  Most of existing image denoising methods learn image priors from either
external data or the noisy image itself to remove noise. However, priors
learned from external data may not be adaptive to the image to be denoised,
while priors learned from the given noisy image may not be accurate due to the
interference of corrupted noise. Meanwhile, the noise in real-world noisy
images is very complex, which is hard to be described by simple distributions
such as Gaussian distribution, making real-world noisy image denoising a very
challenging problem. We propose to exploit the information in both external
data and the given noisy image, and develop an external prior guided internal
prior learning method for real-world noisy image denoising. We first learn
external priors from an independent set of clean natural images. With the aid
of learned external priors, we then learn internal priors from the given noisy
image to refine the prior model. The external and internal priors are
formulated as a set of orthogonal dictionaries to efficiently reconstruct the
desired image. Extensive experiments are performed on several real-world noisy
image datasets. The proposed method demonstrates highly competitive denoising
performance, outperforming state-of-the-art denoising methods including those
designed for real-world noisy images.


  We define Kazhdan-Lusztig bases and study asymptotic forms for affine
$q$-Schur algebras following Du and McGerty. We will show that the analogues of
Lusztig's conjectures for Hecke algebras with unequal parameters hold for
affine $q$-Schur algebras. We will also show that the affine $q$-Schur algebra
$\mathcal{S}_{q,k}^{\vartriangle}(2,2)$ over a field $k$ has finite global
dimension when char $k=0$ and $1+q\neq 0.$


  For a digraph $G$ without multisquares and a field $\mathbb{F}$, we construct
a basis of the vector space of path $n$-chains $\Omega_n(G;\mathbb{F})$ for
$n\geq 0$, generalising the basis of $\Omega_3(G;\mathbb{F})$ constructed by
Grigory'an. For a field $\mathbb{F},$ we consider the $\mathbb{F}$-path Euler
characteristic $\chi^\mathbb{F}(G)$ of a digraph $G$ defined as the alternating
sum of dimensions of path homology groups with coefficients in $\mathbb{F}.$ If
$\Omega_\bullet(G;\mathbb{F})$ is a bounded chain complex, the constructed
bases can be applied to compute $\chi^\mathbb{F}(G)$. We provide an explicit
example of a digraph $\mathcal{G}$ whose $\mathbb{F}$-path Euler characteristic
depends on whether the characteristic of $\mathbb{F}$ is two, revealing the
differences between GLMY theory and the homology theory of spaces. This allows
us to prove that there is no topological space $X$ whose homology is isomorphic
to path homology of the digraph $H_*(X;\mathbb{K})\cong {\rm
PH}_*(\mathcal{G};\mathbb{K})$ simultaneously for $\mathbb{K}=\mathbb{Z}$ and
$\mathbb{K}=\mathbb{Z}/2\mathbb{Z}.$


  This paper addresses the case where data come as point sets, or more
generally as discrete measures. Our motivation is twofold: first we intend to
approximate with a compactly supported measure the mean of the measure
generating process, that coincides with the intensity measure in the point
process framework, or with the expected persistence diagram in the framework of
persistence-based topological data analysis. To this aim we provide two
algorithms that we prove almost minimax optimal. Second we build from the
estimator of the mean measure a vectorization map, that sends every measure
into a finite-dimensional Euclidean space, and investigate its properties
through a clustering-oriented lens. In a nutshell, we show that in a mixture of
measure generating process, our technique yields a representation in
$\mathbb{R}^k$, for $k \in \mathbb{N}^*$ that guarantees a good clustering of
the data points with high probability. Interestingly, our results apply in the
framework of persistence-based shape classification via the ATOL procedure
described in \cite{Royer19}.


  In this work we focus on transferring supervision signals of natural language
generation (NLG) tasks between multiple languages. We propose to pretrain the
encoder and the decoder of a sequence-to-sequence model under both monolingual
and cross-lingual settings. The pre-training objective encourages the model to
represent different languages in the shared space, so that we can conduct
zero-shot cross-lingual transfer. After the pre-training procedure, we use
monolingual data to fine-tune the pre-trained model on downstream NLG tasks.
Then the sequence-to-sequence model trained in a single language can be
directly evaluated beyond that language (i.e., accepting multi-lingual input
and producing multi-lingual output). Experimental results on question
generation and abstractive summarization show that our model outperforms the
machine-translation-based pipeline methods for zero-shot cross-lingual
generation. Moreover, cross-lingual transfer improves NLG performance of
low-resource languages by leveraging rich-resource language data. Our
implementation and data are available at https://github.com/CZWin32768/xnlg.


  This paper provides partial identification of various binary choice models
with misreported dependent variables. We propose two distinct approaches by
exploiting different instrumental variables respectively. In the first
approach, the instrument is assumed to only affect the true dependent variable
but not misreporting probabilities. The second approach uses an instrument that
influences misreporting probabilities monotonically while having no effect on
the true dependent variable. Moreover, we derive identification results under
additional restrictions on misreporting, including bounded/monotone
misreporting probabilities. We use simulations to demonstrate the robust
performance of our approaches, and apply the method to study educational
attainment.


  A non-equilibrium steady state thermodynamics to describe shear flows is
developed using a canonical distribution approach. We construct a canonical
distribution for shear flow based on the energy in the moving frame using the
Lagrangian formalism of the classical mechanics. From this distribution we
derive the Evans-Hanley shear flow thermodynamics, which is characterized by
the first law of thermodynamics $dE = T dS - Q d\gamma$ relating infinitesimal
changes in energy $E$, entropy $S$ and shear rate $\gamma$ with kinetic
temperature $T$. Our central result is that the coefficient $Q$ is given by
Helfand's moment for viscosity. This approach leads to thermodynamic stability
conditions for shear flow, one of which is equivalent to the positivity of the
correlation function of $Q$. We emphasize the role of the external work
required to sustain the steady shear flow in this approach, and show
theoretically that the ensemble average of its power $\dot{W}$ must be
non-negative. A non-equilibrium entropy, increasing in time, is introduced, so
that the amount of heat based on this entropy is equal to the average of
$\dot{W}$. Numerical results from non-equilibrium molecular dynamics simulation
of two-dimensional many-particle systems with soft-core interactions are
presented which support our interpretation.


  The performance of neural decoders can degrade over time due to
nonstationarities in the relationship between neuronal activity and behavior.
In this case, brain-machine interfaces (BMI) require adaptation of their
decoders to maintain high performance across time. One way to achieve this is
by use of periodical calibration phases, during which the BMI system (or an
external human demonstrator) instructs the user to perform certain movements or
behaviors. This approach has two disadvantages: (i) calibration phases
interrupt the autonomous operation of the BMI and (ii) between two calibration
phases the BMI performance might not be stable but continuously decrease. A
better alternative would be that the BMI decoder is able to continuously adapt
in an unsupervised manner during autonomous BMI operation, i.e. without knowing
the movement intentions of the user.
  In the present article, we present an efficient method for such unsupervised
training of BMI systems for continuous movement control. The proposed method
utilizes a cost function derived from neuronal recordings, which guides a
learning algorithm to evaluate the decoding parameters. We verify the
performance of our adaptive method by simulating a BMI user with an optimal
feedback control model and its interaction with our adaptive BMI decoder. The
simulation results show that the cost function and the algorithm yield fast and
precise trajectories towards targets at random orientations on a 2-dimensional
computer screen. For initially unknown and non-stationary tuning parameters,
our unsupervised method is still able to generate precise trajectories and to
keep its performance stable in the long term. The algorithm can optionally work
also with neuronal error signals instead or in conjunction with the proposed
unsupervised adaptation.


  We describe a learning-based approach to hand-eye coordination for robotic
grasping from monocular images. To learn hand-eye coordination for grasping, we
trained a large convolutional neural network to predict the probability that
task-space motion of the gripper will result in successful grasps, using only
monocular camera images and independently of camera calibration or the current
robot pose. This requires the network to observe the spatial relationship
between the gripper and objects in the scene, thus learning hand-eye
coordination. We then use this network to servo the gripper in real time to
achieve successful grasps. To train our network, we collected over 800,000
grasp attempts over the course of two months, using between 6 and 14 robotic
manipulators at any given time, with differences in camera placement and
hardware. Our experimental evaluation demonstrates that our method achieves
effective real-time control, can successfully grasp novel objects, and corrects
mistakes by continuous servoing.


