systems, the size $N$ of the ensemble, and the temperature of the blackbody
radiation.


  Transverse-mass spectra of protons, pions and kaons produced in collisions of
heavy nuclei are analyzed within the model of 3-fluid dynamics. It was
demonstrated that this model consistently reproduces these spectra in wide
ranges of incident energies E_{lab}, from 4A GeV to 160A GeV, rapidity bins and
centralities of the collisions. In particular, the model describes the
"step-like" dependence of kaon inverse slopes on the incident energy. The key
point of this explanation is interplay of hydrodynamic expansion of the system
with its dynamical freeze-out.


  The goal of sentiment-to-sentiment "translation" is to change the underlying
sentiment of a sentence while keeping its content. The main challenge is the
lack of parallel data. To solve this problem, we propose a cycled reinforcement
learning method that enables training on unpaired data by collaboration between
a neutralization module and an emotionalization module. We evaluate our
approach on two review datasets, Yelp and Amazon. Experimental results show
that our approach significantly outperforms the state-of-the-art systems.
Especially, the proposed method substantially improves the content preservation
performance. The BLEU score is improved from 1.64 to 22.46 and from 0.56 to
14.06 on the two datasets, respectively.


  We study the performance of a Bayesian statistician who estimates a rank-one
signal corrupted by non-symmetric rotationally invariant noise with a generic
distribution of singular values. As the signal-to-noise ratio and the noise
structure are unknown, a Gaussian setup is incorrectly assumed. We derive the
exact analytic expression for the error of the mismatched Bayes estimator and
also provide the analysis of an approximate message passing (AMP) algorithm.
The first result exploits the asymptotic behavior of spherical integrals for
rectangular matrices and of low-rank matrix perturbations; the second one
relies on the design and analysis of an auxiliary AMP. The numerical
experiments show that there is a performance gap between the AMP and Bayes
estimators, which is due to the incorrect estimation of the signal norm.


  This paper presents an $\mathcal{E}$-derivation analogue of a result on
derivations due to van den Essen, Wright and Zhao. We prove that the image of a
locally finite $K$-$\mathcal{E}$-derivation of polynomial algebras in two
variables over a field $K$ of characteristic zero is a Mathieu-Zhao subspace.
This result together with that of van den Essen, Wright and Zhao confirms the
LFED conjecture in the case of polynomial algebras in two variables.


  We calibrate the photographic photometry of the revised New Luyten Two-Tenths
catalog (rNLTT) by matching 3448 rNLTT stars to the Sloan Digital Sky Survey
(SDSS). The correction is linear in magnitude and goes from zero at V ~ 14 to
0.32 mag at V=19, in the sense that rNLTT was previously too bright. The
correction implies that the underlying USNO-A2.0 photometry, on which rNLTT
photometry is based, is non-linear. The new calibration somewhat improves the
appearance of the (V,V-J) reduced proper motion diagram in the sense of better
separation between disk and halo stars. We repeat Gould's analysis of 5000 halo
stars in rNLTT. The most important change is to move the peak of the halo
luminosity function about 0.5 mag dimmer, from M_V=10.5 to M_V=11, putting it
into good agreement with the parallax-based determination of Dahn et al.


  Let $X$ be a smooth threefold with a simple normal crossings divisor $D$. We
construct the Donaldson-Thomas theory of the pair $(X|D)$ enumerating ideal
sheaves on $X$ relative to $D$. These moduli spaces are compactified by
studying subschemes in expansions of the target geometry, and the moduli space
carries a virtual fundamental class leading to numerical invariants with
expected properties. We formulate punctual evaluation, rationality and
wall-crossing conjectures, in parallel with the standard theory. Our formalism
specializes to the Li-Wu theory of relative ideal sheaves when the divisor is
smooth, and is parallel to recent work on logarithmic Gromov-Witten theory with
expansions.


  A dipolar gate alternative to the exchange gate based Kane quantum computer
is proposed where the qubits are electron spins of shallow group V donors in
silicon. Residual exchange coupling is treated as gate error amenable to
quantum error correction, removing the stringent requirements on donor
positioning characteristic of all silicon exchange-based implementations [B.
Koiller et al., Phys. Rev. Lett. 88, 027903 (2002)]. Contrary to common
speculation, such a scheme is scalable with no overhead in gating time even
though it is based on long-range dipolar inter-qubit coupling.


  We consider neural networks with a single hidden layer and non-decreasing
homogeneous activa-tion functions like the rectified linear units. By letting
the number of hidden units grow unbounded and using classical non-Euclidean
regularization tools on the output weights, we provide a detailed theoretical
analysis of their generalization performance, with a study of both the
approximation and the estimation errors. We show in particular that they are
adaptive to unknown underlying linear structures, such as the dependence on the
projection of the input variables onto a low-dimensional subspace. Moreover,
when using sparsity-inducing norms on the input weights, we show that
high-dimensional non-linear variable selection may be achieved, without any
strong assumption regarding the data and with a total number of variables
potentially exponential in the number of ob-servations. In addition, we provide
a simple geometric interpretation to the non-convex problem of addition of a
new unit, which is the core potentially hard computational element in the
framework of learning from continuously many basis functions. We provide simple
conditions for convex relaxations to achieve the same generalization error
bounds, even when constant-factor approxi-mations cannot be found (e.g.,
because it is NP-hard such as for the zero-homogeneous activation function). We
were not able to find strong enough convex relaxations and leave open the
existence or non-existence of polynomial-time algorithms.


  In this paper we study the action of a generalization of the Binomial
interpolated operator on the set of linear recurrent sequences. We find how the
zeros of characteristic polynomials are changed and we prove that a subset of
these operators form a group, with respect to a well-defined composition law.
Furthermore, we study a vast class of linear recurrent sequences fixed by these
operators and many other interesting properties. Finally, we apply all the
results to integer sequences, finding many relations and formulas involving
Catalan numbers, Fibonacci numbers, Lucas numbers and triangular numbers.


  Engaging all content providers, including newcomers or minority demographic
groups, is crucial for online platforms to keep growing and working. Hence,
while building recommendation services, the interests of those providers should
be valued. In this paper, we consider providers as grouped based on a common
characteristic in settings in which certain provider groups have low
representation of items in the catalog and, thus, in the user interactions.
Then, we envision a scenario wherein platform owners seek to control the degree
of exposure to such groups in the recommendation process. To support this
scenario, we rely on disparate exposure measures that characterize the gap
between the share of recommendations given to groups and the target level of
exposure pursued by the platform owners. We then propose a re-ranking procedure
that ensures desired levels of exposure are met. Experiments show that, while
supporting certain groups of providers by rendering them with the target
exposure, beyond-accuracy objectives experience significant gains with
negligible impact in recommendation utility.


  We construct a continuous time model for price-mediated contagion
precipitated by a common exogenous stress to the banking book of all firms in
the financial system. In this setting, firms are constrained so as to satisfy a
risk-weight based capital ratio requirement. We use this model to find
analytical bounds on the risk-weights for assets as a function of the market
liquidity. Under these appropriate risk-weights, we find existence and
uniqueness for the joint system of firm behavior and the asset prices. We
further consider an analytical bound on the firm liquidations, which allows us
to construct exact formulas for stress testing the financial system with
deterministic or random stresses. Numerical case studies are provided to
demonstrate various implications of this model and analytical bounds.


  Dense image matching is a fundamental low-level problem in Computer Vision,
which has received tremendous attention from both discrete and continuous
optimization communities. The goal of this paper is to combine the advantages
of discrete and continuous optimization in a coherent framework. We devise a
model based on energy minimization, to be optimized by both discrete and
continuous algorithms in a consistent way. In the discrete setting, we propose
a novel optimization algorithm that can be massively parallelized. In the
continuous setting we tackle the problem of non-convex regularizers by a
formulation based on differences of convex functions. The resulting hybrid
discrete-continuous algorithm can be efficiently accelerated by modern GPUs and
we demonstrate its real-time performance for the applications of dense stereo
matching and optical flow.


  We survey on the recent progress toward mirror symmetry between
Landau-Ginzburg models.


  A conversion-reconversion experimental scheme is proposed where photons
stored in a Fabry-Perot cavity (FP) embracing a dipole conversion magnet
generate two beams of ultralight bosons emitted in opposite directions.
Fractions of the bosons convert in dipole magnets aligned along the two boson
beam lines and generate photons of the same energy and directions of the FP
grandparent photons. The reconversion photons are detected individually by
means of single photon detectors. Such an experiment can determine the bosons
parity by measurements with different angles between the polarization vector of
linearly polarized light injected into the FP and the direction of the magnetic
field Bc of the conversion magnets. It can establish both the bosons mass m and
the coupling constant to two photons gmgg by measurements with different
lengths Lr of the string of powered regeneration magnets of one boson beam
line, while the second boson beam line is left unchanged and used for
normalization. The optimal total length Lc of the string of conversion magnets
depends on m2 and on the energy E of the laser photons. For E=2.4eV Lc is of
the order of 3m if m=10-3eV and of the order of 300m if m=10-4eV. If the
signals observed by the PVLAS experiment are due to the existence of ultralight
bosons with m=10-3eV and gmgg=10-6GeV-1, these regeneration measurements are
feasible with existing tachnology on a site of length below 100m in relatively
short periods of data taking time.


  I review some of the highlights of results from non-hadron collider flavor
experiments shown at the EPS conference in the summer of 2009. These include
highlights of the latest results from the BaBar and Belle B-factories, CLEO-c,
BES-III, NA48, KTeV, KLOE, NA62, MEG, and mu to e conversion experiments.


