  This study investigates the interpretability, classification, and
segmentation of CT-scan images of rock samples, with a particular focus on the
application of DINOv2 within Geosciences. We compared various segmentation
techniques to evaluate their efficacy, efficiency, and adaptability in
geological image analysis. The methods assessed include the Otsu thresholding
method, clustering techniques (K-means and fuzzy C-means), a supervised machine
learning approach (Random Forest), and deep learning methods (UNet and DINOv2).
We tested these methods using ten binary sandstone datasets and three
multi-class calcite datasets. To begin, we provide a thorough interpretability
analysis of DINOv2's features in the geoscientific context, discussing its
suitability and inherent ability to process CT-scanned rock data. In terms of
classification, the out-of-the-box DINOv2 demonstrates an impressive capability
to perfectly classify rock images, even when the CT scans are out of its
original training set. Regarding segmentation, thresholding and unsupervised
methods, while fast, perform poorly despite image preprocessing, whereas
supervised methods show better results. We underscore the computational demands
of deep learning but highlight its minimal intervention, superior
generalization, and performance without additional image preprocessing.
Additionally, we observe a lack of correlation between a network's depth or the
number of parameters and its performance. Our results show that a LoRA
fine-tuned DINOv2 excels in out-of-distribution segmentation and significantly
outperforms other methods in multi-class segmentation. By systematically
comparing these methods, we identify the most efficient strategy for meticulous
and laborious segmentation tasks. DINOv2 proves advantageous, achieving
segmentations that could be described as "better than ground-truth" against
relatively small training sets.


  We characterize the space of new forms for $\Gamma_0(m)$ as a common
eigenspace of certain Hecke operators which depend on primes $p$ dividing the
level $m$. To do that we find generators and relations for a $p$-adic Hecke
algebra of functions on $K={\rm GL}_2(\mathbb{Z}_p)$. We explicitly find the
$n+1$ irreducible representations of $K$ which contain a vector of level $n$
including the unique representation that contains the "new vector" at level
$n$. After translating the $p$-adic Hecke operators that we obtain into
classical Hecke operators we obtain the results about the new space mentioned
above.


  We argue that immature data pipelines are preventing a large portion of
industry practitioners from leveraging the latest research on recommender
systems. We propose our template data stack for machine learning at "reasonable
scale", and show how many challenges are solved by embracing a serverless
paradigm. Leveraging our experience, we detail how modern open source can
provide a pipeline processing terabytes of data with limited infrastructure
work.


  In the present work we focus on the case of (few-site) configurations
respecting the PT-symmetry. We examine the case of such "oligomers" with not
only 2-sites, as in earlier works, but also the cases of 3- and 4-sites. While
in the former case of recent experimental interest, the picture of existing
stationary solutions and their stability is fairly straightforward, the latter
cases reveal a considerable additional complexity of solutions, including ones
that exist past the linear PT-breaking point in the case of the trimer, and
more complex, even asymmetric solutions in the case of the quadrimer with
nontrivial spectral and dynamical properties. Both the linear stability and the
nonlinear dynamical properties of the obtained solutions are discussed.


  In economy, viewed as a quantum system working as a circuit, each process at
the microscale is a quantum gate among agents. The global configuration of
economy is addressed by optimizing the sustainability of the whole circuit.
This is done in terms of geodesics, starting from some approximations. A
similar yet somehow different approach is applied for the closed system of the
whole and for economy as an open system. Computations may partly be explicit,
especially when the reality is represented in a simplified way. The circuit can
be also optimized by minimizing its complexity, with a partly similar
formalism, yet generally not along the same paths.


  Four new probability models are derived which generalize the common
univariate continuous distributions. Classical distributional measures are
derived from Hoel, et al., Introduction to Probability Theory, 1971. Measures
include probability density function, moments generating function, cumulative
distribution function,derivatives, inverse distributions, skewness, kurtosis,
change of variable distributions, log distributions. Maximum likelihood
estimation technique is briefly outlined. Appendices describe applications.
Errata/addenda sheet included.


  Dataset condensation is a crucial tool for enhancing training efficiency by
reducing the size of the training dataset, particularly in on-device scenarios.
However, these scenarios have two significant challenges: 1) the varying
computational resources available on the devices require a dataset size
different from the pre-defined condensed dataset, and 2) the limited
computational resources often preclude the possibility of conducting additional
condensation processes. We introduce You Only Condense Once (YOCO) to overcome
these limitations. On top of one condensed dataset, YOCO produces smaller
condensed datasets with two embarrassingly simple dataset pruning rules: Low
LBPE Score and Balanced Construction. YOCO offers two key advantages: 1) it can
flexibly resize the dataset to fit varying computational constraints, and 2) it
eliminates the need for extra condensation processes, which can be
computationally prohibitive. Experiments validate our findings on networks
including ConvNet, ResNet and DenseNet, and datasets including CIFAR-10,
CIFAR-100 and ImageNet. For example, our YOCO surpassed various dataset
condensation and dataset pruning methods on CIFAR-10 with ten Images Per Class
(IPC), achieving 6.98-8.89% and 6.31-23.92% accuracy gains, respectively. The
code is available at: https://github.com/he-y/you-only-condense-once.


  This paper is dedicated to $L^p$ bounds on eigenfunctions of a
Sch\"odinger-type operator $(-\Delta_g)^{\alpha/2} +V$ on closed Riemannian
manifolds for critically singular potentials $V$. The operator
$(-\Delta_g)^{\alpha/2}$ is defined spectrally in terms of the eigenfunctions
of $-\Delta_g$. We obtain also quasimodes and spectral clusters estimates. As
an application, we derive Strichartz estimates for the fractional wave equation
$(\partial_t^2+(-\Delta_g)^{\alpha/2}+V)u=0$. The wave kernel techniques
recently developed by Bourgain-Shao-Sogge-Yao and Shao-Yao play a key role in
this paper. We construct a new reproducing operator with several local
operators and some good error terms. Moreover, we shall prove that these local
operators satisfy certain variable coefficient versions of the "uniform Sobolev
estimates" by Kenig-Ruiz-Sogge. These enable us to handle the critically
singular potentials $V$ and prove the quasimode estimates.


  We use recent experimental measurements of tau branching fractions to
determine the weak charged current magnetic and electric dipole moments of the
tau and the Michel parameter $\eta$ with unprecedented precision. These results
are then used to constrain the tau compositeness scale and the allowed
parameter space for Higgs doublet models. We also present new constraints on
the mass of the tau neutrino and its mixing with a fourth generation neutrino.


  In recent years, online distillation has emerged as a powerful technique for
adapting real-time deep neural networks on the fly using a slow, but accurate
teacher model. However, a major challenge in online distillation is
catastrophic forgetting when the domain shifts, which occurs when the student
model is updated with data from the new domain and forgets previously learned
knowledge. In this paper, we propose a solution to this issue by leveraging the
power of continual learning methods to reduce the impact of domain shifts.
Specifically, we integrate several state-of-the-art continual learning methods
in the context of online distillation and demonstrate their effectiveness in
reducing catastrophic forgetting. Furthermore, we provide a detailed analysis
of our proposed solution in the case of cyclic domain shifts. Our experimental
results demonstrate the efficacy of our approach in improving the robustness
and accuracy of online distillation, with potential applications in domains
such as video surveillance or autonomous driving. Overall, our work represents
an important step forward in the field of online distillation and continual
learning, with the potential to significantly impact real-world applications.


  Face alignment (or facial landmarking) is an important task in many
face-related applications, ranging from registration, tracking and animation to
higher-level classification problems such as face, expression or attribute
recognition. While several solutions have been presented in the literature for
this task so far, reliably locating salient facial features across a wide range
of posses still remains challenging. To address this issue, we propose in this
paper a novel method for automatic facial landmark localization in 3D face data
designed specifically to address appearance variability caused by significant
pose variations. Our method builds on recent cascaded-regression-based methods
to facial landmarking and uses a gating mechanism to incorporate multiple
linear cascaded regression models each trained for a limited range of poses
into a single powerful landmarking model capable of processing arbitrary posed
input data. We develop two distinct approaches around the proposed gating
mechanism: i) the first uses a gated multiple ridge descent (GRID) mechanism in
conjunction with established (hand-crafted) HOG features for face alignment and
achieves state-of-the-art landmarking performance across a wide range of facial
poses, ii) the second simultaneously learns multiple-descent directions as well
as binary features (SMUF) that are optimal for the alignment tasks and in
addition to competitive landmarking results also ensures extremely rapid
processing. We evaluate both approaches in rigorous experiments on several
popular datasets of 3D face images, i.e., the FRGCv2 and Bosphorus 3D Face
datasets and image collections F and G from the University of Notre Dame. The
results of our evaluation show that both approaches are competitive in
comparison to the state-of-the-art, while exhibiting considerable robustness to
pose variations.


  Mode purity is an important reference for the quality of the optical vortex.
In this work, we propose a self-interference method to directly measure single
component in superposed optical vortices based on phase-shifting technology.
This method has excellent flexibility and robustness, which can be applied to a
variety of occasions and harsh conditions. Careful alignment and optimized
error analysis allow us to generate and measure single component with mode
purity as high as 99.997%.


  The United Nations has identified improving food security and reducing hunger
as essential components of its sustainable development goals. As of 2021,
approximately 828 million people worldwide are experiencing hunger and
malnutrition, with numerous fatalities reported. Climate change significantly
impacts agricultural land suitability, potentially leading to severe food
shortages and subsequent social and political conflicts. To address this
pressing issue, we have developed a machine learning-based approach to predict
the risk of substantial land suitability degradation and changes in irrigation
patterns. Our study focuses on Central Eurasia, a region burdened with economic
and social challenges.
  This study represents a pioneering effort in utilizing machine learning
methods to assess the impact of climate change on agricultural land suitability
under various carbon emissions scenarios. Through comprehensive feature
importance analysis, we unveil specific climate and terrain characteristics
that exert influence on land suitability. Our approach achieves remarkable
accuracy, offering policymakers invaluable insights to facilitate informed
decisions aimed at averting a humanitarian crisis, including strategies such as
the provision of additional water and fertilizers. This research underscores
the tremendous potential of machine learning in addressing global challenges,
with a particular emphasis on mitigating hunger and malnutrition.