  The potential habitability of tidally locked planets orbiting M-dwarf stars
has been widely investigated in recent work, typically with a non-dynamic ocean
and without continents. On Earth, ocean dynamics are a primary means of heat
and nutrient distribution. Continents are a critical source of nutrients,
strongly influence ocean dynamics, and participate in climate regulation. In
this work, we investigate how the size of a substellar land mass affects the
oceans ability to transport heat and upwell nutrients on the tidally locked
planet Proxima Centauri b using the ROCKE-3D coupled ocean-atmosphere General
Circulation Model (GCM). We find that dayside ice-free ocean and nutrient
delivery to the mixed layer via upwelling are maintained across all continent
sizes. We also find that Proxima Centauri bs climate is more sensitive to
differences among atmospheric GCMs than to the inclusion of ocean dynamics in
ROCKE-3D. Finally, we find that Proxima Centauri b transitions from a lobster
state where ocean heat transport distributes heat away from the substellar
point to an eyeball state where heat transport is restricted and surface
temperature decreases symmetrically from the substellar point when the
continent size exceeds about 20 percent of the surface area. Our work suggests
that both a dynamic ocean and continents are unlikely to decrease the
habitability prospects of nearby tidally locked targets like Proxima Centauri b
that could be investigated with future observations by the James Webb Space
Telescope (JWST).


  New critical behavior in unconventional superconductors and superfluids is
established and described by the Wilson-Fisher renormalization-group method.
For certain ordering symmetries a new type of fluctuation-driven first order
phase transitions at finite and zero temperature are predicted. The results can
be applied to a wide class of ferromagnetic superconducting and superfluid
systems, in particular, to itinerant ferromagnets as UGe2 and URhGe.


  We study chiral and nonreciprocal single-photon scattering in a
chiral-giant-molecule waveguide-QED system. Here, the giant molecule consists
of two coupled giant atoms, which interact with two linear waveguides, forming
a four-port quantum device. We obtain the exact analytical expressions of the
four scattering amplitudes using a real-space method. Under the Markovian
limit, we find that the single-photon scattering behavior is determined by the
coupling strength between the giant atoms and the waveguides, the coupling
strength between the two giant atoms, and the nondipole effect caused by the
phase accumulation of photons travelling between the coupling points. It is
also found that chiral and nonreciprocal single-photon scattering can be
realized by introducing the chiral coupling to break the symmetry in the
coupling configuration between the giant molecule and the waveguides. In
addition, an ideal chiral emitter-waveguide coupling enables a directional
single-photon routing. In the non-Markovian regime, the scattering spectra are
characterized by more abundant structures with multiple peaks and dips. In
particular, we demonstrate that the non-Markovian retarded effect can induce
the nonreciprocal single-photon scattering. Our results have potential
applications in the design of optical quantum devices involving giant atoms,
which can provide an efficient platform for studying chiral quantum optics.


  Human visual recognition is a sparse process, where only a few salient visual
cues are attended to rather than traversing every detail uniformly. However,
most current vision networks follow a dense paradigm, processing every single
visual unit (e.g,, pixel or patch) in a uniform manner. In this paper, we
challenge this dense paradigm and present a new method, coined SparseFormer, to
imitate human's sparse visual recognition in an end-to-end manner. SparseFormer
learns to represent images using a highly limited number of tokens (down to 49)
in the latent space with sparse feature sampling procedure instead of
processing dense units in the original pixel space. Therefore, SparseFormer
circumvents most of dense operations on the image space and has much lower
computational costs. Experiments on the ImageNet classification benchmark
dataset show that SparseFormer achieves performance on par with canonical or
well-established models while offering better accuracy-throughput tradeoff.
Moreover, the design of our network can be easily extended to the video
classification with promising performance at lower computational costs. We hope
that our work can provide an alternative way for visual modeling and inspire
further research on sparse neural architectures. The code will be publicly
available at https://github.com/showlab/sparseformer


  We have prepared magnetic graphite samples bombarded by protons at low
temperatures and low fluences to attenuate the large thermal annealing produced
during irradiation. An overall optimization of sample handling allowed us to
find Curie temperatures $ T_c \gtrsim 350$ K at the used fluences. The
magnetization versus temperature shows unequivocally a linear dependence, which
can be interpreted as due to excitations of spin waves in a two dimensional
Heisenberg model with a weak uniaxial anisotropy.


  This paper summarizes my doctoral research on evaluation algorithms for
HEX-programs, which extend Answer Set Programming with means for interfacing
external computations. The focus is on integrating different subprocesses of
HEX-evaluation, such as solving and external calls as well as grounding, and on
applications of HEX-programs in the area of Machine Learning.


  Let G be a reductive group over an algebraically closed field of positive
characteristic. In this article we show an analogue for Morozov theorem for
characteristics that are separably good for G (and under additional hypotheses
on the group). This theorem characterises, when p= 0, subalgebras of parabolic
subgroups of G with respect to their nilradical. If now k is an arbitrary
field, let C be a smooth projective and geometrically connected curve. Let G be
a reductive C-group scheme, which is the twisted form of a constant C-group.
The aforementioned analogue is in particular useful to extend the construction
of the canonical parabolic subgroup of G proposed by M. Atiyah and R. Bott when
k is of characteristic 0, to the characteristic p>0 framework.


  The MEG (minimum equivalent graph) problem is, given a directed graph, to
find a small subset of the edges that maintains all reachability relations
between nodes. The problem is NP-hard. This paper gives a proof that, for
graphs where each directed cycle has at most three edges, the MEG problem is
equivalent to maximum bipartite matching, and therefore solvable in polynomial
time. This leads to an improvement in the performance guarantee of the
previously best approximation algorithm for the general problem in
``Approximating the Minimum Equivalent Digraph'' (1995).


  For a positive integer $n$, if $\sigma(n)$ denotes the sum of the positive
divisors of $n$, then $n$ is called a deficient perfect number if
$\sigma(n)=2n-d$ for some positive divisor $d$ of $n$. In this paper, we prove
some results about odd deficient perfect numbers with four distinct prime
factors.


  Accelerators with power-law memory are proposed in the framework of the
discrete time approach. To describe discrete accelerators we use the capital
stock adjustment principle, which has been suggested by Matthews.The suggested
discrete accelerators with memory describe the economic processes with the
power-law memory and the periodic sharp splashes (kicks). In continuous time
approach the memory is described by fractional-order differential equations. In
discrete time approach the accelerators with memory are described by discrete
maps with memory, which are derived from the fractional-order differential
equation without approximations. In order to derive these maps we use the
equivalence of fractional-order differential equations and the Volterra
integral equations.


  Demand functions for goods are generally cyclical in nature with
characteristics such as trend or stochasticity. Most existing demand
forecasting techniques in literature are designed to manage and forecast this
type of demand functions. However, if the demand function is lumpy in nature,
then the general demand forecasting techniques may fail given the unusual
characteristics of the function. Proper identification of the underlying demand
function and using the most appropriate forecasting technique becomes critical.
In this paper, we will attempt to explore the key characteristics of the
different types of demand function and relate them to known statistical
distributions. By fitting statistical distributions to actual past demand data,
we are then able to identify the correct demand functions, so that the the most
appropriate forecasting technique can be applied to obtain improved forecasting
results. We applied the methodology to a real case study to show the reduction
in forecasting errors obtained.


  Starting from the full many-body Hamiltonian of interacting electrons the
effective self-energy acting on electrons residing in a subspace of the full
Hilbert space is derived. This subspace may correspond to, for example,
partially filled narrow bands, which often characterize strongly correlated
materials. The formalism delivers naturally the frequency-dependent effective
interaction (the Hubbard U) and provides a general framework for constructing
theoretical models based on the Green function language. It also furnishes a
general scheme for first-principles calculations of complex systems in which
the main correlation effects are concentrated on a small subspace of the full
Hilbert space.


  We introduce a hierarchical Bayesian approach to tackle the challenging
problem of size recommendation in e-commerce fashion. Our approach jointly
models a size purchased by a customer, and its possible return event: 1. no
return, 2. returned too small 3. returned too big. Those events are drawn
following a multinomial distribution parameterized on the joint probability of
each event, built following a hierarchy combining priors. Such a model allows
us to incorporate extended domain expertise and article characteristics as
prior knowledge, which in turn makes it possible for the underlying parameters
to emerge thanks to sufficient data. Experiments are presented on real
(anonymized) data from millions of customers along with a detailed discussion
on the efficiency of such an approach within a large scale production system.