  We present a theoretical study of the gravitational wave (GW) driven
inspirals of accreting black hole binaries with mass $M = 10^7 M_\odot$ and
mass ratios between $10^{-3}$ and $10^{-1}$. Our results are based on analytic
estimates, and grid-based hydrodynamics simulations run for many thousands of
binary orbits before the merger. We show that the GW inspiral is evident in the
light curves and color evolution of a binary-hosting quasar, over years to
decades before a merger. The long-term electromagnetic (EM) signature is
characterized by a gradual UV brightening, and X-ray dimming, followed by an
X-ray disappearance hours to days before the GW burst, and finally a years-like
re-brightening as the disk relaxes and refuels the remnant black hole. These
timescales are surprisingly insensitive to the amplitude of viscous stress in
the disk. The spectrum of quasi-thermal disk emission shows two peaks: one in
the UV, and another in the X-ray, associated with the outer and
circum-secondary disks respectively; emission from the inner disk is suppressed
because the secondary consumes most of the inflowing gas. We discuss
implications for real-time and archival EM followup of GW bursts detected by
LISA.


  In ultralong fiber laser key distribution, two sides use standard optical
equipment to create kilometer long fiber lasers in a communication link to
establish a secret key. Its security rests on the assumption that any attacker
would need much more sophisticated equipment and techniques than those of the
legitimate user in order to discover the generated key. We present a challenge
to that assumption with a hidden probe attack in which the eavesdropper hides a
weak signal in the unavoidable noise floor that appears in the laser during
amplification and probes with it the configuration of one or both communication
parties. We comment how this attack can compromise different proposals for
ultralong laser key distribution and propose possible countermeasures.


  The boundary of a boson system plays an important role in determining the
momentum distribution of the bosons. For a boson system with a cylindrical
boundary, the momentum distribution is enhanced at high transverse momenta but
suppressed at low transverse momenta, relative to a Bose-Einstein distribution.
The boundary effects on systems of massless gluons and massive pions are
studied. For gluons in a quark-gluon plasma, the presence of the boundary may
modify the signals for the quark-gluon plasma. For pions in a pion system in
heavy-ion collisions, Coulomb final-state interactions with the nuclear
participants in the vicinity of the central rapidity region further modify the
momentum distribution at low transverse momenta. By including both the boundary
effect and the Coulomb final-state interactions we are able to account for the
behavior of the $\pi^{-}$ transverse momentum spectrum observed in many
heavy-ion experiments, notably at low transverse momenta.


  The Hierarchical Vote Collective of Transformation-based Ensembles
(HIVE-COTE) is a heterogeneous meta ensemble for time series classification.
HIVE-COTE forms its ensemble from classifiers of multiple domains, including
phase-independent shapelets, bag-of-words based dictionaries and
phase-dependent intervals. Since it was first proposed in 2016, the algorithm
has remained state of the art for accuracy on the UCR time series
classification archive. Over time it has been incrementally updated,
culminating in its current state, HIVE-COTE 1.0. During this time a number of
algorithms have been proposed which match the accuracy of HIVE-COTE. We propose
comprehensive changes to the HIVE-COTE algorithm which significantly improve
its accuracy and usability, presenting this upgrade as HIVE-COTE 2.0. We
introduce two novel classifiers, the Temporal Dictionary Ensemble (TDE) and
Diverse Representation Canonical Interval Forest (DrCIF), which replace
existing ensemble members. Additionally, we introduce the Arsenal, an ensemble
of ROCKET classifiers as a new HIVE-COTE 2.0 constituent. We demonstrate that
HIVE-COTE 2.0 is significantly more accurate than the current state of the art
on 112 univariate UCR archive datasets and 26 multivariate UEA archive
datasets.


  We propose a model for a thermally driven microswimmer in which three spheres
are connected by two springs with odd elasticity. We demonstrate that the
presence of odd elasticity leads to the directional locomotion of the
stochastic microswimmer.


  We extend the study of nuclear dependence of the transverse momentum
dependent parton distribution functions and azimuthal asymmetries to
semi-inclusive deep inelastic scattering (SIDIS) off polarized nuclear targets.
We show that azimuthal asymmetries are suppressed for SIDIS off a polarized
nuclear target relative to that off a polarized nucleon due to multiple
scattering inside the nucleus. Using the value of transport parameter inside
large nuclei extracted from jet quenching analyses in SIDIS off nuclear
targets, we also present a numerical estimate of the nuclear suppression of the
azimuthal asymmetry that might be useful to guide the future experimental
studies of SIDIS off polarized nuclear targets.


  Using $e^+e^-$ annihilation data sets collected with the BESIII detector, we
measure the cross sections of the processes $e^+e^- \to e^+e^-$ and $e^+e^- \to
\mu^+\mu^-$ at fifteen center-of-mass energy points in the vicinity of the
$J/\psi$ resonance. By a simultaneous fit to the measured, center-of-mass
energy dependent cross sections of the two processes, the combined quantities
$\Gamma_{ee} \Gamma_{ee} / \Gamma_{\rm tot}$ and $\Gamma_{ee} \Gamma_{\mu\mu} /
\Gamma_{\rm tot}$ are determined to be ($0.346 \pm 0.009$) and ($0.335 \pm
0.006$) keV, respectively, where $\Gamma_{ee}$, $\Gamma_{\mu\mu}$, and
$\Gamma_{\rm tot}$ are the electronic, muonic, and total decay widths of the
$J/\psi$ resonance, respectively. Using the resultant $\Gamma_{ee}
\Gamma_{\mu\mu} / \Gamma_{\rm tot}$ and $\Gamma_{ee} \Gamma_{ee} / \Gamma_{\rm
tot}$, the ratio $\Gamma_{ee} / \Gamma_{\mu\mu}$ is calculated to be $1.031 \pm
0.015$, which is consistent with the expectation of lepton universality within
about two standard deviations. Assuming lepton universality and using the
branching fraction of the $J/\psi$ leptonic decay measured by BESIII in 2013,
$\Gamma_{\rm tot}$ and $\Gamma_{ll}$ are determined to be ($93.0 \pm 2.1$) and
($5.56 \pm 0.11$) keV, respectively, where $\Gamma_{ll}$ is the average
leptonic decay width of the $J/\psi$ resonance.


  We cross-correlate the Herbig & Bell and Hipparcos Catalogues in order to
extract the results for young stellar objects (YSOs). We compare the distances
of individual young stars and the distance of their presumably associated
molecular clouds, taking into account post-Hipparcos distances to the relevant
associations and using Hipparcos intermediate astrometric data to derive new
parallaxes of the pre-main sequence stars based on their grouping. We confirm
that YSOs are located in their associated clouds, as anticipated by a large
body of work, and discuss reasons which make the individual parallaxes of some
YSOs doubtful. We find in particular that the distance of Taurus YSOs as a
group is entirely consistent with the molecular cloud distance, although
Hipparcos distances of some faint Taurus-Auriga stars must be viewed with
caution. We then improve some of the solutions for the binary and multiple
pre-main sequence stars. In particular, we confirm three new astrometric young
binaries discovered by Hipparcos: RY Tau, UX Ori, and IX Oph.


  For safety, AI systems in health undergo thorough evaluations before
deployment, validating their predictions against a ground truth that is assumed
certain. However, this is actually not the case and the ground truth may be
uncertain. Unfortunately, this is largely ignored in standard evaluation of AI
models but can have severe consequences such as overestimating the future
performance. To avoid this, we measure the effects of ground truth uncertainty,
which we assume decomposes into two main components: annotation uncertainty
which stems from the lack of reliable annotations, and inherent uncertainty due
to limited observational information. This ground truth uncertainty is ignored
when estimating the ground truth by deterministically aggregating annotations,
e.g., by majority voting or averaging. In contrast, we propose a framework
where aggregation is done using a statistical model. Specifically, we frame
aggregation of annotations as posterior inference of so-called plausibilities,
representing distributions over classes in a classification setting, subject to
a hyper-parameter encoding annotator reliability. Based on this model, we
propose a metric for measuring annotation uncertainty and provide
uncertainty-adjusted metrics for performance evaluation. We present a case
study applying our framework to skin condition classification from images where
annotations are provided in the form of differential diagnoses. The
deterministic adjudication process called inverse rank normalization (IRN) from
previous work ignores ground truth uncertainty in evaluation. Instead, we
present two alternative statistical models: a probabilistic version of IRN and
a Plackett-Luce-based model. We find that a large portion of the dataset
exhibits significant ground truth uncertainty and standard IRN-based evaluation
severely over-estimates performance without providing uncertainty estimates.


  Certifying individual quantum devices with minimal assumptions is crucial for
the development of quantum technologies. Here, we investigate how to leverage
single-system contextuality to realize self-testing. We develop a robust
self-testing protocol based on the simplest contextuality witness for the
simplest contextual quantum system, the Klyachko-Can-Binicio\u{g}lu-Shumovsky
(KCBS) inequality for the qutrit. We establish a lower bound on the fidelity of
the state and the measurements (to an ideal configuration) as a function of the
value of the witness under a pragmatic assumption on the measurements we call
the KCBS orthogonality condition. We apply the method in an experiment with
randomly chosen measurements on a single trapped $^{40}{\rm Ca}^+$ and
near-perfect detection efficiency. The observed statistics allow us to
self-test the system and provide the first experimental demonstration of
quantum self-testing of a single system. Further, we quantify and report that
deviations from our assumptions are minimal, an aspect previously overlooked by
contextuality experiments.