  It has recently been established that, in a non-demolition measurement of an
observable $\mathcal{N}$ with a finite point spectrum, the density matrix of
the system approaches an eigenstate of $\mathcal{N}$, i.e., it "purifies" over
the spectrum of $\mathcal{N}$. We extend this result to observables with
general spectra. It is shown that the spectral density of the state of the
system converges to a delta function exponentially fast, in an appropriate
sense. Furthermore, for observables with absolutely continuous spectra, we show
that the spectral density approaches a Gaussian distribution over the spectrum
of $\mathcal{N}$. Our methods highlight the connection between the theory of
non-demolition measurements and classical estimation theory.


  The existing studies of the temperature effect of the spin-boson model show
that the tunneling splitting will increase with temperature, no matter how weak
the couplings are between the bath and the spin. However, the small polaron
theory said that in the weak coupling and low temperature regime, the tunneling
is, in fact, dominated by the diagonal transitions whereas this diagonal
contribution to the tunneling should be faded away with increasing temperature.
Taking advantage of the analysis originated from the Feynman-Vernon's influence
functional theory, the influence on the tunneling by the phonon bath can be
expressed as a product of the effects of every single phonon mode, which can be
studied by numerical exact diagonalization. We find that, in the weak coupling
and low temperature regime, all the spin-single-mode systems exhibit the same
decreasing dependence of tunneling on increasing temperature. In turn, with the
conclusion of influence functional theory, the tunneling of the spin-boson
model should decrease and it is independent of the bath structure. In the
strong coupling regime, however, the temperature effect reverses from
suppressing to enhancing the tunneling with the increase of temperature.
Discrepancies between the old theories and the small polaron theory are also
explained.


  Long-term neutrino-radiation hydrodynamics simulations in full general
relativity are performed for the collapse of rotating massive stars that are
evolved from He-stars with their initial mass of $20$ and $32M_\odot$. It is
shown that if the collapsing stellar core has sufficient angular momentum, the
rotationally-supported proto-neutron star (PNS) survives for seconds
accompanying the formation of a massive torus of mass larger than $1\,M_\odot$.
Subsequent mass accretion onto the central region produces a massive and
compact central object, and eventually enhances the neutrino luminosity beyond
$10^{53}$\,erg/s, resulting in a very delayed neutrino-driven explosion in
particular toward the polar direction. The kinetic energy of the explosion can
be appreciably higher than $10^{52}$ erg for a massive progenitor star and
compatible with that of energetic supernovae like broad-line type-Ic
supernovae. By the subsequent accretion, the massive PNS collapses eventually
into a rapidly spinning black hole, which could be a central engine for
gamma-ray bursts if a massive torus surrounds it.


  This work explores the application of various supervised classification
approaches using prosodic information for the identification of spoken North
S\'ami language varieties. Dialects are language varieties that enclose
characteristics specific for a given region or community. These characteristics
reflect segmental and suprasegmental (prosodic) differences but also high-level
properties such as lexical and morphosyntactic. One aspect that is of
particular interest and that has not been studied extensively is how the
differences in prosody may underpin the potential differences among different
dialects. To address this, this work focuses on investigating the standard
acoustic prosodic features of energy, fundamental frequency, spectral tilt,
duration, and their combinations, using sequential and context-independent
supervised classification methods, and evaluated separately over two different
units in speech: words and syllables. The primary aim of this work is to gain a
better understanding on the role of prosody in identifying among the different
language varieties. Our results show that prosodic information holds an
important role in distinguishing between the five areal varieties of North
S\'ami where the inclusion of contextual information for all acoustic prosodic
features is critical for the identification of dialects for words and
syllables.


  The algorithm for generation of exact solutions of the nonlinear equation in
partial derivatives of a divergent type which is included in the formulation of
magnetostatics, hydro-and aerodynamics, quantum mechanics (stationary
Schr\"odinger equation) has been suggested. The properties of smoothness of
solutions in domains with corner points (piecewise smooth boundary) have been
considered. The solutions with unlimited derivatives in the corner point domain
have been presented on the basis of a new class of special functions.


  Whenever the group $\R^n$ acts on an algebra $\calA$, there is a method to
twist $\cal A$ to a new algebra $\calA_\theta$ which depends on an
antisymmetric matrix $\theta$ ($\theta^{\mu \nu}=-\theta^{\nu
\mu}=\mathrm{constant}$). The Groenewold-Moyal plane $\calA_\theta(\R^{d+1})$
is an example of such a twisted algebra. We give a general construction to
realise this twist in terms of $\calA$ itself and certain ``charge'' operators
$Q_\mu$. For $\calA_\theta(\R^{d+1})$, $Q_\mu$ are translation generators. This
construction is then applied to twist the oscillators realising the Kac-Moody
(KM) algebra as well as the KM currents. They give different deformations of
the KM algebra. From one of the deformations of the KM algebra, we construct,
via the Sugawara construction, the Virasoro algebra. These deformations have
implication for statistics as well.


  In this paper, we consider a novel problem of reconstructing a 3D human
avatar from multiple unconstrained frames, independent of assumptions on camera
calibration, capture space, and constrained actions. The problem should be
addressed by a framework that takes multiple unconstrained images as inputs,
and generates a shape-with-skinning avatar in the canonical space, finished in
one feed-forward pass. To this end, we present 3D Avatar Reconstruction in the
wild (ARwild), which first reconstructs the implicit skinning fields in a
multi-level manner, by which the image features from multiple images are
aligned and integrated to estimate a pixel-aligned implicit function that
represents the clothed shape. To enable the training and testing of the new
framework, we contribute a large-scale dataset, MVP-Human (Multi-View and
multi-Pose 3D Human), which contains 400 subjects, each of which has 15 scans
in different poses and 8-view images for each pose, providing 6,000 3D scans
and 48,000 images in total. Overall, benefits from the specific network
architecture and the diverse data, the trained model enables 3D avatar
reconstruction from unconstrained frames and achieves state-of-the-art
performance.


  Fixing molecules in space is a crucial step for the imaging of molecular
structure and dynamics. Here, we demonstrate three-dimensional (3D) field-free
alignment of the prototypical asymmetric top molecule indole using elliptically
polarized, shaped, off-resonant laser pulses. A truncated laser pulse is
produced using a combination of extreme linear chirping and controlled phase
and amplitude shaping using a spatial-light-modulator (SLM) based pulse shaper
of a broadband laser pulse. The angular confinement is detected through
velocity-map imaging of H$^+$ and C$^{2+}$ fragments resulting from
strong-field ionization and Coulomb explosion of the aligned molecules by
intense femtosecond laser pulses. The achieved three-dimensional alignment is
characterized by comparing the result of ion-velocity-map measurements for
different alignment directions and for different times during and after the
alignment laser pulse to accurate computational results. The achieved strong
three-dimensional field-free alignment of $\langle \cos^{2}\delta \rangle=0.89$
demonstrates the feasibility of both, strong three-dimensional alignment of
generic complex molecules and its quantitative characterization.


  Surveys of faint galaxies at high redshifts often result in a "pencil-beam"
geometry that is much longer along the line-of-sight than across the sky. We
explore the effects of this geometry on the abundance and clustering of
Lyman-break galaxies (LBGs) and Lyman-alpha emitters (LAEs) in current and
future surveys based on cosmological N-body simulations which adequately
describe the nonlinear growth of structure on small scales and compare to
linear theory. We find that the probability distribution of the LBG abundance
is skewed toward low values since the narrow transverse dimension of the survey
is more likely to probe underdense regions. Over a range that spans 1--2 orders
of magnitude in galaxy luminosities, the variance in the number of objects
differs from the commonly used analytic prediction and is not dominated by
Poisson noise. Additionally, nonlinear bias on small scales results in a
one-dimensional power spectrum of LAEs using a James Webb Space Telescope
field-of-view that is relatively flat, markedly different from the expectation
of linear perturbation theory. We discuss how these results may affect attempts
to measure the UV background at high redshifts, estimate the relationship
between halo mass and galaxy luminosity, and probe reionization by measuring
the power-modulating effect of ionized regions.


  In this paper, we extend the energy-Casimir stability method for
deterministic Lie-Poisson Hamiltonian systems to provide sufficient conditions
for the stability in probability of stochastic dynamical systems with
symmetries and multiplicative noise. We illustrate this theory with classical
examples of coadjoint motion, including the rigid body, the heavy top and the
compressible Euler equation in two dimensions. The main result of this
extension is that stable deterministic equilibria remain stable in probability
up to a certain stopping time which depends on the amplitude of the noise for
finite dimensional systems and on the amplitude the spatial derivative of the
noise for infinite dimensional systems.


  In order for humans to confidently decide where to employ RL agents for
real-world tasks, a human developer must validate that the agent will perform
well at test-time. Some policy interpretability methods facilitate this by
capturing the policy's decision making in a set of agent rollouts. However,
even the most informative trajectories of training time behavior may give
little insight into the agent's behavior out of distribution. In contrast, our
method conveys how the agent performs under distribution shifts by showing the
agent's behavior across a wider trajectory distribution. We generate these
trajectories by guiding the agent to more diverse unseen states and showing the
agent's behavior there. In a user study, we demonstrate that our method enables
users to score better than baseline methods on one of two agent validation
tasks.


  The nucleation and growth of point islands during submonolayer deposition on
a one-dimensional substrate is simulated for critical island size $i=0,1,2,3$.
The small and large size asymptotics for the gap size and capture zone
distributions (GSD and CZD) are studied. Comparisons to theoretical predictions
from fragmentation equation analyses are made, along with those from the
recently proposed Generalised Wigner Surmise (GWS). We find that the simulation
data can be fully understood in the framework provided by the fragmentation
equations, whilst highlighting the theoretical areas that require further
development. The GWS works well for the small-size CZD behaviour, but
completely fails to describe the large-size CZD asymptotics of the
one-dimensional system.