  We are interested in examples of a.e.c. with amalgamation having some
(extreme) behaviour concerning types. Note we deal with k being sequence-local,
i.e. local for increasing chains of length a regular cardinal (for types,
equality of all restrictions imply equality). . For any cardinal theta>=
aleph_0 we construct an a.e.c. with amalgamation k with L.S.T.(k) = theta,
|tau_K| = theta such that {kappa : kappa is a regular cardinal and K is not
(2^kappa, kappa)-sequence-local} is maximal. In fact we have a direct
characterization of this class of cardinals: the regular kappa such that there
is no uniform kappa^+-complete ultrafilter. We also prove a similar result to
"(2^kappa, kappa)-compact for types".


  Human image animation involves generating a video from a static image by
following a specified pose sequence. Current approaches typically adopt a
multi-stage pipeline that separately learns appearance and motion, which often
leads to appearance degradation and temporal inconsistencies. To address these
issues, we propose VividPose, an innovative end-to-end pipeline based on Stable
Video Diffusion (SVD) that ensures superior temporal stability. To enhance the
retention of human identity, we propose an identity-aware appearance controller
that integrates additional facial information without compromising other
appearance details such as clothing texture and background. This approach
ensures that the generated videos maintain high fidelity to the identity of
human subject, preserving key facial features across various poses. To
accommodate diverse human body shapes and hand movements, we introduce a
geometry-aware pose controller that utilizes both dense rendering maps from
SMPL-X and sparse skeleton maps. This enables accurate alignment of pose and
shape in the generated videos, providing a robust framework capable of handling
a wide range of body shapes and dynamic hand movements. Extensive qualitative
and quantitative experiments on the UBCFashion and TikTok benchmarks
demonstrate that our method achieves state-of-the-art performance. Furthermore,
VividPose exhibits superior generalization capabilities on our proposed
in-the-wild dataset. Codes and models will be available.


  We have analyzed the transformation from initial coordinates $(v,r)$ of the
Vaidya metric with light coordinate $v$ to the most physical diagonal
coordinates $(t,r)$. An exact solution has been obtained for the corresponding
metric tensor in the case of a linear dependence of the mass function of the
Vaidya metric on light coordinate $v$. In the diagonal coordinates, a narrow
region (with a width proportional to the mass growth rate of a black hole) has
been detected near the visibility horizon of the Vaidya accreting black hole,
in which the metric differs qualitatively from the Schwarzschild metric and
cannot be represented as a small perturbation. It has been shown that, in this
case, a single set of diagonal coordinates $(t,r)$ is insufficient to cover the
entire range of initial coordinates $(v,r)$ outside the visibility horizon; at
least three sets of diagonal coordinates are required, the domains of which are
separated by singular surfaces on which the metric components have
singularities (either $g_{00}=0$ or $g_{00}=\infty$.). The energy-momentum
tensor diverges on these surfaces; however, the tidal forces turn out to be
finite, which follows from an analysis of the deviation equations for
geodesics. Therefore, these singular surfaces are exclusively coordinate
singularities that can be referred to as false firewalls because there are no
physical singularities on them. We have also considered the transformation from
the initial coordinates to other diagonal coordinates $(\eta,y)$, in which the
solution is obtained in explicit form, and there is no energy-momentum tensor
divergence.


  This paper reports on laser-induced multiphoton ionization at 266 nm of
liquid argon in a time projection chamber (LAr TPC) detector. The electron
signal produced by the laser beam is a formidable tool for the calibration and
monitoring of next-generation large-mass LAr TPCs. The detector that we
designed and tested allowed us to measure the two-photon absorption
cross-section of LAr with unprecedented accuracy and precision:
sigma_ex=(1.24\pm 0.10stat \pm 0.30syst) 10^{-56} cm^4s{-1}.


  Let R be a regular semi-local integral domain containing a field and K be its
fraction field. Let mu: G --> T be an R-group schemes morphism between
reductive R-group schemes, which is smooth as a scheme morphism. Suppose that T
is an R-torus.Then the map T(R)/mu(G(R)) --> T(K)/mu(G(K)) is injective and
certain purity theorem is true.These and other results are derived from an
extended form of Grothendieck--Serre conjecture proven in the present paper for
rings R as above.


  Earlier work by Diaconis and Saloff-Coste gives a spectral criterion for a
maximum separation cutoff to occur for birth and death chains. Ding, Lubetzky
and Peres gave a related criterion for a maximum total variation cutoff to
occur in the same setting. Here, we provide complementary results which allow
us to compute the cutoff times and windows in a variety of examples.


  In this paper we focus on problems which do not admit a constant-factor
approximation in polynomial time and explore how quickly their approximability
improves as the allowed running time is gradually increased from polynomial to
(sub-)exponential.
  We tackle a number of problems: For Min Independent Dominating Set, Max
Induced Path, Forest and Tree, for any $r(n)$, a simple, known scheme gives an
approximation ratio of $r$ in time roughly $r^{n/r}$. We show that, for most
values of $r$, if this running time could be significantly improved the ETH
would fail. For Max Minimal Vertex Cover we give a non-trivial
$\sqrt{r}$-approximation in time $2^{n/r}$. We match this with a similarly
tight result. We also give a $\log r$-approximation for Min ATSP in time
$2^{n/r}$ and an $r$-approximation for Max Grundy Coloring in time $r^{n/r}$.
  Furthermore, we show that Min Set Cover exhibits a curious behavior in this
super-polynomial setting: for any $\delta > 0$ it admits an
$m^\delta$-approximation, where $m$ is the number of sets, in just
quasi-polynomial time. We observe that if such ratios could be achieved in
polynomial time, the ETH or the Projection Games Conjecture would fail.


  The digitisation campaigns carried out by libraries and archives in recent
years have facilitated access to documents in their collections. However,
exploring and exploiting these documents remain difficult tasks due to the
sheer quantity of documents available for consultation. In this article, we
show how the semantic annotation of the textual content of study corpora of
archival documents allow to facilitate their exploitation and valorisation.
First, we present a methodological framework for the construction of new
interfaces based on textual semantics, then address the current technological
obstacles and their potential solutions. We conclude by presenting a practical
case of the application of this framework.


  We present the distance measurement to z = 0.32 using the 11th data release
of the Sloan Digital Sky Survey-III Baryon Acoustic Oscillation Survey (BOSS).
We use 313,780 galaxies of the low-redshift (LOWZ) sample over 7,341
square-degrees to compute $D_V = (1264 \pm 25)(r_d/r_{d,fid})$ - a sub 2%
measurement - using the baryon acoustic feature measured in the galaxy
two-point correlation function and power-spectrum. We compare our results to
those obtained in DR10. We study observational systematics in the LOWZ sample
and quantify potential effects due to photometric offsets between the northern
and southern Galactic caps. We find the sample to be robust to all systematic
effects found to impact on the targeting of higher-redshift BOSS galaxies, and
that the observed north-south tensions can be explained by either limitations
in photometric calibration or by sample variance, and have no impact on our
final result. Our measurement, combined with the baryonic acoustic scale at z =
0.57, is used in Anderson et al. (2013a) to constrain cosmological parameters.


  We present a set of exactly solvable Ising models, with half-odd-integer
spin-S on a square-type lattice including a quartic interaction term in the
Hamiltonian. The particular properties of the mixed lattice, associated with
mixed half-odd-integer spin-(S,1/2) and only nearest-neighbour interaction,
allow us to map this system either onto a purely spin-1/2 lattice or onto a
purely spin-S lattice. By imposing the condition that the mixed
half-odd-integer spin-(S,1/2) lattice must have an exact solution, we found a
set of exact solutions that satisfy the {\it free fermion} condition of the
eight vertex model. The number of solutions for a general half-odd-integer
spin-S is given by $S+1/2$. Therefore we conclude that this transformation is
equivalent to a simple spin transformation which is independent of the
coordination number.


  We study the integral domains D satisfying the following condition: whenever
I >AB with I,A,B nonzero ideals, there exist ideals A'>A and B'>B such that
I=A'B'.


  We derive an exact expression for the Kubo conductunce in the Quantum Hall
device with the point-like intra-edge backscattering. This involves the
calculation of current-current correlator exactly, which we perform using
form-factor method. In brief, the full set of intermediate states is inserted
in the correlator, and for each term the closed mathematical expression is
obtained. It is shown that by making a special choice of intermediate states in
accordance with the hidden symmetries of the model, one achieves fast
convergence of the series, thus proving the form-factor approach to be
especially powerfull. This review is based on the joint work with H.Saleur and
F.Lesage.