  Motivated by the need to statistically quantify differences between modern
(complex) data-sets which commonly result as high-resolution measurements of
stochastic processes varying over a continuum, we propose novel testing
procedures to detect relevant differences between the second order dynamics of
two functional time series. In order to take the between-function dynamics into
account that characterize this type of functional data, a frequency domain
approach is taken. Test statistics are developed to compare differences in the
spectral density operators and in the primary modes of variation as encoded in
the associated eigenelements. Under mild moment conditions, we show convergence
of the underlying statistics to Brownian motions and construct pivotal test
statistics. The latter is essential because the nuisance parameters can be
unwieldy and their robust estimation infeasible, especially if the two
functional time series are dependent. In addition to these novel features, the
properties of the tests are robust to any choice of frequency band enabling
also to compare energy contents at a single frequency. The finite sample
performance of the tests are verified through a simulation study and are
illustrated with an application to fMRI data.


  This paper demonstrates a system comprised of infrared beacons and a camera
equipped with an optical band-pass filter. Our system can reliably detect and
identify individual beacons at 100m distance regardless of lighting conditions.
We describe the camera and beacon design as well as the image processing
pipeline in detail. In our experiments, we investigate and demonstrate the
ability of the system to recognize our beacons in both daytime and nighttime
conditions. High precision localization is a key enabler for automated vehicles
but remains unsolved, despite strong recent improvements. Our low-cost,
infrastructure-based approach is a potential step towards solving the
localization problem. All datasets are made available here
https://embedded.rwth-aachen.de/doku.php?id=forschung:mobility:infralocalization:concept.


  This paper introduces a novel steepest descent flow in Banach spaces. This
extends previous works on generalized gradient descent, notably the work of
Charpiat et al., to the setting of Finsler metrics. Such a generalized gradient
allows one to take into account a prior on deformations (e.g., piecewise rigid)
in order to favor some specific evolutions. We define a Finsler gradient
descent method to minimize a functional defined on a Banach space and we prove
a convergence theorem for such a method. In particular, we show that the use of
non-Hilbertian norms on Banach spaces is useful to study non-convex
optimization problems where the geometry of the space might play a crucial role
to avoid poor local minima. We show some applications to the curve matching
problem. In particular, we characterize piecewise rigid deformations on the
space of curves and we study several models to perform piecewise rigid
evolution of curves.


  Using the classification theorem due to Kac we prove that any finite
dimensional simple
  Lie superalgebra over an algebraically closed field of characteristic 0 is
generated by one element.


  We propose a method to overcome Auger recombination in nanocrystal quantum
dot lasers using cavity-enhanced spontaneous emission. We derive a numerical
model for a laser composed of nanocrystal quantum dots coupled to optical
nanocavities with small mode-volume. Using this model, we demonstrate that
spontaneous emission enhancement of the biexciton transition lowers the lasing
threshold by reducing the effect of Auger recombination. We analyze a photonic
crystal nanobeam cavity laser as a realistic device structure that implements
the proposed approach.


  The light front wavefunction obtained from anti-de Sitter Quantum
Chromodynamics is used to calculate the light cone distribution amplitudes for
$\rho$ and $K^*$ vector mesons. These distribution amplitudes are then utilized
to calculate the $B \to \rho ,\; K^*$ transition form factors via light cone
sum rules. Two-parameter fits of our results for low to intermediate momentum
transfer $q^2$ that includes the QCD lattice data at high $q^2$ are presented.
Consequently, we give predictions for the semileptoic $B \to \rho \ell \nu$ and
dileptonic $B \to K^* \mu^+ \mu^-$ decays.


  We present the results of studies for magnetogyration (MG) effect in
(Ga0.3In0.7)2Se3 and SiO2 crystals performed with the small-angular
polarimetric mapping technique. It is shown that the MG effect magnitude is
comparable with the experimental error.


  Let $N\geq 1$ and $s\in (0,1)$. In the present work we characterize bounded
open sets $\Omega$ with $ C^2$ boundary (\textit{not necessarily connected})
for which the following overdetermined problem \begin{equation*} ( -\Delta)^s u
= f(u) \text{ in $\Omega$,} \qquad u=0 \text{ in $\mathbb{R}^N\setminus
\Omega$,} \qquad(\partial_{\eta})_s u=Const. \text{ on $\partial \Omega$}
\end{equation*} has a nonnegative and nontrivial solution, where $\eta $ is the
outer unit normal vectorfield along $\partial\Omega$ and for
$x_0\in\partial\Omega$ \[ \left(\partial_{\eta}\right)_{s}u(x_{0})=-\lim_{t\to
0}\frac{u(x_{0}-t\eta(x_0))}{t^s}. \]
  Under mild assumptions on $f$, we prove that $\Omega$ must be a ball. In the
special case $f\equiv 1$, we obtain an extension of Serrin's result in 1971.
The fact that $\Omega$ is not assumed to be connected is related to the
nonlocal property of the fractional Laplacian.
  The main ingredients in our proof are maximum principles and the method of
moving planes.


  We derive an exact expression for the partition function of the Euclidean BTZ
black hole. Using this, we show that for a black hole with large horizon area,
the correction to the Bekenstein-Hawking entropy is $-3/2 log(Area)$, in
agreement with that for the Schwarzschild black hole obtained in the canonical
gravity formalism and also in a Lorentzian computation of BTZ black hole
entropy. We find that the right expression for the logarithmic correction in
the context of the BTZ black hole comes from the modular invariance associated
with the toral boundary of the black hole.


  Multivariate time series forecasting (MTSF) is crucial for decision-making to
precisely forecast the future values/trends, based on the complex relationships
identified from historical observations of multiple sequences. Recently,
Spatial-Temporal Graph Neural Networks (STGNNs) have gradually become the theme
of MTSF model as their powerful capability in mining spatial-temporal
dependencies, but almost of them heavily rely on the assumption of historical
data integrity. In reality, due to factors such as data collector failures and
time-consuming repairment, it is extremely challenging to collect the whole
historical observations without missing any variable. In this case, STGNNs can
only utilize a subset of normal variables and easily suffer from the incorrect
spatial-temporal dependency modeling issue, resulting in the degradation of
their forecasting performance. To address the problem, in this paper, we
propose a novel Graph Interpolation Attention Recursive Network (named GinAR)
to precisely model the spatial-temporal dependencies over the limited collected
data for forecasting. In GinAR, it consists of two key components, that is,
interpolation attention and adaptive graph convolution to take place of the
fully connected layer of simple recursive units, and thus are capable of
recovering all missing variables and reconstructing the correct
spatial-temporal dependencies for recursively modeling of multivariate time
series data, respectively. Extensive experiments conducted on five real-world
datasets demonstrate that GinAR outperforms 11 SOTA baselines, and even when
90% of variables are missing, it can still accurately predict the future values
of all variables.


  In this paper we give a simple proof of the fact that the average over all
dyadic lattices of the dyadic $H^1$-norm of a function gives an equivalent
$H^1$-norm. The proof we present works for both one-parameter and
multi-parameter Hardy spaces.
  The results of such type are known. The first result (for one-parameter Hardy
spces) belongs to Burgess Davis (1980). Also, by duality, such results are
equivalent to the "BMO from dyadic BMO" statements proved by
Garnett-Jones(1982} for one parameter case, and by Pipher-Ward (2008) for
two-parameter case.
  While the paper generalizes these results to the multi-parameter setting,
this is not its main goal. The purpose of the paper is to present an approach
leading to a simple proof, which works in both one-parameter and
multi-parameter cases.
  The main idea of treating square function as a Calderon--Zygmind operator is
a commonplace in harmonic analysis; the main observation, on which the paper is
based, is that one can treat the random dyadic square function this way. After
that, all is proved by using the standard and well-known results about
Calderon--Zygmind operators in the Hilbert-space-valued setting.
  As an added bonus, we get a simple proof of the (equivalent by duality)
inclusion $\text{BMO}\subset \text{BMO}_d$, $H^1_d \subset H^1$ in the
multi-parameter case. Note, that unlike the one-parameter case, the inclusions
in the general situation are far from trivial.


  We study the effective cones of cycles on universal hypersurfaces on a
projective variety $X$, particularly focusing on the case of universal
hypersurfaces in $\mathbb{P}^n$. We determine the effective cones of cycles on
the universal conic over $\mathbb{P}^2$. We also determine every effective cone
of cycles of dimension at most 6 or equal to 10 on any universal plane curve.


  Changing how pre-trained models behave -- e.g., improving their performance
on a downstream task or mitigating biases learned during pre-training -- is a
common practice when developing machine learning systems. In this work, we
propose a new paradigm for steering the behavior of neural networks, centered
around \textit{task vectors}. A task vector specifies a direction in the weight
space of a pre-trained model, such that movement in that direction improves
performance on the task. We build task vectors by subtracting the weights of a
pre-trained model from the weights of the same model after fine-tuning on a
task. We show that these task vectors can be modified and combined together
through arithmetic operations such as negation and addition, and the behavior
of the resulting model is steered accordingly. Negating a task vector decreases
performance on the target task, with little change in model behavior on control
tasks. Moreover, adding task vectors together can improve performance on
multiple tasks at once. Finally, when tasks are linked by an analogy
relationship of the form ``A is to B as C is to D", combining task vectors from
three of the tasks can improve performance on the fourth, even when no data
from the fourth task is used for training. Overall, our experiments with
several models, modalities and tasks show that task arithmetic is a simple,
efficient and effective way of editing models.