  This article deals with the issues of global-in-time existence and asymptotic
analysis of a fluid-particle interaction model in the so-called bubbling
regime. The mixture occupies the physical space $\Omega \subset \mathbb{R}^3$
which may be unbounded. The system under investigation describes the evolution
of particles dispersed in a viscous compressible fluid and is expressed by the
conservation of fluid mass, the balance of momentum and the balance of particle
density often referred as the Smoluchowski equation. The coupling between the
dispersed and dense phases is obtained through the drag forces that the fluid
and the particles exert mutually by action-reaction principle. We show that
solutions exist globally in time under reasonable physical assumptions on the
initial data, the physical domain, and the external potential. Furthermore, we
prove the large-time stabilization of the system towards a unique stationary
state fully determined by the masses of the initial density of particles and
fluid and the external potential.


  We introduce an efficient technique for computing Casimir energies and forces
between objects of arbitrarily complex 3D geometries. In contrast to other
recently developed methods, our technique easily handles non-spheroidal,
non-axisymmetric objects and objects with sharp corners. Using our new
technique, we obtain the first predictions of Casimir interactions in a number
of experimentally relevant geometries, including crossed cylinders and
tetrahedral nanoparticles.


  We have investigated an inhomogeneous Bianchi type-I cosmological model with
electromagnetic field based on Lyra geometry. A new class of exact solutions
have been obtained by considering the potentials of metric and displacement
field are functions of coordinates t and x. The physical behavior of the
obtained model is discussed.


  A new subspace of Morrey spaces whose elements can be approximated by
infinitely differentiable compactly supported functions is introduced.
Consequently, we give an explicit description of the closure of the set of such
functions in Morrey spaces. A generalization of known embeddings of Morrey
spaces into weighted Lesbesgue spaces is also obtained.


  The advent of Bluetooth wireless technology makes it possible to transmit
real-time audio in mobile devices. Bluetooth is cost-efficient and
power-efficient, but it is not suitable for traditional audio encoding and
real-time streaming due to limited bandwidth, high degree of error rates, and
the time-varying nature of the radio link. Therefore, audio streaming over
Bluetooth poses problems such as guzzling of both power and bandwidth. In order
to overcome the above mentioned problems, an algorithm is proposed in this work
to optimize the audio stream from the source to the sink by estimating the
proximity between them. The optimization is achieved by adjusting the bit rate
of the audio stream thus conserving power. We considered carefully various
Bluetooth signal parameters and the most suitable parameter for estimating the
proximity has been determined experimentally. The experiments were carried out
using Class II BS003 Bluesoleil dongle. This work will enable the Bluetooth
users to perform a seamless and optimized streaming of MP3 stereo audio data.


  In the petroleum industry, Quantitative Risk Analysis (QRA) has been one of
the main tools for risk management. To date, QRA has mostly focused on
technical barriers, despite many accidents having human failure as a primary
cause or a contributing factor. Human Reliability Analysis (HRA) allows for the
assessment of the human contribution to risk to be assessed both qualitatively
and quantitatively. Most credible and highly advanced HRA methods have largely
been developed and applied in support of nuclear power plants control room
operations and in context of probabilistic risk analysis. Moreover, many of the
HRA methods have issues that have led to inconsistencies, insufficient
traceability and reproducibility in both the qualitative and quantitative
phases. Given the need to assess human error in the context of the oil
industry, it is necessary to evaluate available HRA methodologies and assess
its applicability to petroleum operations. Furthermore, it is fundamental to
assess these methods against good practices of HRA and the requirements for
advanced HRA methods. The present paper accomplishes this by analyzing seven
HRA methods. The evaluation of the methods was performed in three stages. The
first stage consisted of an evaluation of the degree of adaptability of the
method for the Oil and Gas industry. In the second stage the methods were
evaluated against desirable items in an HRA method. The higher-ranked methods
were evaluated, in the third stage, against requirements for advanced HRA
methods. In addition to the methods' evaluation, this paper presents an
overview of state-of-the-art discussions on HRA, led by the Nuclear industry
community. It remarks that these discussions must be seriously considered in
defining a technical roadmap to a credible HRA method for the Oil and Gas
industry.


  In these lecture notes, we give an overview about non-local field-theories
and their application to polymerized membranes, i.e. membranes with a fixed
internal connectivity. The main technical tool is the multi-local operator
product expansion (MOPE), generalizing ideas from local field theories to the
multi-local situation.


  In topcolor assisted technicolor, topgluons are massive gluons which couple
mainly to top and bottom quarks. We estimate the mass reach for topgluons
decaying to t anti-t at the Tevatron as a function of integrated luminosity.
The mass reach for topgluons decreases with increasing topgluon width, and is
1.0 - 1.1 TeV for Run II (2 fb^-1) and 1.3-1.4 TeV for TeV33 (30 fb^-1).


  An energy eigenfunction in a classically chaotic system is known to have
spatial correlations which (in the limit of small $\hbar$) are governed by a
microcanonical distribution in the classical phase space. This result is valid,
however, only over coordinate distances which are small compared to any
relevant classical distance scales (such as the cyclotron radius for a charged
particle in a magnetic field). We derive a modified formula for the correlation
function in the regime of large separation. This then permits a complete
description, over all length scales, of the statistical properties of chaotic
eigenfunctions in the $\hbar\to 0$ limit. Applications to quantum dots are
briefly discussed.


  In this paper, we consider the dynamics of solutions to complex-valued
evolutionary partial differential equations (PDEs) and show existence of
heteroclinic orbits from nontrivial equilibria to zero via computer-assisted
proofs. We also show that the existence of unbounded solutions along unstable
manifolds at the equilibrium follows from the existence of heteroclinic orbits.
Our computer-assisted proof consists of three separate techniques of rigorous
numerics: an enclosure of a local unstable manifold at the equilibria, a
rigorous integration of PDEs, and a constructive validation of a trapping
region around the zero equilibrium.


  This article is devoted to the construction of pseudomodes of one-dimensional
biharmonic operators with the complex-valued potentials via the WKB method. As
a by-product, the shape of pseudospectrum near infinity can be described. This
is a newly discovered systematic method that goes beyond the standard
semi-classical setting which is a direct consequence. This approach can cover a
wide class of previously inaccessible potentials, from logarithmic to
superexponential ones.


  We consider Schr\"odinger equations for the quantum Painlev\'e equations. We
present hypergeometric solutions of the Schr\"odinger equations for the quantum
Painlev\'e equations, as particular solutions. We also give a representation
theoretic correspondence between Hamiltonians of the Schr\"odinger equations
for the quantum Painlev\'e equations and those of the KZ equation or the
confluent KZ equations.


  We have calculated the effects of giant convection cells also know as
sectoral rolls or banana cells, on p-mode splitting coefficients. We use the
technique of quasi-degenerate perturbation theory formulated by Lavely &
Ritzwoller in order to estimate the frequency shifts. A possible way of
detecting giant cells is to look for even splitting coefficients of 'nearly
degenerate' modes in the observational data since these modes have the largest
shifts. We find that banana cells having an azimuthal wave number of 16 and
maximum vertical velocity of 180 m/s cannot be ruled out from GONG data for
even splitting coefficients.


  Let $X$ be the countable product of Abelian locally compact Polish groups and
$A,B\subset X$ be two Borel sets, which are not Haar-null in $X$. We prove that
the sum-set $A+B:=\{a+b:a\in A,\;\;b\in B\}$ is Haar-open in the sense that for
any non-empty compact subset $K\subset X$ and point $p\in K$ there exists a
point $x\in X$ such that the set $K\cap(A+B+x)$ is a neighborhood of $p$ in
$K$. This is a generalization of the classical Steinhaus Theorem (1920) to
non-locally compact groups. We do not know if this generalization holds for
Banach spaces.


  Optimizing the design of solar cell metallizations is one of the ways to
improve the performance of solar cells. Recently, it has been shown that
Topology Optimization (TO) can be used to design complex metallization patterns
for solar cells that lead to improved performance. TO generates unconventional
design patterns that cannot be obtained with the traditional shape optimization
methods. In this paper, we show that this design process can be improved
further using a deep learning inspired strategy. We present SolarNet, a
CNN-based reparameterization scheme that can be used to obtain improved
metallization designs. SolarNet modifies the optimization domain such that
rather than optimizing the electrode material distribution directly, the
weights of a CNN model are optimized. The design generated by CNN is then
evaluated using the physics equations, which in turn generates gradients for
backpropagation. SolarNet is trained end-to-end involving backpropagation
through the solar cell model as well as the CNN pipeline. Through application
on solar cells of different shapes as well as different busbar geometries, we
demonstrate that SolarNet improves the performance of solar cells compared to
the traditional TO approach.


  It is a common belief that the last missing piece of the Standard Model of
particles physics was found with the discovery of the Higgs boson at the Large
Hadron Collider. However, there remains a major prediction of quantum
tunnelling processes mediated by instanton solutions in the Yang-Mills theory,
that is still untested in the Standard Model. The direct experimental
observation of instanton-induced processes, which are a consequence of the
non-trivial vacuum structure of the Standard Model and of quantum tunnelling in
QFT, would be a major breakthrough in modern particle physics. In this paper,
we present for the first time a full calculation of QCD instanton-induced
processes in proton-proton collisions accounting for quantum corrections due to
both initial and final state gluon interactions, a first implementation in an
MC event generator as well as a basic strategy how to observe these effects
experimentally.


  In the present paper, we consider a class of two players infinite horizon
differential games, with piecewise smooth costs exponentially discounted in
time. Through the analysis of the value functions, we study in which cases it
is possible to establish the existence Nash equilibrium solutions in feedback
form. We also provide examples of piecewise linear costs whose corresponding
games have either infinitely many Nash equilibria or no solutions at all.


  We present the realization of Hurwitz algebras in terms of 2x2 vector
matrices, which maintain the correspondence between the geometry of the vector
spaces used in the classical physics and the underlined algebraic foundation of
the quantum theory. The multiplication rule used is modification of the one
originally introduced by M.Zorn. We demonstrate that our multiplication is not
intrinsically non-associative; the realization of the real and complex numbers
is commutative and associative, the real quaternions maintain associativity and
the real octonion matrices form an alternative algebra. The extension to the
calculus of the matrices (with Hurwitz algebra valued matrix elements) of the
arbitrary dimensions is straightforward. We discuss briefly the applications of
the obtained results to the extensions of the standard Hilbert space
formulation of the quantum physics and to the alternative wave mechanical
formulation of the classical field theory.