  The BCS-to-BEC crossover, as well as the nature of Cooper pairs, in a
superconducting and Fermi superfluid medium is studied from the exact ground
state wavefunction of the reduced BCS Hamiltonian. As the strength of the
interaction increases, the ground state continuously evolves from a
mixed-system of quasifree fermions and pair resonances (BCS), to pair
resonances and quasibound molecules (pseudogap), and finally to a system of
quasibound molecules (BEC). A single unified scenario arises where the
Cooper-pair wavefunction has a unique functional form. Several exact analytic
expressions, such as the binding energy and condensate fraction, are derived.
We compare our results with recent experiments in ultracold atomic Fermi gases.


  The in-medium modification of nucleon-nucleon (NN) cross sections is
investigated by means of particle production in heavy ion collisions (HIC) at
intermediate energies. In particular, the density dependence of the {\it
inelastic} cross sections considerably affects the pion and kaon yields and
their rapidity distributions. However, the $(\pi^{-}/\pi^{+})$- and
$(K^{+}/K^{0})$-ratios depend only moderately on the in-medium behavior of the
inelastic cross sections. It turns out that particle ratios seem to be robust
observables in determining the nuclear equation of state (EoS) and,
particularly, its isovector sector.


  Searches for dark matter production at particle colliders are complementary
to direct-detection and indirect-detection experiments, and especially powerful
for small masses, $m_\chi<100$ GeV. An important collider dark matter signature
is due to the production of a pair of these invisible particles with the
initial-state radiation of a standard model particle. Currently, collider
searches use individual and nearly orthogonal final states to search for
initial-state jets, photons or massive gauge bosons. We combine these results
across final states and across experiments to give the strongest current
collider-based limits in the context of effective field theories, and map these
to limits on dark matter interactions with nuclei and to dark matter
self-annhiliation.


  Noncommutative geometry has become popular mathematics for describing
speculative physics beyond the Standard Model. Noncommutative QED has long been
known to fit within the framework of the Standard-Model Extension (SME). We
argue in this work that noncommutative gravity also fits within the SME
framework.


  The rotating loop quantum gravity black hole is a newly proposed non-singular
black hole, which eliminates spacetime singularities when a regularization
parameter is introduced through loop quantum corrections. This parameter is
expected to give rise to observable effects. In this paper, the dynamical
behavior of a scalar field near a rotating loop quantum gravity black hole is
investigated. Given a small initial perturbation, we obtain the waveform of
massless scalar fields evolving over time. By analyzing the waveform, we find
that the regularization parameter only affects the damping oscillation of
waveform, but not the initial outburst and late-time tail stages. This behavior
is characterized by quasi-normal modes. Under scalar field perturbations, the
loop quantum black holes remain stable. Moreover, we calculate the quasi-normal
modes of massive scalar fields by three numerical methods, which are the Prony,
WKB, and shooting methods, respectively. Our results indicate that the real
part of quasi-normal modes depends only on the regularization parameter, while
the imaginary part does not only on the regularization parameter but also on
the angular momentum. Finally, we study the amplification effect of rotating
black holes, i.e., the superradiance. Our analyses indicate the existence of
stronger superradiance around loop quantum gravity black holes compared to Kerr
ones.


  The problem of intermittency in developed hydrodynamic turbulence is
considered. Explicit formulae taking into account effects of finite size of the
inertial range are presented for the whole set of intermittency exponents. The
formulae fit pretty well experimental data whose apparent discrepancies are
attributed to different sizes of the inertial ranges in different experiments.
Further predictions are given that can be verified by already existing
experimental technique.


  Single-electron tunneling processes through a double quantum dot can induce a
lasing state in an electromagnetic resonator which is coupled coherently to the
dot system. Here we study the noise properties of the transport current in the
lasing regime, i.e., both the zero-frequency shot noise as well as the noise
spectrum. The former shows a remarkable super-Poissonian behavior when the
system approaches the lasing transition, but sub-Poissonian behavior deep in
the lasing state. The noise spectrum contains information about the coherent
dynamics of the coupled dot-resonator system. It shows pronounced structure at
a frequency matching that of the resonator due to the excitation of photons.
For strong interdot Coulomb interaction we find asymmetries in the
auto-correlation noise spectra of the left and right junctions, which we trace
back to asymmetries in the incoherent tunneling channels.


  We study the formation of extreme events in incoherent systems described by
envelope equations, such as the Nonliner Schr\"odinger equation. We derive an
identity that relates the evolution of the kurtosis (a measure of the relevance
of the tails in a probability density function) of the wave amplitude to the
rate of change of the width of the Fourier spectrum of the wave field. The
result is exact for all dispersive systems characterized by a nonlinear term of
the form of the one contained in the Nonlinear Schr\"odinger equation.
Numerical simulations are also performed to confirm our findings. Our work
sheds some light on the origin of rogue waves in incoherent dispersive
nonlinear media ruled by local cubic nonlinearity.


  Given two closed subsets $X, Y$ in $\mathbb{R}^n$, we construct a version of
Morse Theory for $\mathrm{dist}_Y|_X \colon X \to \mathbb{R}$, the restriction
to $X$ of the Euclidean distance function from $Y$. We use the notion of
critical points of Lipschitz functions introduced by Clarke and apply the more
general Morse Theory of continuous selections, as presented by Agrachev,
Pallaschke, and Scholtes. In this framework, nondegenerate critical points have
two indices: a quadratic index as in classical Morse Theory, and a piecewise
linear index that relates to the notion of bottlenecks.
  This framework is flexible enough to simultaneously treat two cases of
interest for computational algebraic geometry: the Bottleneck Degree (BND) and
the Euclidean Distance Degree (EDD). We provide bounds on the number of
critical points of $\mathrm{dist}_Y|_X$ when $X$ and $Y$ are generic real
algebraic hypersurfaces and relate these bounds to the BND and EDD. We also
prove a duality formula relating the Euler Characteristics of $X$ and $Y$ with
the number of critical points of $\mathrm{dist}_Y|_X$ and $\mathrm{dist}_X|_Y$,
respectively.
  Moreover, we introduce a technical toolset of independent interest, which
guarantees that our Morse Theory can be used in the generic algebraic case.


  This paper is concerned with the It\^o stochastic differential equations with
$\mR^{d\times k}$ diffusions in class of H\"older spaces and continuous $\mR^d$
drifts. We derive a uniqueness result of strong solutions for $\cC^\alpha \
(\alpha\geq \frac{1}{2})$ coefficients and this result is new. Our proof is
supported by It\^o's formula and a finer analysis on cut-off and smoothing
techniques.


  The low-energy effective theory of nuclear physics based on chiral symmetry
is reviewed. Topics discussed include the nucleon-nucleon force, few-body
potentials, isospin violation, pion-deuteron scattering, proton-neutron
radiative capture, pion photoproduction on the deuteron, and pion production in
proton-proton collisions.


  Estimating the fidelity with a target state is important in quantum
information tasks. Many fidelity estimation techniques present a suitable
measurement scheme to perform the estimation. In contrast, we present
techniques that allow the experimentalist to choose a convenient measurement
setting. Our primary focus lies on a method that constructs an estimator with
nearly minimax optimal confidence intervals for any specified measurement
setting. We demonstrate, through a combination of theoretical and numerical
results, various desirable properties of the method: robustness against
experimental imperfections, competitive sample complexity, and accurate
estimates in practice. We compare this method with Maximum Likelihood
Estimation and the associated Profile Likelihood method, a Semi-Definite
Programming based approach, direct fidelity estimation, quantum state
verification, and classical shadows. Our method can also be used for estimating
the expectation value of any observable with the same guarantees.


  We introduce the notion of hypersymplectic structure on a Courant algebroid
and we prove the existence of a one-to-one correspondence between
hypersymplectic and hyperk\"ahler structures. This correspondence provides a
simpler way to define a hyperk\"ahler structure on a Courant algebroid. We show
that hypersymplectic structures on Courant algebroids encompass hyperk\"ahler
and hyperk\"ahler structures with torsion on Lie algebroids. In the latter, the
torsion existing at the Lie algebroid level is incorporated in the Courant
structure. Cases of hypersymplectic structures on Courant algebroids which are
doubles of Lie, quasi-Lie and proto-Lie bialgebroids are investigated.


  These ICTP Trieste lecture notes review the pure spinor approach to
quantizing the superstring with manifest D=10 super-Poincare invariance. The
first section discusses covariant quantization of the superparticle and gives a
new proof of equivalence with the Brink-Schwarz superparticle. The second
section discusses the superstring in a flat background and shows how to
construct vertex operators and compute tree amplitudes in a manifestly
super-Poincare covariant manner. And the third section discusses quantization
of the superstring in curved backgrounds which can include Ramond-Ramond flux.