  The ability to monitor respiratory rate is extremely important for medical
treatment, healthcare and fitness sectors. In many situations, mobile methods,
which allow users to undertake every day activities, are required. However,
current monitoring systems can be obtrusive, requiring users to wear
respiration belts or nasal probes. Recent advances in thermographic systems
have shrunk their size, weight and cost, to the point where it is possible to
create smart-phone based respiration rate monitoring devices that are not
affected by lighting conditions. However, mobile thermal imaging is challenged
in scenes with high thermal dynamic ranges. This challenge is further amplified
by general problems such as motion artifacts and low spatial resolution,
leading to unreliable breathing signals. In this paper, we propose a novel and
robust approach for respiration tracking which compensates for the negative
effects of variations in the ambient temperature and motion artifacts and can
accurately extract breathing rates in highly dynamic thermal scenes. It has
three main contributions. The first is a novel Optimal Quantization technique
which adaptively constructs a color mapping of absolute temperature to improve
segmentation, classification and tracking. The second is the Thermal Gradient
Flow method that computes thermal gradient magnitude maps to enhance accuracy
of the nostril region tracking. Finally, we introduce the Thermal Voxel method
to increase the reliability of the captured respiration signals compared to the
traditional averaging method. We demonstrate the extreme robustness of our
system to track the nostril-region and measure the respiratory rate in high
dynamic range scenes.


  This paper presents trainable methods for generating letter to sound rules
from a given lexicon for use in pronouncing out-of-vocabulary words and as a
method for lexicon compression.
  As the relationship between a string of letters and a string of phonemes
representing its pronunciation for many languages is not trivial, we discuss
two alignment procedures, one fully automatic and one hand-seeded which produce
reasonable alignments of letters to phones.
  Top Down Induction Tree models are trained on the aligned entries. We show
how combined phoneme/stress prediction is better than separate prediction
processes, and still better when including in the model the last phonemes
transcribed and part of speech information. For the lexicons we have tested,
our models have a word accuracy (including stress) of 78% for OALD, 62% for CMU
and 94% for BRULEX. The extremely high scores on the training sets allow
substantial size reductions (more than 1/20).
  WWW site: http://tcts.fpms.ac.be/synthesis/mbrdico


  When two Turing modes interact, i.e., Turing-Turing bifurcation occurs,
superposition patterns revealing complex dynamical phenomena appear. In this
paper, superposition patterns resulting from Turing-Turing bifurcation are
investigated in theory. Firstly, the third-order normal form locally
topologically equivalent to original partial functional differential equations
(PFDEs) is derived. When selecting 1D domain and Neumann boundary conditions,
three normal forms describing different spatial patterns are deduced from
original third-order normal form. Also, formulas for computing coefficients of
these normal forms are given, which are expressed in explicit form of original
system parameters. With the aid of three normal forms, spatial patterns of a
diffusive predator-prey system with Crowley-Martin functional response near
Turing-Turing singularity are investigated. For one set of parameters,
diffusive system supports the coexistence of four stable steady states with
different single characteristic wavelengths, which demonstrates our previous
conjecture. For another set of parameters, superposition patterns, tri-stable
patterns that a pair of stable superposition steady states coexists with the
stable coexistence equilibrium or another stable steady state, as well as
quad-stable patterns that a pair of stable superposition steady states and
another pair of stable steady states coexist, arise. Finally, numerical
simulations are shown to support theory analysis.


  Verbal autopsy procedures are widely used for estimating cause-specific
mortality in areas without medical death certification. Data on symptoms
reported by caregivers along with the cause of death are collected from a
medical facility, and the cause-of-death distribution is estimated in the
population where only symptom data are available. Current approaches analyze
only one cause at a time, involve assumptions judged difficult or impossible to
satisfy, and require expensive, time-consuming, or unreliable physician
reviews, expert algorithms, or parametric statistical models. By generalizing
current approaches to analyze multiple causes, we show how most of the
difficult assumptions underlying existing methods can be dropped. These
generalizations also make physician review, expert algorithms and parametric
statistical assumptions unnecessary. With theoretical results, and empirical
analyses in data from China and Tanzania, we illustrate the accuracy of this
approach. While no method of analyzing verbal autopsy data, including the more
computationally intensive approach offered here, can give accurate estimates in
all circumstances, the procedure offered is conceptually simpler, less
expensive, more general, as or more replicable, and easier to use in practice
than existing approaches. We also show how our focus on estimating aggregate
proportions, which are the quantities of primary interest in verbal autopsy
studies, may also greatly reduce the assumptions necessary for, and thus
improve the performance of, many individual classifiers in this and other
areas. As a companion to this paper, we also offer easy-to-use software that
implements the methods discussed herein.


  A mixture of multivariate contaminated normal distributions is developed for
model-based clustering. In addition to the parameters of the classical normal
mixture, our contaminated mixture has, for each cluster, a parameter
controlling the proportion of mild outliers and one specifying the degree of
contamination. Crucially, these parameters do not have to be specified a
priori, adding a flexibility to our approach. Parsimony is introduced via
eigen-decomposition of the component covariance matrices, and sufficient
conditions for the identifiability of all the members of the resulting family
are provided. An expectation-conditional maximization algorithm is outlined for
parameter estimation and various implementation issues are discussed. Using a
large scale simulation study, the behaviour of the proposed approach is
investigated and comparison with well-established finite mixtures is provided.
The performance of this novel family of models is also illustrated on
artificial and real data.


  A meson-exchange piN model, previously constructed using three-dimensional
reduction scheme of the Bethe-Salpeter equation for a model Lagrangian
involving \pi, \eta, N, \Delta, rho, and \sigma fields, is extended to energies
up to 2 GeV by including the \eta N channel and all the four stars \pi N
resonances up to the F-waves. The effects of other 2 pion channels are taken
into account phenomenologically. The extended model gives an excellent fit to
both piN phase shifts and inelasticity parameters in all channels up to the
F-waves. However, a few of the extracted resonance parameters differ
considerably from the PDG values.


  We show that the topological string partition function with D-branes on a
compact Calabi-Yau manifold has new anomalies that spoil the recursive
structure of the holomorphic anomaly equation and introduce dependence on wrong
moduli (such as complex structure moduli in the A-model), unless the disk
one-point functions vanish. This provides a microscopic explanation for the
recent result of Walcher in arXiv:0712.2775 on counting of BPS states in
M-theory using the topological string partition function. The relevance of
vanishing disk one-point functions to large $N$ duality for compact Calabi-Yau
manifolds is noted.


  We propose a new method towards distinguishing the Dirac versus Majorana
nature of neutrino masses from the spectrum of gravitational waves (GWs)
associated with neutrino mass genesis. Motivated by the principle of generating
small neutrino masses without tiny Yukawa couplings, we assume generic seesaw
mechanisms for both Majorana and Dirac neutrino masses. For Majorana neutrinos,
we further assume a spontaneously broken gauged $U(1)_{B-L}$ symmetry,
independently of the type of Majorana seesaw mechanism, which gives a cosmic
string induced GW signal flat over a wide range of frequencies. For Dirac
neutrinos, we assume the spontaneous breaking of a $Z_2$ symmetry, the minimal
symmetry choice associated with all Dirac seesaw mechanisms, which is softly
broken, generating a peaked GW spectrum from the annihilation of the resulting
domain walls. In fact, the GW spectra for all types of Dirac seesaws with such
a broken $Z_2$ symmetry are identical, subject to a mild caveat. As an
illustrative example, we study the simplest respective type-I seesaw
mechanisms, and show that the striking difference in the shapes of the GW
spectra can help differentiate between these Dirac and Majorana seesaws,
complementing results of neutrinoless double beta decay experiments. We also
discuss detailed implications of the recent NANOGrav data for Majorana and
Dirac seesaw models.


  The large separation in the low radial order regime is considered as a highly
valuable observable to derive mean densities of $\delta$ Scuti stars, due to
its independence with rotation. Up to now, theoretical studies of this
$\Delta\nu$-${\bar \rho}$ relation have been limited to 1D non-rotating models,
and 2D pseudo-evolutionary models. The present work aims at completing this
scenario by investigating quantitatively the impact of rotation in this
relation on a large grid of 1D asteroseismic models representative of $\delta$
Scuti stars. These include rotation effects on both the stellar evolution and
the interaction with pulsation. This allowed us to compute the stellar
deformation, get the polar and equatorial radii, and correct the stellar mean
densities. We found that the new $\Delta\nu$-${\bar \rho}$ relation for
rotating models is compatible with previous works. We explained the dispersion
of the points around the linear fits as caused mainly by the distribution of
the stellar mass, and partially by the evolutionary stage. The new fit is found
to be close to the previous theoretical studies for lower masses
($1.3-1.81\,\mathrm{M}_{\odot}$). However, the opposite holds for the
observations: for the higher masses ($1.81-3\,\mathrm{M}_{\odot}$) the fit is
more compatible with the empirical relation. We applied these results to
characterise the two well-known $\delta$ Scuti stars observed by CoRoT,
HD174936 and HD174966, and compared the physical parameters with those of
previous works. Inclusion of rotation in the modelling causes a tendency
towards greater masses, radii, luminosities and lower density values.
Comparison between $\Delta\nu$ and Gaia's luminosities also allowed us to
constraint the inclination angles and rotational velocities of both stars. The
present results pave the way to systematically constrain the angle of
inclination of $\delta$ Scuti stars


  A number of transition-metal (TM) doped group-IV semiconductors,
R$_{x}$Y$_{1-x}$ (R=Cr, Mn and Fe; Y=Si, Ge), have been studied by the first
principles calculations. The obtained results show that antiferromagnetic (AFM)
order is energetically more favored than ferromagnetic (FM) order in Cr-doped
Ge and Si with $x$=0.03125 and 0.0625. In 6.25% Fe-doped Ge, FM interaction
dominates in all range of the R-R distances while for Fe-doped Ge at 3.125% and
Fe-doped Si at both concentrations of 3.125% and 6.25%, only in a short R-R
range can the FM states exist. In the Mn-doped case, the RKKY-like mechanism
seems to be suitable for the Ge host matrix, while for the Mn-doped Si, the
short-range AFM interaction competes with the long-range FM interaction. The
different origin of the magnetic orders in these diluted magnetic
semiconductors (DMSs) makes the microscopic mechanism of the ferromagnetism in
the DMSs more complex and attractive.