  Large language models (LLMs) excel in abstractive summarization tasks,
delivering fluent and pertinent summaries. Recent advancements have extended
their capabilities to handle long-input contexts, exceeding 100k tokens.
However, in question answering, language models exhibit uneven utilization of
their input context. They tend to favor the initial and final segments,
resulting in a U-shaped performance pattern concerning where the answer is
located within the input. This bias raises concerns, particularly in
summarization where crucial content may be dispersed throughout the source
document(s). Besides, in summarization, mapping facts from the source to the
summary is not trivial as salient content is usually re-phrased. In this paper,
we conduct the first comprehensive study on context utilization and position
bias in summarization. Our analysis encompasses 6 LLMs, 10 datasets, and 5
evaluation metrics. We introduce a new evaluation benchmark called MiddleSum on
the which we benchmark two alternative inference methods to alleviate position
bias: hierarchical summarization and incremental summarization. Our code and
data can be found here: https://github.com/ntunlp/MiddleSum.


  Hybrid plasmonic lasers provide deep subwavelength optical confinement,
strongly enhanced light-matter interaction and together with nanoscale
footprint promise new applications in optical communication, bio-sensing and
photolithography. The subwavelength hybrid plasmonic lasers reported so far
often use bottom up grown nanowires, nanorods and nanosquares, making it
difficult to integrate these devices into industry-relevant high density
plasmonic circuits. Here, we report the first experimental demonstration of
AlGaInP based, red-emitting hybrid plasmonic lasers at room temperature using
lithography based fabrication processes. Resonant cavities with deep
subwavelength 2D and 3D mode confinement of lambda square/56 and lambda
cube/199, respectively are demonstrated. A range of cavity geometries
(waveguides, rings, squares and disks) show very low lasing thresholds of
0.6-1.8 mJ/cm square with wide gain bandwidth (610 nm-685 nm), which are
attributed to the heterogeneous geometry of the gain material, the optimized
etching technique, and the strong overlap of the gain material with the
plasmonic modes. Most importantly, we establish the connection between mode
confinements and enhanced absorption and stimulated emission, which play a
critical role in maintaining low lasing thresholds at extremely small hybrid
plasmonic cavities. Our results pave the way for the further integration of
dense arrays of hybrid plasmonic lasers with optical and electronic technology
platforms.


  Background: Outcome measures that are count variables with excessive zeros
are common in health behaviors research. There is a lack of empirical data
about the relative performance of prevailing statistical models when outcomes
are zero-inflated, particularly compared with recently developed approaches.
  Methods: The current simulation study examined five commonly used analytical
approaches for count outcomes, including two linear models (with outcomes on
raw and log-transformed scales, respectively) and three count
distribution-based models (i.e., Poisson, negative binomial, and zero-inflated
Poisson (ZIP) models). We also considered the marginalized zero-inflated
Poisson (MZIP) model, a novel alternative that estimates the effects on overall
mean while adjusting for zero-inflation. Extensive simulations were conducted
to evaluate their the statistical power and Type I error rate across various
data conditions.
  Results: Under zero-inflation, the Poisson model failed to control the Type I
error rate, resulting in higher than expected false positive results. When the
intervention effects on the zero (vs. non-zero) and count parts were in the
same direction, the MZIP model had the highest statistical power, followed by
the linear model with outcomes on raw scale, negative binomial model, and ZIP
model. The performance of a linear model with a log-transformed outcome
variable was unsatisfactory. When only one of the effects on the zero (vs.
non-zero) part and the count part existed, the ZIP model had the highest
statistical power.
  Conclusions: The MZIP model demonstrated better statistical properties in
detecting true intervention effects and controlling false positive results for
zero-inflated count outcomes. This MZIP model may serve as an appealing
analytical approach to evaluating overall intervention effects in studies with
count outcomes marked by excessive zeros.


  Designing light-weight CNN models with little parameters and Flops is a
prominent research concern. However, three significant issues persist in the
current light-weight CNNs: i) the lack of architectural consistency leads to
redundancy and hindered capacity comparison, as well as the ambiguity in
causation between architectural choices and performance enhancement; ii) the
utilization of a single-branch depth-wise convolution compromises the model
representational capacity; iii) the depth-wise convolutions account for large
proportions of parameters and Flops, while lacking efficient method to make
them light-weight. To address these issues, we factorize the four vital
components of light-weight CNNs from coarse to fine and redesign them: i) we
design a light-weight overall architecture termed LightNet, which obtains
better performance by simply implementing the basic blocks of other
light-weight CNNs; ii) we abstract a Meta Light Block, which consists of
spatial operator and channel operator and uniformly describes current basic
blocks; iii) we raise RepSO which constructs multiple spatial operator branches
to enhance the representational ability; iv) we raise the concept of receptive
range, guided by which we raise RefCO to sparsely factorize the channel
operator. Based on above four vital components, we raise a novel light-weight
CNN model termed as FalconNet. Experimental results validate that FalconNet can
achieve higher accuracy with lower number of parameters and Flops compared to
existing light-weight CNNs.


  Photonic states with large and fixed photon numbers, such as Fock states,
enable quantum-enhanced metrology but remain an experimentally elusive
resource. A potentially simple, deterministic and scalable way to generate
these states consists of fully exciting $N$ quantum emitters equally coupled to
a common photonic reservoir, which leads to a collective decay known as Dicke
superradiance. The emitted $N$-photon state turns out to be a highly entangled
multimode state, and to characterise its metrological properties in this work
we: (i) develop theoretical tools to compute the Quantum Fisher Information of
general multimode photonic states; (ii) use it to show that Dicke superradiant
photons in 1D waveguides achieve Heisenberg scaling, which can be saturated by
a parity measurement; (iii) and study the robustness of these states to
experimental limitations in state-of-art atom-waveguide QED setups.


  Extraction of categorised named entities from text is a complex task given
the availability of a variety of Named Entity Recognition (NER) models and the
unstructured information encoded in different source document formats.
Processing the documents to extract text, identifying suitable NER models for a
task, and obtaining statistical information is important in data analysis to
make informed decisions. This paper presents TNNT, a toolkit that automates the
extraction of categorised named entities from unstructured information encoded
in source documents, using diverse state-of-the-art Natural Language Processing
(NLP) tools and NER models. TNNT integrates 21 different NER models as part of
a Knowledge Graph Construction Pipeline (KGCP) that takes a document set as
input and processes it based on the defined settings, applying the selected
blocks of NER models to output the results. The toolkit generates all results
with an integrated summary of the extracted entities, enabling enhanced data
analysis to support the KGCP, and also, to aid further NLP tasks.


  Imaging techniques based on single-pixel detection, such as ghost imaging,
can reconstruct or recognize a target scene from multiple measurements using a
sequence of random mask patterns. However, the processing speed is limited by
the low rate of the pattern generation. In this study, we propose an ultrafast
method for random speckle pattern generation, which has the potential to
overcome the limited processing speed. The proposed approach is based on
multimode fiber speckles induced by fast optical phase modulation. We
experimentally demonstrate dynamic speckle projection with phase modulation at
10 GHz rates, which is five to six orders of magnitude higher than conventional
modulation approaches using spatial light modulators. Moreover, we combine the
proposed generation approach with a wavelength-division multiplexing technique
and apply it for image classification. As a proof-of-concept demonstration, we
show that 28x28-pixel images of digits acquired at GHz rates can be accurately
classified using a simple neural network. The proposed approach opens a novel
pathway for an all-optical image processor.


  We report on Hybrid-Monte-Carlo simulations of the tight-binding model with
long-range Coulomb interactions for the electronic properties of graphene. We
investigate the spontaneous breaking of sublattice symmetry corresponding to a
transition from the semimetal to an antiferromagnetic insulating phase. Our
short-range interactions thereby include the partial screening due to electrons
in higher energy states from ab initio calculations based on the constrained
random phase approximation [T.O.Wehling {\it et al.}, Phys.Rev.Lett.{\bf 106},
236805 (2011)]. In contrast to a similar previous Monte-Carlo study
[M.V.Ulybyshev {\it et al.}, Phys.Rev.Lett.{\bf 111}, 056801 (2013)] we also
include a phenomenological model which describes the transition to the
unscreened bare Coulomb interactions of graphene at half filling in the
long-wavelength limit. Our results show, however, that the critical coupling
for the antiferromagnetic Mott transition is largely insensitive to the
strength of these long-range Coulomb tails. They hence confirm the prediction
that suspended graphene remains in the semimetal phase when a realistic static
screening of the Coulomb interactions is included.


  The appearance of detached recirculation regions in wakes with base bleed
determines the aerodynamic properties of many natural organisms and
technological applications. In this work we introduce an analytical model which
captures certain key dimensions of the recirculation region in the wake of
porous plates of infinite aspect ratio, along with the porosity range \ks{over
which} it exists, when vortex shedding is absent or suppressed. The model is
used to interpret why the recirculation region (i) emerges, (ii) migrates away
from the body with increasing base bleed, (iii) disappears at a critical bleed
and (iv) is partially insensitive to variations in the Reynolds number. The
model predictions show considerable agreement with data from laboratory
experiments and numerical simulations. exists. The predictions show
considerable agreement with data from laboratory experiments and numerical
simulations.


  We quantize the spontaneously broken abelian U(1) Higgs model by using the
improved BFT and BFV formalisms. We have constructed the BFT physical fields,
and obtain the first class observables including the Hamiltonian in terms of
these fields. We have also explicitly shown that there are exact form
invariances between the second class and first class quantities. Then,
according to the BFV formalism, we have derived the corresponding Lagrangian
having U(1) gauge symmetry. We also discuss at the classical level how one
easily gets the first class Lagrangian from the symmetry-broken second class
Lagrangian.