  Comparative analysis of different types of initial mass spectra of primordial
black holes (PBHs) is carried out. It is assumed that primordial density
fluctuations have power law spectrum and the spectral index is constant
throughout all scales. It is shown that densities of background radiations
(neutrinos, gamma-quanta) from PBH evaporations strongly depend on the type of
gravitational collapse and on the way of taking into account the spread of
horizon masses at which PBHs can form. Constraints on spectral index values
based on PBH evaporation process and on atmospheric and solar neutrino data are
obtained.


  The event GW170817/GRB 170817A, discovered via the successful joint
observation of its gravitational wave radiation and its multi-wavelength
electromagnetic counterparts, was the first definite "smoking-gun" from the
merger of two neutron stars (NSs). However, the remnant of the merger remains
unknown. Piro et al. recently claimed that a low-significance X-ray variability
in GRB 170817A. By systematically comparing the properties of variability in
the afterglow of GRB 170817A and X-ray flares in GRB afterglows, we find that
this X-ray variability seems to share similar statistical correlations with
X-ray flares in GRB afterglows. We further investigate several possible merger
product scenarios to see whether they can produce the observed X-ray
variability in GRB 170817A. The first scenario invokes a stable magnetar as the
central engine producing the later X-ray variability via differential rotation
or fall-back accretion onto the NS. The second scenario invokes a black hole as
the central engine with a fall-back accretion process. The final scenario is a
central engine with a long-lived supra-massive NS. We find that the first two
scenarios have difficulty producing the later X-ray variability, which requires
either an impractical NS magnetic field or an extraordinarily large stellar
envelope and an extremely long accretion timescale. However, the third scenario
seems to be consistent with observations, and the later X-ray variability can
be produced by the magnetosphere which is expelled following the collapse of
the NS with a $B_p\in(3.6, 13.5)\times10^{13}$ G.


  A class of scalar models with non-polynomial interaction, which naturally
admits an analytical resummation of the series of tadpole diagrams is studied
in perturbation theory. In particular, we focus on a model containing only one
renormalizable coupling that appear as a multiplicative coefficient of the
squared field. A renormalization group analysis of the Green functions of the
model shows that these are only approximated solutions of the flow equations,
with errors proportional to powers of the coupling, therefore smaller in the
region of weak coupling. The final output of the perturbative analysis is that
the renormalized model is non-interacting with finite mass and vanishing
vertices or, in an effective theory limited by an ultraviolet cut-off, the
vertices are suppressed by powers of the inverse cut-off. The relation with
some non-polynomial interactions derived long ago, as solutions of the
linearized functional renormalization group flow equations, is also discussed.


  We study theoretically resonant inelastic x-ray scattering (RIXS) at the Cu
$L_3$-edge in a typical parent compound of high-$T_c$ cuprate superconductors
La$_2$CuO$_4$ on the basis of a detailed electronic band structure. We
construct a realistic and precise tight-binding model by employing the
maximally-localized Wannier functions derived from a first-principles
electronic structure calculation, and then take account of the Coulomb
repulsion between d electrons at each Cu site. The antiferromagnetic ground
state is described within the Hartree-Fock approximation, and take account of
electron correlations in the intermediate states of RIXS within the
random-phase approximation (RPA). Calculated RIXS spectra agree well with the
experimentally observed features including low-energy magnon excitation,
$d$-$d$ excitations, and charge-transfer excitations, over a wide
excitation-energy range. In particular, we stress the importance of photon
polarization dependence: the intensity of magnon excitation and the spectral
structure of $d$-$d$ excitations depend significantly not only on the
polarization direction of incident incoming photons but also that of outgoing
photons. It is demonstrated that the single-magnon excitation intensity is
maximized when the polarization directions of incoming and outgoing photons are
perpendicular to each other.


  Purpose: The introduction of Gold NanoParticles (GNPs) in radiotherapy
requires consideration of GNP size, location, and quantity, and more, as well
as beam quality. The work is presented in two parts, with Part I (this work)
investigating accurate and efficient MC modeling to calculate nucleus and
cytoplasm Dose Enhancement Factors (n,cDEFs). Part II then evaluates cell dose
enhancement factors across macroscopic length scales. Methods: Different
methods of modeling gold within cells are compared: a contiguous volume of
either pure gold or gold-tissue mixture or discrete GNPs. MC simulations with
EGSnrc are performed to calculate n,cDEF for a cell considering 10 to 370 keV
incident photons, gold concentrations from 4 to 24~mg of gold per gram, and
three different GNP configurations: GNPs distributed around the surface of the
nucleus or packed into one or four endosomes. Results: n,cDEFs are sensitive to
the model of gold in the cell, with differences of up to 17% observed between
models. Across cell/nucleus radii, source energies, and gold concentrations,
n,cDEF are highest for GNPs in the perinuclear configuration, compared with
GNPs in endosomes. Across all simulations of the default cell, nDEFs and cDEFs
range from one to 6.83 and 3.87, respectively. If the cell size is changed,
much higher n,cDEFs are observed. n,cDEF are maximized at photon energies at or
just above the K- or L-edges of gold. Conclusions: This work demonstrates many
physics trends on DEFs at the cellular level, including that cellular DEFs are
sensitive to gold modeling approach, GNP configuration, cell/nucleus size, gold
concentration, and incident source energy. These data will allow one to
optimize or estimate DEF using not only GNP uptake, but account for incident
photon energy and intracellular configuration of GNPs. Part II will expand the
investigation, applying the cell model in cm-scale phantoms.


  Graphical WYSIWYG editors programming languages are popular since they allow
to control the diagram layout to express intention via secondary notation such
as proximity and topology. However, such editors typically require users to do
manual layout. Conversely, automatic layout of diagrams typically fails to
capture intention because graphs are usually considered to not contain any
order. Model order can combine the desire for control of secondary notation
with automatic layout, without additional overhead, since the textual model
already employs secondary notation. We illustrate how model order can exert
control on the example of programming languages SCCharts and Lingua Franca. We
also propose a first guidebook how such model order configurations can be
extracted for other programming languages with a graphical notation.


  This note establishes the full range of $L^p$--$L^q$ Fourier extension
estimates for the model $n$-dimensional quadratic submanifold in ${\mathbb
R}^{n(n+3)/2}$ parametrized by $\gamma(x_1,\ldots,x_n) := (x_1,\ldots,x_n, (x_i
x_j)_{1 \leq i \leq j \leq n})$. This class of submanifolds is extremal in the
sense that an $n$-dimensional quadratic submanifold of ${\mathbb R}^d$ can only
satisfy nontrivial Fourier extension inequalities when $d \leq
\frac{n(n+3)}{2}$. The proof is via an inflation-type argument, with the
unexpected twist that a significant amount of "overinflation" is necessary but
in no way limits the sharpness of the argument.


  We present an improved study of spectroscopic observables in the $SU(2)$
Yang-Mills theory with two adjoint fermions. We make an improvement on the
precision of previous results which clarify the scale of finite volume effects
present. This analysis adds to the evidence for near-conformal dynamics of this
theory, while indicating a preference for a low anomalous mass dimension of the
massless theory.


  The formation and local symmetry of spin-lattice polaron has been
investigated semiclassically in the planar Holstein t-J-like models within the
exact diagonalization method. Due to the interplay of strong correlations and
electron-lattice interaction, the doped hole may either move freely or lead to
the localized spin-lattice distortion and form a Holstein polaron. The
formation of polaron breaks the translational symmetry by suppression of
antiferromagnetic correlations and inducement of ferromagnetic correlations
locally. Moreover, the breaking of local rotational symmetry around the polaron
has been shown. The ground state is generically a parity singlet and the first
excited state maybe a parity doublet. Further consequences of the density of
states spectra for comparison with future STM experiments are discussed.


  Analytic expressions for the angular distributions of the $b$-quarks
associated with single $t$-quark production in $p \bar p \to W^* \to t \bar b
\to b \bar b W$ and of the leptons from the subsequent decay $W \to l\nu$ are
obtained in the laboratory system. CP violation in the $t$-production vertex is
assumed. Different angular and total cross section CP violating asymmetries are
considered. Relations testing CP violation solely in the $t$-decay vertex are
also obtained. A numerical analysis is performed in the MSSM with a CP
violating phase of the trilinear coupling $A_{\tilde t}$. The asymmetries are
typically of the order $10^{-3}$ - $10^{-4}$.