  The classical core entropy for a post critically finite (PCF) polynomial f
with deg(f)>1 is defined to be the topological entropy of f restricted to its
Hubbard tree. We fully generalize this notion by a new quantity, called the
(general) core entropy, which is well defined whenever f has a connected Julia
set. If f is PCF, the core entropy equals the classical version. If two
polynomials are J-equivalent they share the same core entropy. If f is
renormalizable there is a direct connection between the core entropy of f and
that corresponding to the small Julia set. We also analyze the map that sends
every parameter c in the Mandelbrot set to the core entropy of the polynomial
z^2+c. In particular, the level set of this entropy map at log2 is of full
harmonic measure and the Mandelbrot set is locally connected at each point in
this level set.


  Until recently, the strong interstellar scattering observed towards the
Galactic center (GC) black hole, Sgr A*, was thought to come from dense gas
within the GC region. The pulse broadening towards the transient magnetar SGR
J1745-2900 near Sgr A* has shown that the source of the scattering is instead
located much closer to Earth, possibly in a nearby spiral arm. We show that a
single HII region along the line of sight, 1.5-4.8 kpc away from Earth with
density $n_e$ of a few 100 cm$^{-3}$ and radius R = 1.8-3.2 pc can explain the
observed angular broadening of Sgr A*. Clouds closer to the GC overproduce the
observed DM, providing an independent location constraint that agrees with that
from the magnetar pulse broadening. Our model predicts that sources within 10
pc should show the same scattering origin as the magnetar and Sgr A*, while the
nearest known pulsars with separations > 20 pc should not. The radio spectrum
of Sgr A* should show a cutoff from free-free absorption at 0.2-1 GHz. For a
magnetic field strength $B = 15-70 \mu$G, the HII region could produce the
rotation measure of the magnetar, the largest of any known pulsar, without
requiring the gas near Sgr A* to be strongly magnetised.


  Like humans, document summarization models can interpret a document's
contents in a number of ways. Unfortunately, the neural models of today are
largely black boxes that provide little explanation of how or why they
generated a summary in the way they did. Therefore, to begin prying open the
black box and to inject a level of control into the substance of the final
summary, we developed a novel select-and-generate framework that focuses on
explainability. By revealing the latent centrality and interactions between
sentences, along with scores for sentence novelty and relevance, users are
given a window into the choices a model is making and an opportunity to guide
those choices in a more desirable direction. A novel pair-wise matrix captures
the sentence interactions, centrality, and attribute scores, and a mask with
tunable attribute thresholds allows the user to control which sentences are
likely to be included in the extraction. A sentence-deployed attention
mechanism in the abstractor ensures the final summary emphasizes the desired
content. Additionally, the encoder is adaptable, supporting both Transformer-
and BERT-based configurations. In a series of experiments assessed with ROUGE
metrics and two human evaluations, ESCA outperformed eight state-of-the-art
models on the CNN/DailyMail and NYT50 benchmark datasets.


  Bound states in the continuum (BICs) are localized states existing within a
continuous spectrum of delocalized waves. Emerging multilayer photonic
integrated circuit (PIC) platforms allow implementation of low index 1D guided
modes within a high-index 2D slab mode continuum; however, conventional wisdom
suggests that this always leads to large radiation losses. Here we demonstrate
low-loss BIC guided modes for multiple mode polarizations and spatial orders in
single- and multi-ridge low-index waveguides within a two-layer heterogeneously
integrated electro-optically active photonic platform. The transverse electric
(TE) polarized quasi-BIC guided mode with low, <1.4 dB/cm loss enables a
Mach-Zehnder electro-optic amplitude modulator comprising a single straight
Si3N4 ridge waveguide integrated with a continuous LiNbO3 slab layer. The
abrupt optical transitions at the edges of the slab function as compact and
efficient directional couplers eliminating the need for additional components.
The modulator exhibits a low insertion loss of 2.3 dB and a high extinction
ratio of 25 dB. The developed general theoretical model may enable innovative
BIC-based approaches for important PIC functions, such as agile spectral
filtering and switching, and may suggest new photonic architectures for quantum
and neural network applications based on controlled interactions between
multiple guided and delocalized modes.


  Measurement-Based Quantum Computing (MBQC), proposed in 2001 is a model of
quantum computing that achieves quantum computation by performing a series of
adaptive single-qubit measurements on an entangled cluster state. Our project
is aimed at introducing MBQC to a wide audience ranging from high school
students to quantum computing researchers through a Tangram puzzle with a
modified set of rules, played on an applet. The rules can be understood without
any background in quantum computing. The player is provided a quantum circuit,
shown using gates from a universal gate set, which the player must map
correctly to a playing board using polyominos. Polyominos or 'puzzle blocks'
are the building blocks of our game. They consist of square tiles joined
edge-to-edge to form different colored shapes. Each tile represents a
single-qubit measurement basis, differentiated by its color. Polyominos rest on
a square-grid playing board, which signifies a cluster state. We show that
mapping a quantum circuit to MBQC is equivalent to arranging a set of
polyominos, each corresponding to a gate in the circuit on the playing board,
subject to certain rules, which involve rotating and deforming polyominos. We
state the rules in simple terms with no reference to quantum computing. The
player has to place polyominos on the playing board conforming to the rules.
Any correct solution creates a valid realization of the quantum circuit in
MBQC. A higher-scoring correct solution fills up less space on the board,
resulting in a lower-overhead embedding of the circuit in MBQC, an open and
challenging research problem.


  With the rapid development of quantum science and technology, quantum
batteries have also emerged. However, there are still many unresolved issues in
the field of quantum batteries. For example, how to improve battery space
utilization, maximize battery energy storage, and how to increase and control
the charging power of quantum batteries. A major challenge is how to achieve
better charging power without reducing the energy storage of the quantum
batteries. Here, we propose a controllable dual-cavity quantum battery which
can increase the charging power without diminishing capacity of the quantum
batteries by manipulating the number of atoms . This control method can
effectively adjust the charging power of quantum batteries from $N^2$ times to
$N^2.5$ times, and even to $N^3$ times. By adjusting the number of atoms,
quantum batteries can achieve theoretical "fast charging" and "slow charging".


  In this paper, we give the following result: If $D$ is a digraph of order
$n$, and if $d_{D}^{+}(u) + d_{D}^{-}(v) \ge n$ for every two distinct vertices
$u$ and $v$ with $(u, v) \notin A(D)$, then $D$ has a directed $2$-factor with
exactly $k$ directed cycles of length at least $3$, where $n \ge 12k+3$. This
result is equivalent to the following result: If $G$ is a balanced bipartite
graph of order $2n$ with partite sets $X$ and $Y$, and if $d_{G}(x)+d_{G}(y)
\ge n + 2$ for every two vertices $x \in X$ and $y \in Y$ with $xy \notin
E(G)$, then for every perfect matching $M$, $G$ has a $2$-factor with exactly
$k$ cycles of length at least $6$ containing every edge of $M$, where $n \ge
12k+3$. These results are generalizations of theorems concerning Hamilton
cycles due to Woodall (1972) and Las Vergnas (1972), respectively.


  Exclusive and kinematically complete high-statistics measurements of
quasifree polarized $\vec{n}p$ scattering have been performed in the energy
region of the narrow resonance structure $d^*$ with $I(J^P) = 0(3^+)$, $M
\approx$ 2380 MeV/$c^2$ and $\Gamma \approx$ 70 MeV observed recently in the
double-pionic fusion channels $pn \to d\pi^0\pi^0$ and $pn \to d\pi^+\pi^-$.
The experiment was carried out with the WASA detector setup at COSY having a
polarized deuteron beam impinged on the hydrogen pellet target and utilizing
the quasifree process $\vec{d}p \to np + p_{spectator}$. That way the $np$
analyzing power $A_y$ was measured over a large angular range. The obtained
$A_y$ angular distributions deviate systematically from the current SAID SP07
NN partial-wave solution. Incorporating the new $A_y$ data into the SAID
analysis produces a pole in the $^3D_3 - ^3G_3$ waves as expected from the
$d^*$ resonance hypothesis.


  We study how present data probe standard and non-standard properties of
neutrinos and the possible existence of new light particles, freely-streaming
or interacting, among themselves or with neutrinos. Our results include: sum
m_nu < 0.40 eV at 99.9% C.L.; that extra massless particles have abundance
Delta N_nu = 2 pm 1 if freely-streaming and Delta N_nu = 0 pm 1.3 if
interacting; that 3 interacting neutrinos are disfavored at about 4 sigma. We
investigate the robustness of our results by fitting to different sub-sets of
data. We developed our own cosmological computational tools, somewhat different
from the standard ones.