  Spatial-wise dynamic convolution has become a promising approach to improving
the inference efficiency of deep networks. By allocating more computation to
the most informative pixels, such an adaptive inference paradigm reduces the
spatial redundancy in image features and saves a considerable amount of
unnecessary computation. However, the theoretical efficiency achieved by
previous methods can hardly translate into a realistic speedup, especially on
the multi-core processors (e.g. GPUs). The key challenge is that the existing
literature has only focused on designing algorithms with minimal computation,
ignoring the fact that the practical latency can also be influenced by
scheduling strategies and hardware properties. To bridge the gap between
theoretical computation and practical efficiency, we propose a latency-aware
spatial-wise dynamic network (LASNet), which performs coarse-grained spatially
adaptive inference under the guidance of a novel latency prediction model. The
latency prediction model can efficiently estimate the inference latency of
dynamic networks by simultaneously considering algorithms, scheduling
strategies, and hardware properties. We use the latency predictor to guide both
the algorithm design and the scheduling optimization on various hardware
platforms. Experiments on image classification, object detection and instance
segmentation demonstrate that the proposed framework significantly improves the
practical inference efficiency of deep networks. For example, the average
latency of a ResNet-101 on the ImageNet validation set could be reduced by 36%
and 46% on a server GPU (Nvidia Tesla-V100) and an edge device (Nvidia Jetson
TX2 GPU) respectively without sacrificing the accuracy. Code is available at
https://github.com/LeapLabTHU/LASNet.


  We present a detailed numerical study of the one-dimensional Holstein model
with a view to understanding the self-trapping process of electrons or excitons
in crystals with short-range particle-lattice interactions. Applying a very
efficient variational Lanczos method, we are able to analyze the ground-state
properties of the system in the weak-- and strong-coupling, adiabatic and
non-adiabatic regimes on lattices large enough to eliminate finite-size
effects. In particular, we obtain the complete phase diagram and comment on the
existence of a critical length for self-trapping in spatially restricted
one-dimensional systems. In order to characterize large and small polaron
states we calculate self-consistently the lattice distortions and the
particle-phonon correlation functions. In the strong-coupling case, two
distinct types of small polaron states are shown to be possible according to
the relative importance of static displacement field and dynamic polaron
effects. Special emphasis is on the intermediate coupling regime, which we also
study by means of direct diagonalization preserving the full dynamics and
quantum nature of phonons. The crossover from large to small polarons shows up
in a strong decrease of the kinetic energy accompanied by a substantial change
in the optical absorption spectra. We show that our numerical results in all
important limiting cases reveal an excellent agreement with both analytical
perturbation theory predictions and very recent density matrix renormalization
group data.


  Quantizing deep convolutional neural networks for image super-resolution
substantially reduces their computational costs. However, existing works either
suffer from a severe performance drop in ultra-low precision of 4 or lower
bit-widths, or require a heavy fine-tuning process to recover the performance.
To our knowledge, this vulnerability to low precisions relies on two
statistical observations of feature map values. First, distribution of feature
map values varies significantly per channel and per input image. Second,
feature maps have outliers that can dominate the quantization error. Based on
these observations, we propose a novel distribution-aware quantization scheme
(DAQ) which facilitates accurate training-free quantization in ultra-low
precision. A simple function of DAQ determines dynamic range of feature maps
and weights with low computational burden. Furthermore, our method enables
mixed-precision quantization by calculating the relative sensitivity of each
channel, without any training process involved. Nonetheless, quantization-aware
training is also applicable for auxiliary performance gain. Our new method
outperforms recent training-free and even training-based quantization methods
to the state-of-the-art image super-resolution networks in ultra-low precision.


  Effectively performing object rearrangement is an essential skill for mobile
manipulators, e.g., setting up a dinner table or organizing a desk. A key
challenge in such problems is deciding an appropriate manipulation order for
objects to effectively untangle dependencies between objects while considering
the necessary motions for realizing the manipulations (e.g., pick and place).
To our knowledge, computing time-optimal multi-object rearrangement solutions
for mobile manipulators remains a largely untapped research direction. In this
research, we propose ORLA*, which leverages delayed (lazy) evaluation in
searching for a high-quality object pick and place sequence that considers both
end-effector and mobile robot base travel. ORLA* also supports multi-layered
rearrangement tasks considering pile stability using machine learning.
Employing an optimal solver for finding temporary locations for displacing
objects, ORLA* can achieve global optimality. Through extensive simulation and
ablation study, we confirm the effectiveness of ORLA* delivering quality
solutions for challenging rearrangement instances. Supplementary materials are
available at: https://gaokai15.github.io/ORLA-Star/


  The 3.5 keV line is a purported emission line observed in galaxies, galaxy
clusters, and the Milky Way whose origin is inconsistent with known atomic
transitions and has previously been suggested to arise from dark matter decay.
We systematically re-examine the bulk of the evidence for the 3.5 keV line,
attempting to reproduce six previous analyses that found evidence for the line.
Surprisingly, we only reproduce one of the analyses; in the other five we find
no significant evidence for a 3.5 keV line when following the described
analysis procedures on the original data sets. For example, previous results
claimed 4$\sigma$ evidence for a 3.5 keV line from the Perseus cluster; we
dispute this claim, finding no evidence for a 3.5 keV line. We find evidence
for background mismodeling in multiple analyses. We show that analyzing these
data in narrower energy windows diminishes the effects of mismodeling but
returns no evidence for a 3.5 keV line. We conclude that there is little robust
evidence for the existence of the 3.5 keV line. Some of the discrepancy of our
results from those of the original works may be due to the earlier reliance on
local optimizers, which we demonstrate can lead to incorrect results. For ease
of reproducibility, all code and data are publicly available.


  Composites with high strength and high fracture resistance are desirable for
structural and protective applications. Most composites, however, suffer from
poor damage tolerance and are prone to unpredictable fractures. Understanding
the behavior of materials with an irregular reinforcement phase offers
fundamental guidelines for tailoring their performance. Here, we study the
fracture nucleation and propagation in two phase composites, as a function of
the topology of their irregular microstructures. We use a stochastic algorithm
to design the polymeric reinforcing network, achieving independent control of
topology and geometry of the microstructure. By tuning the local connectivity
of isodense tiles and their assembly into larger structures, we tailor the
mechanical and fracture properties of the architected composites, at the local
and global scale. Finally, combining different reinforcing networks into a
spatially determined meso-scale assembly, we demonstrate how the spatial
propagation of fractures in architected composite materials can be designed and
controlled a priori.


  The correction to the polarizability of helium due to black-body radiation is
calculated near room temperature. A precise theoretical determination of the
black-body radiation correction to the polarizability of helium is essential
for dielectric gas thermometry and for the determination of the Boltzmann
constant. We find that the correction, for not too high temperature, is roughly
proportional to a modified hyperpolarizability (two-color hyperpolarizability),
which is different from the ordinary hyperpolarizability of helium. Our
explicit calculations provide a definite numerical result for the effect and
indicate that the effect of black-body radiation can be excluded as a limiting
factor for dielectric gas thermometry using helium or argon.


  It is possible to find the optimized radiation dose per session for a
radiotherapy (RT) treatment, using a population dynamics model. This has
already been done in a previous work for a protocol with 30 sessions and a
fixed dose per session. Extending this model to other protocols, with a
variable number of sessions, we could change the radiation dosage while keeping
the success probability of treatment at its maximum value. This could help the
RT oncology service managers to plan the sequence of patients and treatments
adapting it to the facilities of the oncology service. Besides, if tumor
surrounding tissue is not able to afford a high dosage, it could be useful to
extend the treatment to a higher number of low dose radiation sessions, keeping
an optimal treatment.


  We present period domains of complex Hodge structures and some of their basic
properties from representation theory point of view. Specifically we introduce
the automorphic cohomology of period domains and the complex structure on
symmetric spaces.


  Adopting the mean-field composite fermion picture, we describe the
magneto-transport properties of a two-dimensional electron gas with laterally
modulated density around filling factor 1/2. The occurrence of a strong
positive magnetoresistance at low effective magnetic fields as well as Weiss
oscillations, which were observed in recent experiments in such systems, can be
explained within a semi-classical Boltzmann equation approach, provided one
goes beyond a second order approximation in the modulation strength.


  Gaia is regularly producing Alerts on objects where photometric variability
has been detected. The physical nature of these objects has often to be
determined with the complementary observations from ground-based facilities. We
have compared the list of Gaia Alerts (until 20181101) with archival LAMOST and
SDSS spectroscopic data. The date of the ground-based observation rarely
corresponds to the date of the Alert, but this allows at least the
identification of the source if it is persistent, or the host galaxy if the
object was only transient like a supernova. A list of Gaia Nuclear Transients
from Kostrzewa-Rutkowska et al. (2018) has been included in this search also.
We found 26 Gaia Alerts with spectra in LAMOST+SDSS labelled as stars (12 with
multi-epoch spectra). A majority of them are CVs. Similarly 206 Gaia Alerts
have associated spectra labelled as galaxies (49 with multi-epoch spectra).
Those spectra were generally obtained on a date different from the Alert date,
are mostly emission-line galaxies, leading to the suspicion that most of the
Alerts were due to a SN. As for the GNT list, we found 55 associated spectra
labelled as galaxies (13 with multi-epoch spectra). In two galaxies, Gaia17aal
and GNTJ170213+2543, was the date of the spectroscopic observation close enough
to the Alert date: we find a trace of the SN itself in their LAMOST spectrum,
both classified here as a type Ia SN. The GNT sample has a higher proportion of
AGNs, suggesting that some of the detected variations are also due to the AGN
itself. Similar for Quasars, we found 30 Gaia Alerts but 68 GNT cases have
single epoch quasar spectra, while 12 plus 23 have multi-epoch spectra. For ten
out of these 35, their multi-epoch spectra show appearance or disappearance of
the broad Balmer lines and also variations in the continuum, qualifying them as
"Changing Look Quasars".


  We consider the non-relativistic Chern-Simons equations proposed by Zhang,
Hansen and Kivelson as the mean field theory of the fractional Hall effect. We
prove the existence of the vortex lattice solutions (i.e. solution with lattice
symmetry and with topological degree one per lattice cell) similar to the
Abrikosov solutions of superconductivity. We derive an asymptotic expression
for the energy per unit area and show that it attains minimum at the hexagonal
lattice.


  I suggest an extension of the SM by introducing a dark sector with the local
$U(1)_{D}$ symmetry. The particles in the dark sector bring about the new
physics beyond the SM. In particular the global $B-L$ symmetry is violated just
above the electroweak scale, this becomes a common origin of the tiny neutrino
mass, the cold dark mater and the baryon asymmetry. The model can not only
account for the tiny neutrino mass and the "WIMP Miracle", but also achieve the
leptogenesis around the electroweak scale. Finally, it is very possible that
the model predictions are tested in near future experiments.