  Open quantum systems provide an essential theoretical basis for the
development of novel quantum technologies, since any real quantum system
inevitably interacts with its environment. Lindblad master equations capture
the effect of Markovian environments. Closed quantum systems can be treated
using flow equations with the particle conserving generator. We generalize this
generator to non-Hermitian matrices and open quantum systems governed by
Lindbladians, comparing our results with recently proposed generators by Rosso
et al. (arXiv:2007.12044). In comparison, we find that our advocated generator
provides an efficient flow with good accuracy in spite of truncations.


  We present an extension to the Poisson-Boltzmann model where the dipolar
features of solvent molecules are taken explicitly into account. The
formulation is derived at mean-field level and can be extended to any order in
a systematic expansion. It is applied to a two-plate system with oppositely
charged surfaces. The ion distribution and profiles in the dipolar order
parameter are calculated and can result in a large correction to the
inter-plate pressure.


  We implement and benchmark the frozen core approximation, a technique
commonly adopted in electronic structure theory to reduce the computational
cost by means of mathematically fixing the chemically inactive core electron
states. The accuracy and efficiency of this approach are well controlled by a
single parameter, the number of frozen orbitals. Explicit corrections for the
frozen core orbitals and the unfrozen valence orbitals are introduced,
safeguarding against seemingly minor numerical deviations from the assumed
orthonormality conditions of the basis functions. A speedup of over two-fold
can be achieved for the diagonalization step in all-electron density-functional
theory simulations containing heavy elements, without any accuracy degradation
in terms of the electron density, total energy, and atomic forces. This is
demonstrated in a benchmark study covering 103 materials across the periodic
table, and a large-scale simulation of CsPbBr3 with 2,560 atoms. Our study
provides a rigorous benchmark of the precision of the frozen core approximation
(sub-meV per atom for frozen core orbitals below -200 eV) for a wide range of
test cases and for chemical elements ranging from Li to Po. The algorithms
discussed here are implemented in the open-source Electronic Structure
Infrastructure software package.


  This paper discusses the feasibility of experimental control of the flow
direction of atomic Bose-Einstein condensates in a double-well potential using
phase-imprinting. The flow is induced by the application of a time-dependent
potential gradient, providing a clear signature of macroscopic quantum
tunneling in atomic condensates. By studying both initial state preparation and
subsequent tunneling dynamics we find the parameters to optimise the phase
induced Josephson current. We find that the effect is largest for condensates
up to a few thousand atoms, and is only weakly-dependent on trap geometry.


  A systematic treatment of the magnetic fluctuations effect on the properties
of the normal-to-superconducting phase transition in a zero external magnetic
field is given within the self-consistent approximation and the
quasi-macroscopic Ginzburg-Landau model. New results for thin superconducting
films are presented. Thermodynamic quantities having a direct experimental
interest as the order parameter jump, latent heat, and specific heat are
considered and numerically evaluated for bulk Al and thin Al films. The
possibility for an experimental verification of the theoretical predictions is
discussed.


  Multi-quark states were predicted by Gell-Mann when the quark model was first
formulated. Recently, numerous exotic states that are considered to be
multi-quark states have been experimentally confirmed (four-quark mesons and
five-quark baryons). Theoretical research indicates that the four-quark state
might comprise molecular and/or tetraquark structures. We consider that the
meson containing four different flavors $su\bar b\bar d$ should exist and decay
via the $X(5568)\to B_s\pi$ channel. However, except for the D0 collaboration,
all other experimental collaborations have reported negative observations for
$X(5568)$ in this golden portal. This contradiction has stimulated the interest
of both theorists and experimentalists. To address this discrepancy, we propose
that the assumed $X(5568)$ is a mixture of a molecular state and tetraquark,
which contributes destructively to $X(5568)\to B_s\pi$. The cancellation may be
accidental and it should be incomplete. In this scenario, there should be two
physical states with the same flavor ingredients, with spectra of $5344\pm307$
and $6318\pm315$. $X(5568)$ lies in the error range of the first state. We
predict the width of the second state (designated as $S_2$) as
$\Gamma(X_{S_2}\to B_s\pi)=224\pm97$ MeV. We strongly suggest searching for it
in future experiments.


  We give an explicit form of particle-size distributions of convex similar
bodies for random plane and random line, which naturally generalize famous
Wicksell's corpuscle problem. The results are achieved by applying the Method
of Model Solutions for solving well-known Santal\'o's integral equations. We
also give a partial result related to the question of existence and uniqueness
of these solutions. We finally illustrate our approach on several examples.


  This paper is inspired by Wang, Wang and Zhang's work [ Observability and
unique continuation inequalities for the Schr\"odinger equation. J. Eur. Math.
Soc. 21, 3513--3572 (2019)], where they present several observability and
unique continuation inequalities for the free Schr\"{o}dinger equation in
$\mathbb{R}^{n}$. We extend all such observability and unique continuation
inequalities for the Schr\"{o}dinger equations on half-line with inverse-square
potentials. Technically, the proofs essentially rely on the representation of
the solution, a Nazarov type uncertainty principle for the Hankel transform and
an interpolation inequality for functions whose Hankel transform have compact
support.


  Given their location on the Hertzsprung-Russell (HR) diagram, thoroughly
characterized subgiant stars can place stringent constraints on a wide range of
astrophysical problems. Accordingly, they are prime asteroseismic targets for
the Transiting Exoplanet Survey Satellite (TESS) mission. In this work, we
infer stellar properties for a sample of 347 subgiants located in the TESS
Continuous Viewing Zones (CVZs), which we select based on their likelihood of
showing asteroseismic oscillations. We investigate how well they can be
characterized using classical constraints (photometry, astrometry), and
validate our results using spectroscopic values. We derive luminosities,
effective temperatures, and radii with mean 1$\sigma$ random (systematic)
uncertainties of 4.5% (2%), 33 K (60 K), and 2.2% (2%), as well as more
model-dependent quantities such as surface gravities, masses, and ages. We use
our sample to demonstrate that subgiants are ideal targets for mass and age
determination based on HR diagram location alone, discuss the advantages of
stellar parameters derived from a detailed characterization over widely
available catalogs, show that the generally used 3D extinction maps tend to
overestimate the extinction for nearby stars (distance $\lesssim$ 500 pc), and
find a correlation that supports the rotation-activity connection in post main
sequence stars. The complementary roles played by classical and asteroseismic
data sets will open a window to unprecedented astrophysical studies using
subgiant stars.


  Recently, many attempts have been made to construct a transformer base
U-shaped architecture, and new methods have been proposed that outperformed
CNN-based rivals. However, serious problems such as blockiness and cropped
edges in predicted masks remain because of transformers' patch partitioning
operations. In this work, we propose a new U-shaped architecture for medical
image segmentation with the help of the newly introduced focal modulation
mechanism. The proposed architecture has asymmetric depths for the encoder and
decoder. Due to the ability of the focal module to aggregate local and global
features, our model could simultaneously benefit the wide receptive field of
transformers and local viewing of CNNs. This helps the proposed method balance
the local and global feature usage to outperform one of the most powerful
transformer-based U-shaped models called Swin-UNet. We achieved a 1.68% higher
DICE score and a 0.89 better HD metric on the Synapse dataset. Also, with
extremely limited data, we had a 4.25% higher DICE score on the NeoPolyp
dataset. Our implementations are available at:
https://github.com/givkashi/Focal-UNet


  Microparticles including paraffin are currently used for textiles coating in
order to deaden thermal shocks. We will show that polymer nanoparticles
embedded in those microsized capsules allow for decreasing the thermal
conductivity of the coating and enhance the protection in the stationary
regime. A reasonable volume fraction of polymer nanoparticles reduces the
conductivity more than predicted by Maxwell mixing rules. Besides, measurements
prove that the polymer nanoparticles do not affect the latent heat and even
improve the phase change behaviour as well as the mechanical properties.


  This paper is an effort to evaluate the numerical indices for the assessment
of the frequency response analysis (FRA) to provide a deeper understanding of
their characteristics. The study introduces the indices in the literature and
categorizes them into two groups. The results of an actual FRA experimental
setup on an electrical machine are employed to examine the indices from the
various aspects. The main features of the indices are extracted, and the better
ones in various aspects are marked. Moreover, based on the observations from
the experimental studies, a new numerical index for comparing FRA results is
proposed in this paper to enhance FRA results assessment and interpretation in
both electrical machines and transformers. The advantages of the proposed index
are also shown by comparing it with the existing ones.