  We establish a classical analog of the Nambu-Goldstone theorem for
spontaneous breaking of spacetime symmetries. It provides a counting rule for
independent Nambu-Goldstone fields and states which of them are gapped. We
demonstrate that only those symmetry group generators give rise to independent
Nambu-Goldstone fields that act non-trivially on a vacuum at the origin of
coordinates. Other generators give rise to auxiliary fields that must be
excluded from a theory by the means of inverse Higgs constraints. The physical
meaning of the inverse Higgs phenomenon and an application of our results to
theories of massive gravity are discussed.


  We propose a scheme or procedure for doing practical calculations with
generalized seniority. It reduces the total computing time by calculating and
storing in advance a set of intermediate quantities, taking advantage of the
memory capability of modern computers. The requirements and performance of the
algorithm are analyzed in detail.


  Let $G_n(z)=\xi_0+\xi_1z+...+\xi_n z^n$ be a random polynomial with i.i.d.
coefficients (real or complex). We show that the arguments of the roots of
$G_n(z)$ are uniformly distributed in $[0,2\pi]$ asymptotically as
$n\to\infty$. We also prove that the condition $\E\ln(1+|\xi_0|)<\infty$ is
necessary and sufficient for the roots to asymptotically concentrate near the
unit circumference.


  The distribution of early-type galaxy velocity dispersions, phi(sigma), is
measured using a sample drawn from the SDSS database. Its shape differs
significantly from that which one obtains by simply using the mean correlation
between luminosity, L, and velocity dispersion, sigma, to transform the
luminosity function into a velocity function: ignoring the scatter around the
mean sigma-L relation is a bad approximation. An estimate of the contribution
from late-type galaxies is also made, which suggests that phi(sigma) is
dominated by early-type galaxies at velocities larger than ~ 200 km/s.


  Charge transfer in collisions of Na_n^+ cluster ions with Cs atoms is
investigated theoretically in the microscopic framework of non-adiabatic
quantum molecular dynamics. The competing reaction channels and related
processes affecting the charge transfer (electronic excitations, fragmentation,
temperature) are described. Absolute charge transfer cross sections for
Na_n^+(2.7 keV) + Cs --> Na_n + Cs^+ have been calculated in the size range 4
<= n <= 11 reproducing the size dependence of the experimental cross sections.
The energy dependence of the cross section is predicted for n=4,7,9. An exotic
charge transfer channel producing Cs^- is found to have a finite probability.


  We discuss non-Euclidean deterministic and stochastic algorithms for
optimization problems with strongly and uniformly convex objectives. We provide
accuracy bounds for the performance of these algorithms and design methods
which are adaptive with respect to the parameters of strong or uniform
convexity of the objective: in the case when the total number of iterations $N$
is fixed, their accuracy coincides, up to a logarithmic in $N$ factor with the
accuracy of optimal algorithms.


  Electric dipole moments are sensitive probes of new phases in the Higgs
Yukawa couplings. We calculate the complete two-loop QCD anomalous dimension
matrix for the mixing of CP-odd scalar and tensor operators and apply our
results for a phenomenological study of CP violation in the bottom and charm
Yukawa couplings. We find large shifts of the induced Wilson coefficients at
next-to-leading-logarithmic order. Using the experimental bound on the electric
dipole moment of the neutron, we update the constraints on CP-violating phases
in the bottom and charm quark Yukawas.


  Sound propagation is considered in range-independent environments and
environments consisting of a range-independent background on which a weak
range-dependent perturbation is superimposed. Recent work on propagation of
both types of environment, involving both ray- and mode-based wavefield
descriptions, have focused on the importance of $\alpha $, a ray-based
``stability parameter,'' and $\beta ,$ a mode-based ``waveguide invariant.'' It
is shown that, when $\beta $ is evaluated using asymptotic mode theory, $%
\beta =\alpha .$ Using both ray and mode concepts, known results relating to
the manner by which $\alpha $ (or $\beta $) controls both the unperturbed
wavefield structure and the stability of the perturbed wavefield are briefly
reviewed.


  The probabilistic Latent Semantic Indexing model assumes that the expectation
of the corpus matrix is low-rank and can be written as the product of a
topic-word matrix and a word-document matrix. In this paper, we study the
estimation of the topic-word matrix under the additional assumption that the
ordered entries of its columns rapidly decay to zero. This sparsity assumption
is motivated by the empirical observation that the word frequencies in a text
often adhere to Zipf's law. We introduce a new spectral procedure for
estimating the topic-word matrix that thresholds words based on their corpus
frequencies, and show that its $\ell_1$-error rate under our sparsity
assumption depends on the vocabulary size $p$ only via a logarithmic term. Our
error bound is valid for all parameter regimes and in particular for the
setting where $p$ is extremely large; this high-dimensional setting is commonly
encountered but has not been adequately addressed in prior literature.
Furthermore, our procedure also accommodates datasets that violate the
separability assumption, which is necessary for most prior approaches in topic
modeling. Experiments with synthetic data confirm that our procedure is
computationally fast and allows for consistent estimation of the topic-word
matrix in a wide variety of parameter regimes. Our procedure also performs well
relative to well-established methods when applied to a large corpus of research
paper abstracts, as well as the analysis of single-cell and microbiome data
where the same statistical model is relevant but the parameter regimes are
vastly different.


  Recognizing facial expressions is one of the central problems in computer
vision. Temporal image sequences have useful spatio-temporal features for
recognizing expressions. In this paper, we propose a new 3D Convolution Neural
Network (CNN) that can be trained end-to-end for facial expression recognition
on temporal image sequences without using facial landmarks. More specifically,
a novel 3D convolutional layer that we call Local Binary Volume (LBV) layer is
proposed. The LBV layer, when used with our newly proposed LBVCNN network,
achieve comparable results compared to state-of-the-art landmark-based or
without landmark-based models on image sequences from CK+, Oulu-CASIA, and UNBC
McMaster shoulder pain datasets. Furthermore, our LBV layer reduces the number
of trainable parameters by a significant amount when compared to a conventional
3D convolutional layer. As a matter of fact, when compared to a 3x3x3
conventional 3D convolutional layer, the LBV layer uses 27 times less trainable
parameters.


  A code $X$ is not primitivity preserving if there is a primitive list
${\mathbf w} \in {\tt lists} X$ whose concatenation is imprimitive. We
formalize a full characterization of such codes in the binary case in the proof
assistant Isabelle/HOL. Part of the formalization, interesting on its own, is a
description of $\{x,y\}$-interpretations of the square $xx$ if $|y| \leq |x|$.
We also provide a formalized parametric solution of the related equation
$x^jy^k = z^\ell$.


  We develop a general theory of the relation between quantum phase transitions
(QPTs) characterized by nonanalyticities in the energy and bipartite
entanglement. We derive a functional relation between the matrix elements of
two-particle reduced density matrices and the eigenvalues of general two-body
Hamiltonians of $d$-level systems. The ground state energy eigenvalue and its
derivatives, whose non-analyticity characterizes a QPT, are directly tied to
bipartite entanglement measures. We show that first-order QPTs are signalled by
density matrix elements themselves and second-order QPTs by the first
derivative of density matrix elements. Our general conclusions are illustrated
via several quantum spin models.


  This article implements a simple convex approach and block techniques to
obtain several new refined versions of numerical radius inequalities for
Hilbert space operators. This includes comparisons among the norms of the
operators, their Cartesian parts, their numerical radii, the numerical radius
of the product of two operators, and the Aluthge transform.


  Energy harvesting (EH) from ambient radio-frequency (RF) electromagnetic
waves is an efficient solution for fully autonomous and sustainable
communication networks. Most of the related works presented in the literature
are based on specific (and small-scale) network structures, which although give
useful insights on the potential benefits of the RF-EH technology, cannot
characterize the performance of general networks. In this paper, we adopt a
large-scale approach of the RF-EH technology and we characterize the
performance of a network with random number of transmitter-receiver pairs by
using stochastic-geometry tools. Specifically, we analyze the outage
probability performance and the average harvested energy, when receivers employ
power splitting (PS) technique for "simultaneous" information and energy
transfer. A non-cooperative scheme, where information/energy are conveyed only
via direct links, is firstly considered and the outage performance of the
system as well as the average harvested energy are derived in closed form in
function of the power splitting. For this protocol, an interesting optimization
problem which minimizes the transmitted power under outage probability and
harvesting constraints, is formulated and solved in closed form. In addition,
we study a cooperative protocol where sources' transmissions are supported by a
random number of potential relays that are randomly distributed into the
network. In this case, information/energy can be received at each destination
via two independent and orthogonal paths (in case of relaying). We characterize
both performance metrics, when a selection combining scheme is applied at the
receivers and a single relay is randomly selected for cooperative diversity.


  The unique working mechanics of roller-type peristaltic pumps have allowed
their applications to span a wide variety of sectors and industries. The
roller-type pump's accurate dosing and hydrostatic capabilities can
theoretically allow for the pump to be used for hydraulic actuation (as an
electro-hydrostatic actuator) for low pressure applications. This however
requires accurate control of the peristaltic pump and its flow rate. The
associated pressure pulsations will also have an impact on the pump's selection
criteria. Accurate control of roller-type peristaltic pumps commonly rely on
flow-meters, which increases the cost of the pump and can complicate control
strategies. Current modelling approaches either do not rely on first principle
modelling and require expensive simulation software, or do not apply for larger
Reynolds numbers at larger flow rates. The most applicable model focusses on
the flow rate for each roller individually. This implies that the model
requires alterations in order to accommodate pumps with varying numbers of
rollers. This paper presents an alternative modelling methodology towards the
volume flow rate, pulsatile flow rate qualities, and pressure pulsations
commonly found on peristaltic pumps. The model instead focusses on the flow
rate at the inlet and the outlet of the pump, rather than on each individual
roller. This model is highly scalable and allows for varying number of rollers.
The model is validated using a 3D printed peristaltic pump and pulsatile flow
rate test bench. The pump is capable of accommodating roller housings with
varying numbers of rollers (3 or 2) in order to validate the model.