  Weak SU(3) symmetry is successfully applied to the weak hadronic decay
amplitudes of octet hyperons. Weak nonmesonic and mesonic decays of various
dibaryons with strangeness, their dominant decay modes, and lifetimes are
calculated. Production estimates for BNL's Relativistic Heavy-Ion Collider are
presented employing wave function coalescence. Signals for detecting strange
dibaryon states in heavy-ion collisions and revealing information about the
unknown hyperon-hyperon interactions are outlined.


  Content-aware recommendation approaches are essential for providing
meaningful recommendations for \textit{new} (i.e., \textit{cold-start}) items
in a recommender system. We present a content-aware neural hashing-based
collaborative filtering approach (NeuHash-CF), which generates binary hash
codes for users and items, such that the highly efficient Hamming distance can
be used for estimating user-item relevance. NeuHash-CF is modelled as an
autoencoder architecture, consisting of two joint hashing components for
generating user and item hash codes. Inspired from semantic hashing, the item
hashing component generates a hash code directly from an item's content
information (i.e., it generates cold-start and seen item hash codes in the same
manner). This contrasts existing state-of-the-art models, which treat the two
item cases separately. The user hash codes are generated directly based on user
id, through learning a user embedding matrix. We show experimentally that
NeuHash-CF significantly outperforms state-of-the-art baselines by up to 12\%
NDCG and 13\% MRR in cold-start recommendation settings, and up to 4\% in both
NDCG and MRR in standard settings where all items are present while training.
Our approach uses 2-4x shorter hash codes, while obtaining the same or better
performance compared to the state of the art, thus consequently also enabling a
notable storage reduction.


  We consider an electron-phonon system in two and three dimensions on square,
hexagonal and cubic lattices. The model is a modification of the standard
Holstein model where the optical branch is appropriately curved in order to
have a reflection positive Hamiltonian. Using infrared bounds together with a
recent result on the coexistence of long-range order for electron and phonon
fields, we prove that, at sufficiently low temperatures and sufficiently strong
electron-phonon coupling, there is a Peierls instability towards a period two
charge-density wave at half-filling. Our results take into account the quantum
fluctuations of the elastic field in a rigorous way and are therefore
independent of any adiabatic approximation. The strong coupling and low
temperature regime found here is independent of the strength of the quantum
fluctuations of the elastic field.


  Developing information technology to democratize scientific knowledge and
support citizen empowerment is a challenging task. In our case, a local
community suffered from air pollution caused by industrial activity. The
residents lacked the technological fluency to gather and curate diverse
scientific data to advocate for regulatory change. We collaborated with the
community in developing an air quality monitoring system which integrated
heterogeneous data over a large spatial and temporal scale. The system afforded
strong scientific evidence by using animated smoke images, air quality data,
crowdsourced smell reports, and wind data. In our evaluation, we report
patterns of sharing smoke images among stakeholders. Our survey study shows
that the scientific knowledge provided by the system encourages agonistic
discussions with regulators, empowers the community to support policy making,
and rebalances the power relationship between stakeholders.


  The method of a conformal transformation is applied to a general class of
single field inflation models with non-minimal coupling to gravity and
non-standard kinetic terms, in order to reduce the cosmological perturbative
calculation to the conventional minimal coupling case to all orders in
perturbation theory. Our analysis is made simple by the fact that all
perturbation variables in the comoving gauge are conformally invariant to all
orders. The structure of the vacuum, on which cosmological correlation
functions are evaluated, is also discussed. We show how quantization in the
Jordan frame for non-minimally coupled inflation models can be equivalently
implemented in the Einstein frame. It is thereafter argued that the general
N-point cosmological correlation functions (of the curvature perturbation) are
independent of the conformal frame.


  When we speak about parametric programming, sensitivity analysis, or related
topics, we usually mean the problem of studying specified perturbations of the
data such that for a given optimization problem some optimality criterion
remains satisfied. In this paper, we turn to another question. Suppose that $A$
is a matrix having a specific property $\mathcal{P}$. What are the maximal
allowable variations of the data such that the property still remains valid for
the matrix? We study two basic forms of perturbations. The first is a
perturbation in a given direction, which is closely related to parametric
programming. The second type consists of all possible data variations in a
neighbourhood specified by a certain matrix norm; this is related to the
tolerance approach to sensitivity analysis, or to stability. The matrix
properties discussed in this paper are positive definiteness; P-matrix,
H-matrix and P-matrix property; total positivity; inverse M-matrix property and
inverse nonnegativity.


  Regular triangulations of products of lattice polytopes are constructed with
the additional property that the dual graphs of the triangulations are
bipartite. The (weighted) size difference of this bipartition is a lower bound
for the number of real roots of certain sparse polynomial systems by recent
results of Soprunova and Sottile [Adv. Math. 204(1):116-151, 2006]. Special
attention is paid to the cube case.


  Despite considerations of mass loss from stellar evolution suggesting
otherwise, the content of gas in globular clusters seems poor and hence its
measurement very elusive. One way of constraining the presence of ionized gas
in a globular cluster is through its dispersive effects on the radiation of the
millisecond pulsars included in the cluster. This effect led Freire et al. in
2001 to the first detection of any kind of gas in a globular cluster in the
case of 47 Tucanae. By exploiting the results of 12 additional years of timing,
as well as the observation of new millisecond pulsars in 47 Tucanae, we
revisited this measurement: we first used the entire set of available timing
parameters in order to measure the dynamical properties of the cluster and the
three-dimensional position of the pulsars. Then we applied and tested various
gas distribution models: assuming a constant gas density, we confirmed the
detection of ionized gas with a number density of $n= 0.23\pm 0.05$ cm$^{-3}$,
larger than the previous determination (at 2$\sigma$ uncertainty). Models
predicting a decreasing density or following the stellar distribution density
are highly disfavoured. We are also able to investigate the presence of an
intermediate mass black hole in the centre of the cluster, showing that is not
required by the available data, with an upper limit for the mass at $\sim 4000$
M$_{\odot}$.


  Here we show that for $k\in \mathbb N,$ the closure of the $k$-rank numerical
range of a contraction $A$ acting on an infinite-dimensional Hilbert space
$\mathcal{H}$ is the intersection of the closure of the $k$-rank numerical
ranges of all unitary dilations of $A$ to $\mathcal{H}\oplus\mathcal{H}.$ The
same is true for $k=\infty$ provided the $\infty$-rank numerical range of $A$
is non-empty. These generalize a finite dimensional result of Gau, Li and Wu.
We also show that when both defect numbers of a contraction are equal and
finite ($=N$), one may restrict the intersection to a smaller family consisting
of all unitary $N$-dilations. A result of {Bercovici and Timotin} on unitary
$N$-dilations is used to prove it. Finally, we have investigated the same
problem for the $C$-numerical range and obtained the answer in negative.


  I review the energy spectra of low mass X-ray binaries (LMXBs) containing
weakly magnetized accreting neutron stars (NS), emphasizing the most recent
broad band (0.1-200 keV) spectral and timing observations performed by
Beppo-SAX and RXTE. Drawing on the similarities between black hole candidate
(BHC) and NS accretion, I discuss the accretion geometry and emission processes
of NS LMXBs.


  We present a probabilistic approach to generate a small, query-able summary
of a dataset for interactive data exploration. Departing from traditional
summarization techniques, we use the Principle of Maximum Entropy to generate a
probabilistic representation of the data that can be used to give approximate
query answers. We develop the theoretical framework and formulation of our
probabilistic representation and show how to use it to answer queries. We then
present solving techniques and give three critical optimizations to improve
preprocessing time and query accuracy. Lastly, we experimentally evaluate our
work using a 5 GB dataset of flights within the United States and a 210 GB
dataset from an astronomy particle simulation. While our current work only
supports linear queries, we show that our technique can successfully answer
queries faster than sampling while introducing, on average, no more error than
sampling and can better distinguish between rare and nonexistent values.


  The term NeuralODE describes the structural combination of an Artifical
Neural Network (ANN) and a numerical solver for Ordinary Differential Equations
(ODEs), the former acts as the right-hand side of the ODE to be solved. This
concept was further extended by a black-box model in the form of a Functional
Mock-up Unit (FMU) to obtain a subclass of NeuralODEs, named NeuralFMUs. The
resulting structure features the advantages of first-principle and data-driven
modeling approaches in one single simulation model: A higher prediction
accuracy compared to conventional First Principle Models (FPMs), while also a
lower training effort compared to purely data-driven models. We present an
intuitive workflow to setup and use NeuralFMUs, enabling the encapsulation and
reuse of existing conventional models exported from common modeling tools.
Moreover, we exemplify this concept by deploying a NeuralFMU for a consumption
simulation based on a Vehicle Longitudinal Dynamics Model (VLDM), which is a
typical use case in automotive industry. Related challenges that are often
neglected in scientific use cases, like real measurements (e.g. noise), an
unknown system state or high-frequent discontinuities, are handled in this
contribution. For the aim to build a hybrid model with a higher prediction
quality than the original FPM, we briefly highlight two open-source libraries:
FMI.jl for integrating FMUs into the Julia programming environment, as well as
an extension to this library called FMIFlux.jl, that allows for the integration
of FMUs into a neural network topology to finally obtain a NeuralFMU.


  We explore the nematic order of model goethite nanorods in an external
magnetic field within Onsager-Parsons density functional theory. The goethite
rods are represented by monodisperse, charged spherocylinders with a permanent
magnetic moment along the rod main axis, forcing the particles to align
parallel to the magnetic field at low field strength. The intrinsic diamagnetic
susceptibility anisometry of the rods is negative which leads to a preferred
perpendicular orientation at higher field strength. It is shown that these
counteracting effects may give rise to intricate phase behavior, including a
pronounced stability of biaxial nematic order and the presence of reentrant
phase transitions and demixing phenomena. The effect of the applied field on
the nematic-to-smectic transition will also be addressed.