  The immunity of Ising superconductors to external magnetic fields originates
from a spin locking of the paired electrons to an intrinsic Zeeman-like field.
The spin-momentum locking in non-centrosymmetric crystalline materials leads to
type-I Ising pairing in which the direction of the intrinsic field can be
deduced from the spin expectation values. Conversely, in centrosymmetric
crystals the electron spins locked to the orbitals can form Ising type-II pairs
consisting of spin-orbit split doublets. Due to time-reversal symmetry, the
doublets are spin degenerate, making it difficult to read the spin polarization
of bands and the direction of spin-orbit fields. Here we present an efficient
approach to determine the direction of the intrinsic field using the
spin-mixing parameter $b^2$. Using first principles calculations based on the
density functional theory, we study monolayer transition metal dichalcogenide
superconductors PdTe$_2$, NbTe$_2$, and TiSe$_2$ with the 1T structure. We
calculate $b^2$ for individual Fermi pockets and provide a general picture of
possible Ising type-II pairing within the full Brillouin zone. In order to
complement our first principles results, we use group theory to provide a
detailed picture of spin-orbit coupling and spin mixing in the relevant bands
forming Fermi pockets. We demonstrate that contrary to the anticipated effects
of spin-orbit locking, not every spin-orbit split spin doublet actively
participates in Ising pairing. Finally, by connecting the spin-mixing parameter
$b^2$ with the intrinsic out-of-plane Zeeman field we estimate the upper
in-plane critical magnetic field.


  We scrutinize the diagrammatic perturbation theory of noninteracting
electrons in a random potential with the aim to accomplish a consistent
comprehensive theory of quantum diffusion. Ward identity between the
one-electron self-energy and the two-particle irreducible vertex is generally
not guaranteed in the perturbation theory with only elastic scatterings. We
show how the Ward identity can be established in practical approximations and
how the functions from the perturbation expansion should be used to obtain a
fully consistent conserving theory. We derive the low-energy asymptotics of the
conserving full two-particle vertex from which we find an exact representation
of the diffusion pole and of the static diffusion constant in terms of Green
functions of the perturbation expansion. We illustrate the construction on the
leading vertex corrections to the mean-field diffusion due to maximally-crossed
diagrams responsible for weak localization.


  Effects of low-temperature chemistry induced by ultrafine water droplet
evaporation on reaction front development from an ignition spot with
temperature gradient are studied in this work. The Eulerian-Eulerian method is
used to simulate the gas-liquid two-phase reactive flows and the physical model
is one-dimensional spherical reactor with stoichiometric gaseous n-heptane/air
mixture and ultrafine monodisperse water droplets (initial diameter 5
micrometres). Homogeneous ignitions of two-phase mixtures are first simulated.
The water droplets can complete evaporation in the reactor prior to ignition,
and hence pronouncedly reduce gas temperature, which may induce the
low-chemistry reactions. It is found that the turnover temperature for negative
temperature coefficient range increases with droplet volume fraction.
Three-stage ignitions are present when the volume fraction is beyond a critical
value, i.e., low-temperature, intermediate-temperature, and high-temperature
ignitions. The chemical explosive mode analysis also confirms the low-chemistry
reactions induced by the evaporation of ultrafine water droplets. Then reaction
front development from an ignition spot with temperature gradient in two-phase
mixtures is analysed based on one-dimensional simulations. Different modes for
reaction front origin in the spot are identified, based on the initial gas
temperature and lower turnover temperature. Specifically, the reaction front
can be initiated at the left and right ends of the ignition spot, and inside
it. Detailed reaction front developments corresponding to the above three modes
are discussed. Besides, the pressure wave from high-temperature ignition is
important, compared to those from low- and intermediate-chemistries.


  More and more off-the-shelf drones provide frameworks that enable the
programming of flight paths. These frameworks provide vendor-dependent
programming and communication interfaces that are intended for flight path
definitions. However, they are often limited to outdoor and GPS-based use only.
A key disadvantage of such a solution is that they are complicated to use and
require readjustments when changing the drone model. This is time-consuming
since it requires redefining the flight path for the new framework. This
workshop paper proposes additional features for DronOS, a community-driven
framework that enables model-independent automatisation and programming of
drones. We enhanced DronOS to include additional functions to account for the
specific design constraints in human-drone-interaction. This paper provides a
starting point for discussing the requirements involved in designing a drone
system with other researchers within the human-drone interaction community. We
envision DronOS as a community-driven framework that can be applied to generic
drone models, hence enabling the automatisation for any commercially available
drone. Our goal is to build DronOS as a software tool that can be easily used
by researchers and practitioners to prototype novel drone-based systems.


  We develop a fully non-parametric, easy-to-use, and powerful test for the
missing completely at random (MCAR) assumption on the missingness mechanism of
a dataset. The test compares distributions of different missing patterns on
random projections in the variable space of the data. The distributional
differences are measured with the Kullback-Leibler Divergence, using
probability Random Forests. We thus refer to it as "Projected Kullback-Leibler
MCAR" (PKLM) test. The use of random projections makes it applicable even if
very few or no fully observed observations are available or if the number of
dimensions is large. An efficient permutation approach guarantees the level for
any finite sample size, resolving a major shortcoming of most other available
tests. Moreover, the test can be used on both discrete and continuous data. We
show empirically on a range of simulated data distributions and real datasets
that our test has consistently high power and is able to avoid inflated type-I
errors. Finally, we provide an R-package PKLMtest with an implementation of our
test.


  Einstein-Podolsky-Rosen (EPR) steering allows two parties to verify their
entanglement, even if one party's measurements are untrusted. This concept has
not only provided new insights into the nature of non-local spatial
correlations in quantum mechanics, but also serves as a resource for one-sided
device-independent quantum information tasks. Here, we investigate how EPR
steering behaves when one-half of a maximally-entangled pair of qudits
(multidimensional quantum systems) is cloned by a universal cloning machine. We
find that EPR steering, as verified by a criterion based on the mutual
information between qudits, can only be found in one of the copy subsystems but
not both. We prove that this is also true for the single-system analogue of EPR
steering. We find that this restriction, which we term "no-cloning of quantum
steering", elucidates the physical reason why steering can be used to secure
sources and channels against cloning-based attacks when implementing quantum
communication and quantum computation protocols.


  Minimizing traffic accidents between vehicles and pedestrians is one of the
primary research goals in intelligent transportation systems. To achieve the
goal, pedestrian orientation recognition and prediction of pedestrian's
crossing or not-crossing intention play a central role. Contemporary approaches
do not guarantee satisfactory performance due to limited field-of-view, lack of
generalization, and high computational complexity. To overcome these
limitations, we propose a real-time predictive pedestrian collision warning
service (P2CWS) for two tasks: pedestrian orientation recognition (100.53 FPS)
and intention prediction (35.76 FPS). Our framework obtains satisfying
generalization over multiple sites because of the proposed site-independent
features. At the center of the feature extraction lies 3D pose estimation. The
3D pose analysis enables robust and accurate recognition of pedestrian
orientations and prediction of intentions over multiple sites. The proposed
vision framework realizes 89.3% accuracy in the behavior recognition task on
the TUD dataset without any training process and 91.28% accuracy in intention
prediction on our dataset achieving new state-of-the-art performance. To
contribute to the corresponding research community, we make our source codes
public which are available at https://github.com/Uehwan/VisionForPedestrian


  The Shortest Path Reconfiguration problem has as input a graph G (with unit
edge lengths) with vertices s and t, and two shortest st-paths P and Q. The
question is whether there exists a sequence of shortest st-paths that starts
with P and ends with Q, such that subsequent paths differ in only one vertex.
This is called a rerouting sequence.
  This problem is shown to be PSPACE-complete. For claw-free graphs and chordal
graphs, it is shown that the problem can be solved in polynomial time, and that
shortest rerouting sequences have linear length. For these classes, it is also
shown that deciding whether a rerouting sequence exists between all pairs of
shortest st-paths can be done in polynomial time. Finally, a polynomial time
algorithm for counting the number of isolated paths is given.


  We investigate the emission of electromagnetic waves from biaxial
subwavelength metamaterials. For tunable anisotropic structures that exhibit a
vanishing dielectric response along a given axis, we find remarkable variation
in the launch angles of energy associated with the emission of leaky wave
radiation. We write closed form expressions for the energy transport velocity
and corresponding radiation angle $\phi$, defining the cone of radiation
emission, both as a functions of frequency, and material and geometrical
parameters. Full wave simulations exemplify the broad range of directivity that
can be achieved in these structures.