  Let $L$ be the $n$-th order linear differential operator $Ly = \phi_0y^{(n)}
+ \phi_1y^{(n-1)} + \cdots + \phi_ny$ with variable coefficients. A
representation is given for $n$ linearly independent solutions of $Ly=\lambda r
y$ as power series in $\lambda$, generalizing the SPPS (spectral parameter
power series) solution which has been previously developed for $n=2$. The
coefficient functions in these series are obtained by recursively iterating a
simple integration process, begining with a solution system for $\lambda=0$. It
is shown how to obtain such an initializing system working upwards from
equations of lower order. The values of the successive derivatives of the power
series solutions at the basepoint of integration are given, which provides a
technique for numerical solution of $n$-th order initial value problems and
spectral problems.


  Molecular recognition and discrimination of carbohydrates are important
because carbohydrates perform essential roles in most living organisms for
energy metabolism and cell-to-cell communication. Nevertheless, it is difficult
to identify or distinguish various carbohydrate molecules owing to the lack of
a significant distinction in the physical or chemical characteristics. Although
there has been considerable effort to develop a sensing platform for individual
carbohydrates selectively using chemical receptors or an ensemble array, their
detection and discrimination limits have been as high in the millimolar
concentration range. Here we show a highly sensitive and selective detection
method for the discrimination of carbohydrate molecules using nano-slot-antenna
array-based sensing chips which operate in the terahertz frequency range. This
THz metamaterial sensing tool recognizes various types of carbohydrate
molecules over a wide range of molecular concentrations. Strongly localized and
enhanced terahertz transmission by nano-antennas can effectively increase the
molecular absorption cross sections, thereby enabling the detection of these
molecules even at low concentrations. We verified the performance of
nano-antenna sensing chip by both THz spectra and images of transmittance.
Screening and identification of various carbohydrates can be applied to test
even real market beverages with a high sensitivity and selectivity.


  A $H$-partition of a finite undirected simple graph $G$ is a labeling of
$G$'s vertices such that the constraints expressed by the model graph $H$ are
satisfied. For every model graph $H$, it can be decided in non-deterministic
polynomial time whether a given input graph $G$ admits a $H$-partition.
Moreover, it has been shown by Dantas et al. that for most model graphs, this
decision problem is in deterministic polynomial time. In this paper, we show
that these polynomial-time algorithms for finding $H$-partitions can be
expressed in Datalog with stratified negation. Moreover, using the answer set
solver Clingo, we have conducted experiments to compare straightforward
guess-and-check programs with Datalog programs. Our experiments indicate that
in Clingo, guess-and-check programs run faster than their equivalent Datalog
programs.


  Existing self-supervised monocular depth estimation methods can get rid of
expensive annotations and achieve promising results. However, these methods
suffer from severe performance degradation when directly adopting a model
trained on a fixed resolution to evaluate at other different resolutions. In
this paper, we propose a resolution adaptive self-supervised monocular depth
estimation method (RA-Depth) by learning the scale invariance of the scene
depth. Specifically, we propose a simple yet efficient data augmentation method
to generate images with arbitrary scales for the same scene. Then, we develop a
dual high-resolution network that uses the multi-path encoder and decoder with
dense interactions to aggregate multi-scale features for accurate depth
inference. Finally, to explicitly learn the scale invariance of the scene
depth, we formulate a cross-scale depth consistency loss on depth predictions
with different scales. Extensive experiments on the KITTI, Make3D and NYU-V2
datasets demonstrate that RA-Depth not only achieves state-of-the-art
performance, but also exhibits a good ability of resolution adaptation.


  A new global basis of B-splines is defined in the space of generalized
quadratic splines (GQS) generated by Merrien subdivision algorithm. Then,
refinement equations for these B-splines and the associated corner-cutting
algorithm are given. Afterwards, several applications are presented. First a
global construction of monotonic and/or convex generalized splines
interpolating monotonic and/or convex data. Second, convergence of sequences of
control polygons to the graph of a GQS. Finally, a Lagrange interpolant and a
quasi-interpolant which are exact on the space of affine polynomials and whose
infinite norms are uniformly bounded independently of the partition.


  We construct free resolutions for quotient rings $R/\langle \mathcal{I}',
\mathcal{I}\mathcal{J}, \mathcal{J}'\rangle$, give conditions for the quotient
to be realized as a fiber product, and give criteria for the construction to be
minimal. We then specialize this result to fiber products over a field $k$ and
recover explicit formulas for Betti numbers, graded Betti numbers, and
Poincar\'{e} series.


  Recently, deep learning-based tooth segmentation methods have been limited by
the expensive and time-consuming processes of data collection and labeling.
Achieving high-precision segmentation with limited datasets is critical. A
viable solution to this entails fine-tuning pre-trained multiview-based models,
thereby enhancing performance with limited data. However, relying solely on
two-dimensional (2D) images for three-dimensional (3D) tooth segmentation can
produce suboptimal outcomes because of occlusion and deformation, i.e.,
incomplete and distorted shape perception. To improve this fine-tuning-based
solution, this paper advocates 2D-3D joint perception. The fundamental
challenge in employing 2D-3D joint perception with limited data is that the
3D-related inputs and modules must follow a lightweight policy instead of using
huge 3D data and parameter-rich modules that require extensive training data.
Following this lightweight policy, this paper selects skeletons as the 3D
inputs and introduces MSFormer, a novel method for tooth segmentation. MSFormer
incorporates two lightweight modules into existing multiview-based models: a
3D-skeleton perception module to extract 3D perception from skeletons and a
skeleton-image contrastive learning module to obtain the 2D-3D joint perception
by fusing both multiview and skeleton perceptions. The experimental results
reveal that MSFormer paired with large pre-trained multiview models achieves
state-of-the-art performance, requiring only 100 training meshes. Furthermore,
the segmentation accuracy is improved by 2.4%-5.5% with the increasing volume
of training data.


  In 70's there was discovered a construction how to attach to some
algebraic-geometric data an infinite-dimensional subspace in the space k((z))
of the Laurent power series. The construction is known as the Krichever
correspondence. It was applied in the theory of integrable systems,
particularly, for the KP and KdV equations. We show that the Krichever
construction can be generalized to the case of dimension 2. We also include a
known description of connection between the KP hierarchy in the Lax form and
the vector fields on infinite Grassmanian manifolds and a construction of the
semi-infinite monomes for the field k((z)) which is an important part of the
theory of Sato Grassmanian. The text was published in Communications in
Algebra, 29(2001), No.9, 4157-4181. This version includes a corrected proof of
the proposition 2. Also, we include some additional remarks on the deduction of
concrete equations from the Lax hierarchy and appendix 2.


  We study cyclic scheduling for generate-at-will (GAW) multi-source status
update systems with heterogeneous service times and packet drop probabilities,
with the aim of minimizing the weighted sum age of information (AoI), called
system AoI, or the weighted sum peak AoI (PAoI), called system PAoI. In
particular, we obtain well-performing cyclic schedulers which can easily scale
to thousands of information sources and which also have low online
implementation complexity. The proposed schedulers are comparatively studied
against existing scheduling algorithms in terms of computational load and
system AoI/PAoI performance, to validate their effectiveness.


  We propose a new class of computer generated holograms whose far fields
possess designer-specified polarization response. We dub these Jones matrix
holograms. We provide a simple procedure for their implementation using
form-birefringent metasurfaces. Jones matrix holography generalizes a wide body
of past work with a consistent mathematical framework, particularly in the
field of metasurfaces, and suggests previously unrealized devices, examples of
which are demonstrated here. In particular, we demonstrate holograms whose
far-fields implement parallel polarization analysis and custom waveplate-like
behavior.


  Counterterm actions are constructed along the ADM formalism. It is shown that
the counterterm action can be intrinsically written in terms of intrinsic
boundary geometry. Using the expression of counterterm action, we obtain a
general form of the counterterm action available for any $d$-dimensional
spherical boundary. In the description, we also derive {\it arbitrary}
dimensional holographic conformal anomaly. It is also shown that counterterm
actions for AF spaces can be obtained from the AdS description just as taking
the limit of $\ell \to \infty$. An asymptotically flat spacetime with
non-spherical boundary is speculated. In the example, additional counterterms
to eliminate (leading) divergent terms due to deviation of boundary from round
sphere are imagined by observing (4-dimensional) holographic anomaly
proportional to $\Box R$. Argument of the deceptive-like anomaly is given by
comparing with the holographic description of 5-dimensional Kerr-AdS spacetime.


  Text-to-SQL systems (also known as NL-to-SQL systems) have become an
increasingly popular solution for bridging the gap between user capabilities
and SQL-based data access. These systems translate user requests in natural
language to valid SQL statements for a specific database. Recent Text-to-SQL
systems have benefited from the rapid improvement of transformer-based language
models. However, while Text-to-SQL systems that incorporate such models
continuously reach new high scores on -- often synthetic -- benchmark datasets,
a systematic exploration of their robustness towards different data models in a
real-world, realistic scenario is notably missing. This paper provides the
first in-depth evaluation of the data model robustness of Text-to-SQL systems
in practice based on a multi-year international project focused on Text-to-SQL
interfaces. Our evaluation is based on a real-world deployment of FootballDB, a
system that was deployed over a 9 month period in the context of the FIFA World
Cup 2022, during which about 6K natural language questions were asked and
executed. All of our data is based on real user questions that were asked live
to the system. We manually labeled and translated a subset of these questions
for three different data models. For each data model, we explore the
performance of representative Text-to-SQL systems and language models. We
further quantify the impact of training data size, pre-, and post-processing
steps as well as language model inference time. Our comprehensive evaluation
sheds light on the design choices of real-world Text-to-SQL systems and their
impact on moving from research prototypes to real deployments. Last, we provide
a new benchmark dataset to the community, which is the first to enable the
evaluation of different data models for the same dataset and is substantially
more challenging than most previous datasets in terms of query complexity.