  Marker-less 3D human motion capture from a single colour camera has seen
significant progress. However, it is a very challenging and severely ill-posed
problem. In consequence, even the most accurate state-of-the-art approaches
have significant limitations. Purely kinematic formulations on the basis of
individual joints or skeletons, and the frequent frame-wise reconstruction in
state-of-the-art methods greatly limit 3D accuracy and temporal stability
compared to multi-view or marker-based motion capture. Further, captured 3D
poses are often physically incorrect and biomechanically implausible, or
exhibit implausible environment interactions (floor penetration, foot skating,
unnatural body leaning and strong shifting in depth), which is problematic for
any use case in computer graphics. We, therefore, present PhysCap, the first
algorithm for physically plausible, real-time and marker-less human 3D motion
capture with a single colour camera at 25 fps. Our algorithm first captures 3D
human poses purely kinematically. To this end, a CNN infers 2D and 3D joint
positions, and subsequently, an inverse kinematics step finds space-time
coherent joint angles and global 3D pose. Next, these kinematic reconstructions
are used as constraints in a real-time physics-based pose optimiser that
accounts for environment constraints (e.g., collision handling and floor
placement), gravity, and biophysical plausibility of human postures. Our
approach employs a combination of ground reaction force and residual force for
plausible root control, and uses a trained neural network to detect foot
contact events in images. Our method captures physically plausible and
temporally stable global 3D human motion, without physically implausible
postures, floor penetrations or foot skating, from video in real time and in
general scenes. The video is available at
http://gvv.mpi-inf.mpg.de/projects/PhysCap


  Photonic integrated circuits (PICs) are attractive platforms to perform
large-scale quantum information processing. While highly-functional PICs (e.g.
silicon based photonic-circuits) and high-performance single photon sources
(SPSs, e.g. compound-semiconductor quantum dots (QDs)) have been independently
demonstrated, their combination for single-photon-based applications has still
been limited. This is largely due to the complexities of introducing SPSs into
existing PIC platforms, which are generally realized with different materials
and using distinct fabrication protocols. Here, we report a novel approach to
combine SPSs and PICs prepared independently. We employ transfer printing, by
which multiple desired SPSs can be integrated in a simple pick-and-place manner
with a theoretical waveguide coupling efficiency >99%, fulfilling the demanding
requirements of large-scale quantum applications. Experimentally, we
demonstrated QD-based SPSs with high waveguide coupling efficiencies, together
with the integration of two SPSs into a waveguide. Our approach will accelerate
scalable fusion between modern PICs and cutting-edge quantum technologies.


  A unified diagrammatic treatment single and double electron photoemission
currents is presented. The irreducible lesser density-density response function
is the starting point of these derivations. Diagrams for higher order processes
in which several electrons are observed in coincidence can likewise be
obtained. For physically relevant situations in which the photoemission
cross-section can be written as the Fermi Golden rule, the diagrams from the
nonequilibrium Green's function approach can be put direct correspondence with
that of the scattering theory.


  Ensuring generalization to unseen environments remains a challenge. Domain
shift can lead to substantially degraded performance unless shifts are
well-exercised within the available training environments. We introduce a
simple robust estimation criterion -- transfer risk -- that is specifically
geared towards optimizing transfer to new environments. Effectively, the
criterion amounts to finding a representation that minimizes the risk of
applying any optimal predictor trained on one environment to another. The
transfer risk essentially decomposes into two terms, a direct transfer term and
a weighted gradient-matching term arising from the optimality of
per-environment predictors. Although inspired by IRM, we show that transfer
risk serves as a better out-of-distribution generalization criterion, both
theoretically and empirically. We further demonstrate the impact of optimizing
such transfer risk on two controlled settings, each representing a different
pattern of environment shift, as well as on two real-world datasets.
Experimentally, the approach outperforms baselines across various
out-of-distribution generalization tasks. Code is available at
\url{https://github.com/Newbeeer/TRM}.


  The exclusive semileptonic decay form factors and widths of $B_c$ meson in
the $c\bar c\ (\eta_c,J/\psi)$ states based on heavy quark effective theory are
computed. The spectroscopic parameters of $B_c$ and the $c\bar c$ states
deduced using the phenomenological coulomb plus power form of the $q-\bar q$
potential $(CPP_\nu)$ with power index $\nu$ have been employed to compute the
Isgur wise function as well as the decay form factors. The universal behaviour
of the Isgur-wise function at the maximum momentum transfer has been observed
for different choices of $\nu$ between 0.5 to 2.0. However, such an
universality is not observed for the choice of $\nu<0.5$. Our predictions for
the branching ratio $B_c\rightarrow\eta_c\ell^+\nu_\ell$ lie 0.50 $%$ - 0.56
$%$ while that for $B_c\rightarrow J/\psi\ell^+\nu_\ell$ lie 1.8 $%$ - 2.0 $%$
for the choice of the potential index in the range $0.5\leq\nu\leq2.0$.


  YBa$_{2}$Cu$_{3}$O$_{7-{\delta}}$ coated conductors (CCs) have achieved high
critical current densities ($\textit{J}_{c}$) that can be further increased
through the introduction of additional defects using particle irradiation.
However, these gains are accompanied by increases in the flux creep rate, a
manifestation of competition between the different types of defects. Here, we
study this competition to better understand how to design pinning landscapes
that simultaneously increase $\textit{J}_{c}$ and reduce creep. CCs grown by
metal organic deposition show non-monotonic changes in the
temperature-dependent creep rate, $\textit{S}(\textit{T})$. Notably, in low
fields, there is a conspicuous dip to low $\textit{S}$ as temperature
($\textit{T}$) increases from ~20 K to ~65 K. Oxygen-, proton-, and
Au-irradiation substantially increase $\textit{S}$ in this temperature range.
Focusing on an oxygen-irradiated CC, we investigate the contribution of
different types of irradiation-induced defects to the flux creep rate.
Specifically, we study $\textit{S}(\textit{T})$ as we tune the relative density
of point defects to larger defects by annealing both an as-grown and an
irradiated CC in O$_{2}$ at temperatures $\textit{T}_{A}$ = 250${\deg}$C to
600${\deg}$C. We observe a steady decrease in $\textit{S}$($\textit{T}$ > 20 K)
with increasing $\textit{T}_{A}$, unveiling the role of pre-existing
nanoparticle precipitates in creating the dip in $\textit{S}(\textit{T})$ and
point defects and clusters in increasing $\textit{S}$ at intermediate
temperatures.


  We present a review of the normal form theory for weakly dispersive nonlinear
wave equations where the leading order phenomena can be described by the KdV
equation. This is an infinite dimensional extension of the well-known
Poincar\'e-Dulac normal form theory for ordinary differential equations. We
also provide a detailed analysis of the interaction problem of solitary wavesas
an important application of the normal form theory. Several explicit examples
are discussed based on the normal form theory, and the results are compared
with their numerical simulations. Those examples include the ion acoustic wave
equation, the Boussinesq equation as a model of the shallow water waves, the
regularized long wave equation and the Hirota bilinear equation having a 7th
order linear dispersion.


  In this paper we propose a recursive online algorithm for estimating the
parameters of a time-varying ARCH process. The estimation is done by updating
the estimator at time point $t-1$ with observations about the time point $t$ to
yield an estimator of the parameter at time point $t$. The sampling properties
of this estimator are studied in a non-stationary context -- in particular,
asymptotic normality and an expression for the bias due to non-stationarity are
established. By running two recursive online algorithms in parallel with
different step sizes and taking a linear combination of the estimators, the
rate of convergence can be improved for parameter curves from H\"{o}lder
classes of order between 1 and 2.


  We present the analysis of the magnetic field ($B$-field) structure of
galaxies measured with far-infrared (FIR) and radio (3 and 6 cm) polarimetric
observations. We use the first data release of the Survey on extragALactic
magnetiSm with SOFIA (SALSA) of 14 nearby ($<20$ Mpc) galaxies with resolved (5
arcsec-18 arcsec; $90$ pc--$1$ kpc) imaging polarimetric observations using
HAWC+/SOFIA from $53$ to $214$ \um. We compute the magnetic pitch angle
($\Psi_{B}$) profiles as a function of the galactrocentric radius. We introduce
a new magnetic alignment parameter ($\zeta$) to estimate the
disordered-to-ordered $B$-field ratio in spiral $B$-fields. We find FIR and
radio wavelengths to not generally trace the same $B$-field morphology in
galaxies. The $\Psi_{B}$ profiles tend to be more ordered with galactocentric
radius in radio ($\zeta_{\rm{6cm}} = 0.93\pm0.03$) than in FIR
($\zeta_{\rm{154\mu m}} = 0.84\pm0.14$). For spiral galaxies, FIR $B$-fields
are $2-75$\% more turbulent than the radio $B$-fields. For starburst galaxies,
we find that FIR polarization is a better tracer of the $B$-fields along the
galactic outflows than radio polarization. Our results suggest that the
$B$-fields associated with dense, dusty, turbulent star-forming regions, those
traced at FIR, are less ordered than warmer, less-dense regions, those traced
at radio, of the interstellar medium. The FIR $B$-fields seem to be more
sensitive to the activity of the star-forming regions and the morphology of the
molecular clouds within a vertical height of few hundred pc in the disk of
spiral galaxies than the radio $B$-fields.


  We introduce a sketch-and-solve approach to speed up the Peng-Wei
semidefinite relaxation of k-means clustering. When the data is appropriately
separated we identify the k-means optimal clustering. Otherwise, our approach
provides a high-confidence lower bound on the optimal k-means value. This lower
bound is data-driven; it does not make any assumption on the data nor how it is
generated. We provide code and an extensive set of numerical experiments where
we use this approach to certify approximate optimality of clustering solutions
obtained by k-means++.


  The performance of machine learning algorithms heavily relies on the
availability of a large amount of training data. However, in reality, data
usually reside in distributed parties such as different institutions and may
not be directly gathered and integrated due to various data policy constraints.
As a result, some parties may suffer from insufficient data available for
training machine learning models. In this paper, we propose a multi-party dual
learning (MPDL) framework to alleviate the problem of limited data with poor
quality in an isolated party. Since the knowledge sharing processes for
multiple parties always emerge in dual forms, we show that dual learning is
naturally suitable to handle the challenge of missing data, and explicitly
exploits the probabilistic correlation and structural relationship between dual
tasks to regularize the training process. We introduce a feature-oriented
differential privacy with mathematical proof, in order to avoid possible
privacy leakage of raw features in the dual inference process. The approach
requires minimal modifications to the existing multi-party learning structure,
and each party can build flexible and powerful models separately, whose
accuracy is no less than non-distributed self-learning approaches. The MPDL
framework achieves significant improvement compared with state-of-the-art
multi-party learning methods, as we demonstrated through simulations on
real-world datasets.