  In this paper, we present an advanced approach to solving the inverse rig
problem in blendshape animation, using high-quality corrective blendshapes. Our
algorithm introduces novel enhancements in three key areas: ensuring high data
fidelity in reconstructed meshes, achieving greater sparsity in weight
distributions, and facilitating smoother frame-to-frame transitions. While the
incorporation of corrective terms is a known practice, our method
differentiates itself by employing a unique combination of $l_1$ norm
regularization for sparsity and a temporal smoothness constraint through
roughness penalty, focusing on the sum of second differences in consecutive
frame weights. A significant innovation in our approach is the temporal
decoupling of blendshapes, which permits simultaneous optimization across
entire animation sequences. This feature sets our work apart from existing
methods and contributes to a more efficient and effective solution. Our
algorithm exhibits a marked improvement in maintaining data fidelity and
ensuring smooth frame transitions when compared to prior approaches that either
lack smoothness regularization or rely solely on linear blendshape models. In
addition to superior mesh resemblance and smoothness, our method offers
practical benefits, including reduced computational complexity and execution
time, achieved through a novel parallelization strategy using clustering
methods. Our results not only advance the state of the art in terms of
fidelity, sparsity, and smoothness in inverse rigging but also introduce
significant efficiency improvements. The source code will be made available
upon acceptance of the paper.


  Regional data analysis is concerned with the analysis and modeling of
measurements that are spatially separated by specifically accounting for
typical features of such data. Namely, measurements in close proximity tend to
be more similar than the ones further separated. This might hold also true for
cross-dependencies when multivariate spatial data is considered. Often,
scientists are interested in linear transformations of such data which are easy
to interpret and might be used as dimension reduction. Recently, for that
purpose spatial blind source separation (SBSS) was introduced which assumes
that the observed data are formed by a linear mixture of uncorrelated, weakly
stationary random fields. However, in practical applications, it is well-known
that when the spatial domain increases in size the weak stationarity
assumptions can be violated in the sense that the second order dependency is
varying over the domain which leads to non-stationary analysis. In our work we
extend the SBSS model to adjust for these stationarity violations, present
three novel estimators and establish the identifiability and affine
equivariance property of the unmixing matrix functionals defining these
estimators. In an extensive simulation study, we investigate the performance of
our estimators and also show their use in the analysis of a geochemical dataset
which is derived from the GEMAS geochemical mapping project.


  This paper surveys recent work on Lie algebras of differential operators and
their application to the construction of quasi-exactly solvable Schroedinger
operators.


  Oxide heterostructures are of great interest both for fundamental and
applicative reasons. In particular the two-dimensional electron gas at the
LaAlO$_3$/SrTiO$_3$ or LaTiO$_3$/SrTiO$_3$ interfaces displays many different
physical properties and functionalities. However there are clear indications
that the interface electronic state is strongly inhomogeneous and therefore it
is crucially relevant to investigate possible intrinsic electronic mechanisms
underlying this inhomogeneity. Here the electrostatic potential confining the
electron gas at the interface is calculated self-consistently, finding that the
electron confinement at the interface may induce phase separation, to avoid a
thermodynamically unstable state with a negative compressibility. This provides
a generic robust and intrinsic mechanism for the experimentally observed
inhomogeneous character of these interfaces.


  Proximal soil sensors are taking hold in the understanding of soil
hydrogeological processes involved in precision agriculture. In this context,
permanently installed gamma ray spectroscopy stations represent one of the best
space-time trade off methods at field scale. This study proved the feasibility
and reliability of soil water content monitoring through a seven-month
continuous acquisition of terrestrial gamma radiation in a tomato test field.
By employing a 1 L sodium iodide detector placed at a height of 2.25 m, we
investigated the gamma signal coming from an area having a ~25 m radius and
from a depth of approximately 30 cm. Experimental values, inferred after a
calibration measurement and corrected for the presence of biomass, were
corroborated with gravimetric data acquired under different soil moisture
conditions, giving an average absolute discrepancy of about 2%. A quantitative
comparison was carried out with data simulated by AquaCrop, CRITeRIA, and
IRRINET soil-crop system models. The different goodness of fit obtained in bare
soil condition and during the vegetated period highlighted that CRITeRIA showed
the best agreement with the experimental data over the entire data-taking
period while, in presence of the tomato crop, IRRINET provided the best
results.


  Inverse Compton (IC) scattering is one of two viable mechanisms that can
produce the prompt gamma-ray emission in Gamma-Ray Bursts. IC requires low
energy seed photons and a population of relativistic electrons that upscatter
them. The same electrons can upscatter the gamma-ray photons to even higher
energies in the TeV range. Using the current upper limits on the prompt optical
emission we show here that under general conservative assumption the IC
mechanism suffers from an "energy crisis". Namely, IC will over-produce a very
high energy component that would carry much more energy than the observed
prompt gamma-rays. Our analysis is general and it makes no assumptions on the
specific mechanism that produces the relativistic electrons population.


  We study quantum properties of SU$(2|1)$ supersymmetric (deformed ${\cal
N}=4$, $d=1$ supersymmetric) extension of the superintegrable
Smorodinsky--Winternitz system on a complex Euclidian space $\mathbb{C}^N$. The
full set of wave functions is constructed and the energy spectrum is
calculated. It is shown that SU$(2|1)$ supersymmetry implies the bosonic and
fermionic states to belong to separate energy levels, thus exhibiting the
"even-odd" splitting of the spectra. The superextended hidden symmetry
operators are also defined and their action on SU$(2|1)$ multiplets of the wave
functions is given. An equivalent description of the same system in terms of
superconformal SU$(2|1,1)$ quantum mechanics is considered and a new
representation of the hidden symmetry generators in terms of the SU$(2|1,1)$
ones is found.


  We study the response of a two-dimensional hexagonal packing of rigid,
frictionless spherical grains due to a vertically downward point force on a
single grain at the top layer. We use a statistical approach, where each
configuration of the contact forces is equally likely. We find that the
response is double-peaked, independantly of the details of boundary conditions.
The two peaks lie precisely on the downward lattice directions emanating from
the point of application of the force. We examine the influence of the
confining pressure applied to the packing.


  A separable form of pairing interaction in the $^{1}S_{0}$ channel has been
introduced and successfully applied in the description of both static and
dynamic properties of superfluid nuclei. By adjusting the parameters to
reproduce the pairing properties of the Gogny force in nuclear matter, this
separable pairing force is successful in depicting the pairing properties of
ground states and vibrational excitations of spherical nuclei on almost the
same footing as the original Gogny force. In this article, we extend these
investigations for Relativistic Hartree Bogoliubov theory in deformed nuclei
with axial symmetry (RHBZ) using the same separable pairing interaction. In
order to preserve translational invariance we construct one- and
two-dimensional Talmi-Moshinsky brackets for the cylindrical harmonic
oscillator basis. We show that the matrix elements of this force can then be
expanded in a series of separable terms. The convergence of this expansion is
investigated for various deformations. We observe a relatively fast
convergence. This allows for a considerable reduction in computing time as
compared to RHBZ-calculations with the full Gogny force in the pairing channel.
As an example we solve the RHBZ equations with this separable pairing force for
the ground states of the chain of Sm-isotopes. Good agreement with the
experimental data as well as with other theoretical results is achieved.


  With the increasing use of neural networks in critical systems, runtime
monitoring becomes essential to reject unsafe predictions during inference.
Various techniques have emerged to establish rejection scores that maximize the
separability between the distributions of safe and unsafe predictions. The
efficacy of these approaches is mostly evaluated using threshold-agnostic
metrics, such as the area under the receiver operating characteristic curve.
However, in real-world applications, an effective monitor also requires
identifying a good threshold to transform these scores into meaningful binary
decisions. Despite the pivotal importance of threshold optimization, this
problem has received little attention. A few studies touch upon this question,
but they typically assume that the runtime data distribution mirrors the
training distribution, which is a strong assumption as monitors are supposed to
safeguard a system against potentially unforeseen threats. In this work, we
present rigorous experiments on various image datasets to investigate: 1. The
effectiveness of monitors in handling unforeseen threats, which are not
available during threshold adjustments. 2. Whether integrating generic threats
into the threshold optimization scheme can enhance the robustness of monitors.


  Proper motions in a sunspot group with a delta-configuration and close to the
solar disc center have been studied by employing local correlation tracking
techniques. The analysis is based on more than one hour time series of G-band
images. Radial outflows with a mean speed of 0.67 km s^{-1} have been detected
around the spots, the well-known sunspots moats. However, these outflows are
not found in those umbral core sides without penumbra. Moreover, moat flows are
only found in those sides of penumbrae located in the direction marked by the
penumbral filaments. Penumbral sides perpendicular to them show no moat flow.
These results strongly suggest a relation between the moat flow and the
well-known, filament aligned, Evershed flow. The standard picture of a moat
flow originated from a blocking of the upward propagation of heat is commented
in some detail.