  Task oriented Dialogue Systems generally employ intent detection systems in
order to map user queries to a set of pre-defined intents. However, user
queries appearing in natural language can be easily ambiguous and hence such a
direct mapping might not be straightforward harming intent detection and
eventually the overall performance of a dialogue system. Moreover, acquiring
domain-specific clarification questions is costly. In order to disambiguate
queries which are ambiguous between two intents, we propose a novel method of
generating discriminative questions using a simple rule based system which can
take advantage of any question generation system without requiring annotated
data of clarification questions. Our approach aims at discrimination between
two intents but can be easily extended to clarification over multiple intents.
Seeking clarification from the user to classify user intents not only helps
understand the user intent effectively, but also reduces the roboticity of the
conversation and makes the interaction considerably natural.


  In this article, the weak-strong uniqueness principle is proved for an
Euler-Poisson system in the whole space, with initial data so that the strong
solution exists. Some results on Riesz potentials are used to justify the
considered weak formulation. Then, one follows the relative energy methodology
and, in order to handle the solution of Poisson's equation, employs the theory
of Riesz potentials.


  This paper is concerned with the Riemann problem for the isentropic Chaplygin
gas magnetogasdynamics equations and the formation of delta shocks and vacuum
states as pressure and magnetic field vanish. Firstly, the Riemann problem of
the isentropic magnetogasdynamics equations for Chaplygin gas is solved
analytically. Secondly, it is rigorously proved that, as both the pressure and
the magnetic field vanish, the Riemann solution containing two shock waves
tends to a delta shock solution to the transport equations, and the
intermediate density between the two shocks tends to a weighted
$\delta$-measure which forms the delta shock; while the Riemann solution
containing two rarefaction waves tends to a two-contact-discontinuity solution
to the transport equations, the termediate state between the two contact
discontinuities is a vacuum state.


  The methods developed by authors are applied to some reductions of BBGKY
hierarchy, namely, various examples of Vlasov-like systems which are important
both for fusion modeling and for particular physical problems related to
plasma/beam physics. We mostly concentrate on phenomena of localization and
pattern formation.


  Binary millisecond pulsars (MSPs) provide several opportunities for research
of fundamental physics. However, finding them can be challenging. Several
subdwarf B (sdB) binary systems with possible neutron star companions have been
identified, allowing us to perform a targeted search for MSPs within these
systems. Six sdBs with companions in the neutron star mass range, as determined
from their optical light curves, were observed with the Green Bank and
Westerbork radio telescopes. The data were searched for periodic signals as
well as single pulses. No radio pulsations from sdB systems were detected, down
to an average sensitivity limit of 0.11 mJy. We did, however, discover a pulsar
in the field of sdB HE0532-4503. Follow-up observations with the Giant
Metrewave Radio Telescope showed that this pulsar, J0533-4524, is not spatially
coincident with the sdB system. The pulsar has a relatively low magnetic field
but still emits giant pulses. We place an upper limit of three to the number of
radio pulsars in the six sdB systems. The non-detections may be explained by a
combination of the MSP beaming fraction, luminosity, and a recycling fraction
<0.5. Alternatively, the assumption of co-rotation between the MSP and sdB may
break down, which implies the systems are more edge-on than previously thought.
This would shift the predicted companion masses into the white dwarf range. It
would also explain the relative lack of edge-on sdB systems with massive
companions.


  We present theoretical and experimental results on spatial quantum
correlations induced by multiple scattering of nonclassical light. A continuous
mode quantum theory is derived that enables determining the spatial quantum
correlation function from the fluctuations of the total transmittance and
reflectance. Utilizing frequency-resolved quantum noise measurements, we
observe that the strength of the spatial quantum correlation function can be
controlled by changing the quantum state of an incident bright squeezed-light
source. Our results are found to be in excellent agreement with the developed
theory and form a basis for future research on, e.g., quantum interference of
multiple quantum states in a multiple scattering medium.


  Young giant exoplanets emit infrared radiation that can be linearly polarized
up to several percent. This linear polarization can trace: 1) the presence of
atmospheric cloud and haze layers, 2) spatial structure, e.g. cloud bands and
rotational flattening, 3) the spin axis orientation and 4) particle sizes and
cloud top pressure. We introduce a novel high-contrast imaging scheme that
combines angular differential imaging (ADI) and accurate near-infrared
polarimetry to characterize self-luminous giant exoplanets. We implemented this
technique at VLT/SPHERE-IRDIS and developed the corresponding observing
strategies, the polarization calibration and the data-reduction approaches. By
combining ADI and polarimetry we can characterize planets that can be directly
imaged with a very high signal-to-noise ratio. We use the IRDIS pupil-tracking
mode and combine ADI and principal component analysis to reduce speckle noise.
We take advantage of IRDIS' dual-beam polarimetric mode to eliminate
differential effects that severely limit the polarimetric sensitivity
(flat-fielding errors, differential aberrations and seeing), and thus further
suppress speckle noise. To correct for instrumental polarization effects, we
apply a detailed Mueller matrix model that describes the telescope and
instrument and that has an absolute polarimetric accuracy $\leq0.1\%$. Using
this technique we have observed the planets of HR 8799 and the (sub-stellar)
companion PZ Tel B. Unfortunately, we do not detect a polarization signal in a
first analysis. We estimate preliminary $1\sigma$ upper limits on the degree of
linear polarization of $\sim1\%$ and $\sim0.1\%$ for the planets of HR 8799 and
PZ Tel B, respectively. The achieved sub-percent sensitivity and accuracy show
that our technique has great promise for characterizing exoplanets through
direct-imaging polarimetry.


  In this note we exploit polynomial preconditioners for the Conjugate Gradient
method to solve large symmetric positive definite linear systems in a parallel
environment. We put in connection a specialized Newton method to solve the
matrix equation X^{-1} = A and the Chebyshev polynomials for preconditioning.
We propose a simple modification of one parameter which avoids clustering of
extremal eigenvalues in order to speed-up convergence. We provide results on
very large matrices (up to 8 billion unknowns) in a parallel environment
showing the efficiency of the proposed class of preconditioners.


  This paper develops low-dimensional moment methods for advective problems on
networks of domains. The evolution of a density function is described by a
linear advection-diffusion-reaction equation on each domain, combined via
advective flux coupling across domains in the network graph. The PDEs'
coefficients vary in time and across domains but they are fixed along each
domain. As a result, the solution on each domain is frequently close to a
Gaussian that moves, decays, and widens. For that reason, this work studies
moment methods that track only three degrees of freedom per domain -- in
contrast to traditional PDE discretization methods that tend to require many
more variables per domain. A simple ODE-based moment method is developed, as
well as an asymptotic-preserving scheme. We apply the methodology to an
application that models the life cycle of forest pests that undergo different
life stages and developmental pathways. The model is calibrated for the spotted
lanternfly, an invasive species present in the Eastern USA. We showcase that
the moment method, despite its significant low-dimensionality, can successfully
reproduce the prediction of the pest's establishment potential, compared to
much higher-dimensional computational approaches.


  In the previous paper [MR2430243] we computed some geometric quantities such
as curvature and flag curvature for a general left invariant Finsler metric on
a two-step nilpotent group. In the present paper we give a more complete
description of the Chern--Rund connection defined by a left invariant Randers
metric on the 3 dimensional Heisenberg group.


  We present a solution to the Round-Trip Migration case of the Transformation
Tool Contest 2020, based on the Henshin model transformation language. The task
is to support four scenarios of transformations between two versions of the
same data metamodel, a problem inspired by the application scenario of Web API
migration, where such a round-trip migration methodology might mitigate
drawbacks of the conventional "instant" migration style. Our solution relies on
Henshin's visual syntax, which seems well-suited to capture the problem on an
intuitive level, since the syntax is already similar to the scenario
illustrations in the case description. We discuss the five evaluation criteria
expressiveness, comprehensibility, bidirectionality, performance, and
reusability.


  Considering quantum random walks, we construct discrete-time approximations
of the eigenvalues processes of minors of Hermitian Brownian motion. It has
been recently proved by Adler, Nordenstam and van Moerbeke that the process of
eigenvalues of two consecutive minors of an Hermitian Brownian motion is a
Markov process, whereas if one considers more than two consecutive minors, the
Markov property fails. We show that there are analog results in the
noncommutative counterpart and establish the Markov property of eigenvalues of
some particular submatrices of Hermitian Brownian motion.


  We have computed the variation of the vacancy formation energy with pressure
for Ta. Total energy calculations were performed for 16 and 54 atom supercells
using a mixed basis pseudopotential method which uses pseudo-atomic orbitals
and low energy plane waves as the basis set, within density functional theory
(LDA and GGA). The vacancy formation energy is found to increase from 2.95 eV
at ambient pressures to 6.96 eV at 300 GPa, and the vacancy formation volume
decreases from being 53.4% of the bulk volume per atom at ambient pressure to
19.6% at 300 GPa, for a 54 atom supercell. The structural relaxation energy is
found to increase with pressure from 14% of the vacancy formation energy at
ambient pressure to 16% at 300 GPa.


  For two classes of Mean Field Game systems we study the convergence of
solutions as the interest rate in the cost functional becomes very large,
modeling agents caring only about a very short time-horizon, and the cost of
the control becomes very cheap. The limit in both cases is a single first order
integro-partial differential equation for the evolution of the mass density.
The first model is a 2nd order MFG system with vanishing viscosity, and the
limit is an aggregation equation. The result has an interpretation for models
of collective animal behaviour and of crowd dynamics. The second class of
problems are 1st order MFGs of acceleration and the limit is the kinetic
equation associated to the Cucker-Smale model. The first problem is analyzed by
PDE methods, whereas the second is studied by variational methods in the space
of probability measures on trajectories.