  Particle number fluctuations, no matter how small, are present in
experimental set-ups. One should rigorously take these fluctuations into
account, especially, for entanglement detection. In this context, we generalize
the spin squeezing inequalities introduced by T\'oth et al. in Phys. Rev. Lett.
99, 250405 (2007). These new inequalities are fulfilled by all separable states
even when the number of particle is not constant, and may present quantum
fluctuations. These inequalities are useful for detecting entanglement in
many-body systems when the super-selection rule does not apply, or when only a
subspace of the total systems Hilbert space is considered. We also define
general dichotomic observables for which we obtain a coordinate independent
form of the generalized spin squeezing inequalities. We give an example where
our generalized coordinate independent spin squeezing inequalities present a
clear advantage over the original ones.


  We develop unbiased implicit variational inference (UIVI), a method that
expands the applicability of variational inference by defining an expressive
variational family. UIVI considers an implicit variational distribution
obtained in a hierarchical manner using a simple reparameterizable distribution
whose variational parameters are defined by arbitrarily flexible deep neural
networks. Unlike previous works, UIVI directly optimizes the evidence lower
bound (ELBO) rather than an approximation to the ELBO. We demonstrate UIVI on
several models, including Bayesian multinomial logistic regression and
variational autoencoders, and show that UIVI achieves both tighter ELBO and
better predictive performance than existing approaches at a similar
computational cost.


  In this paper we present the results of a mid infrared study of G49.5-0.4, or
W51A, part of the massive starbirth complex W51. Combining public data from the
$Spitzer$ IRAC camera, and Gemini mid infrared camera T-ReCS at 7.73, 9.69,
12.33 and 24.56 \micron, with spatial resolution of $\sim$0.5\arcsec, we have
identified the mid infrared counterparts of 8 ultracompact HII regions, showing
that two radio sources are deeply embedded in molecular clouds and another is a
cloud of ionized gas. From the T-ReCS data we have unveiled the central core of
W51 region, revealing massive young stellar candidates. We modeled the spectral
energy distribution of the detected sources suggesting the embedded objects are
sources with spectral types ranging from B3 to O5, but the majority of the fits
indicate stellar objects with B1 spectral types. We also present an extinction
map of IRS~2, showing that a region with lower extinction corresponds to the
region where a proposed jet of gas has impacted the foreground cloud. From this
map, we also derived the total extinction towards the enigmatic source IRS~2E,
which amounts to $\sim$60 magnitudes in the $V$ band. We calculated the color
temperature due to thermal emission of the circumstellar dust of the detected
sources; the temperatures are in the interval of $\sim$100 -- 150 K, which
corresponds to the emission of dust located at 0.1 pc from the central source.
Finally, we show a possible mid infrared counterpart of a detected source at mm
wavelengths that was found by \cite{zap08,zap09} to be a massive young stellar
object undergoing a high accretion rate.


  We establish Manin's conjecture for a cubic surface split over Q and whose
singularity type is 2A_2+A_1. For this, we make use of a deep result about the
equidistribution of the values of a certain restricted divisor function in
three variables in arithmetic progressions. This result is due to Friedlander
and Iwaniec (and was later improved by Heath-Brown) and draws on the work of
Deligne.


  Light-matter interactions can be dramatically modified by the surrounding
environment. Here we report on the first experimental observation of molecular
spontaneous emission inside a highly nonlocal metamaterial based on a plasmonic
nanorod assembly. We show that the emission process is dominated not only by
the topology of its local effective medium dispersion, but also by the nonlocal
response of the composite, so that metamaterials with different geometric
parameters but the same local effective medium properties exhibit different
Purcell factors. A record-high enhancement of a decay rate is observed, in
agreement with the developed quantitative description of the Purcell effect in
a nonlocal medium. An engineered material nonlocality introduces an additional
degree of freedom into quantum electrodynamics, enabling new applications in
quantum information processing, photo-chemistry, imaging, and sensing.


  In this article, we are concerned with the Langlands functoriality
conjecture. Cogdell, Kim, Piatetski-Shapiro and Shahidi proved functioriality
conjecture in the case of a globally generic cuspidal automorphic
representation for the split classical groups, unitary groups or even
quasi-split special orthogonal groups in characteristic zero. Lomel\'i extends
this result to split classical groups and unitary groups in positive
characteristic. Thus, in this article we prove the Langlands functoriality
conjecture for the even quasi-split non-split special orthogonal groups in
positive characteristic i.e. we lift globally generic cuspidal automorphic
representations of quasi-split non-split even special orthogonal groups to
generic automorphic representations of suitable general linear groups in
positive characteristic. As an application of this result, we prove the
compatibility of the local gamma factors and the unramified Ramanujan
conjecture.


  We study the different quantum phases that occur in massive ${\cal N}=2$
supersymmetric QCD with gauge groups $SU(2)$ and $SU(3)$ as the coupling
$\Lambda/M$ is gradually increased from 0 to infinity. The phases can be
identified by computing the exact partition function by saddle-points,
combining supersymmetric localization and the Seiberg-Witten formalism. In all
cases, we find two phases, a weak coupling and a strong coupling phase,
separated by a critical point described by a superconformal field theory or
involving superconformal sectors. In crossing the critical point, the dominant
saddle-point hops from one singularity of the curve to another one. The
theories seem to undergo a second-order phase transition with divergent
susceptibility.


  The absence of an exhaustive bibliography of novels published in the British
Isles and Ireland during the 19th century blocks several lines of research in
sociologically-inclined literary history and book history. Without a detailed
account of novelistic production, it is difficult to characterize, for example,
the population of individuals who pursued careers as novelists. This paper
contributes to efforts to develop such an account by estimating yearly rates of
new novel publication in the British Isles and Ireland between 1789 and 1919.
This period witnessed, in aggregate, the publication of between 40,000 and
63,000 previously unpublished novels. The number of new novels published each
year counts as essential information for researchers interested in
understanding the development of the text industry between 1789 and 1919.


  Parametric estimation for diffusion processes is considered for high
frequency observations over a fixed time interval. The processes solve
stochastic differential equations with an unknown parameter in the diffusion
coefficient. We find easily verified conditions on approximate martingale
estimating functions under which estimators are consistent, rate optimal, and
efficient under high frequency (in-fill) asymptotics. The asymptotic
distributions of the estimators are shown to be normal variance-mixtures, where
the mixing distribution generally depends on the full sample path of the
diffusion process over the observation time interval. Utilising the concept of
stable convergence, we also obtain the more easily applicable result that for a
suitable data dependent normalisation, the estimators converge in distribution
to a standard normal distribution. The theory is illustrated by a simulation
study comparing an efficient and a non-efficient estimating function for an
ergodic and a non-ergodic model.


  In this paper, we consider (random) sampling of signals concentrated on a
bounded Corkscrew domain $\Omega$ of a metric measure space, and reconstructing
concentrated signals approximately from their (un)corrupted sampling data taken
on a sampling set contained in $\Omega$. We establish a weighted stability of
bi-Lipschitz type for a (random) sampling scheme on the set of concentrated
signals in a reproducing kernel space. The weighted stability of bi-Lipschitz
type provides a weak robustness to the sampling scheme, however due to the
nonconvexity of the set of concentrated signals, it does not imply the unique
signal reconstruction. From (un)corrupted samples taken on a finite sampling
set contained in $\Omega$, we propose an algorithm to find approximations to
signals concentrated on a bounded Corkscrew domain $\Omega$. Random sampling is
a sampling scheme where sampling positions are randomly taken according to a
probability distribution. Next we show that, with high probability, signals
concentrated on a bounded Corkscrew domain $\Omega$ can be reconstructed
approximately from their uncorrupted (or randomly corrupted) samples taken at
i.i.d. random positions drawn on $\Omega$, provided that the sampling size is
at least of the order $\mu(\Omega) \ln (\mu(\Omega))$, where $\mu(\Omega)$ is
the measure of the concentrated domain $\Omega$. Finally, we demonstrate the
performance of proposed approximations to the original concentrated signal when
the sampling procedure is taken either with small density or randomly with
large size.


  In this paper, we can obtain curvature estimates for spacelike admissible
graphic hypersurfaces in the $(n+1)$-dimensional Lorentz-Minkowski space
$\mathbb{R}^{n+1}_{1}$, and through which the existence of spacelike admissible
graphic hypersurfaces, with prescribed $2$-th Weingarten curvature and
Dirichlet boundary data, defined over a strictly convex domain in the
hyperbolic plane $\mathscr{H}^{n}(1)\subset\mathbb{R}^{n+1}_{1}$ of center at
origin and radius $1$, can be proven.


  The geometry-dependent ionization behavior of the ammonia molecule is
investigated. Different theoretical approaches for obtaining the ionization
yield are compared, all of them showing a strong dependence of the ionization
yield on the inversion coordinate at long wavelengths ($\geq$ 800 nm). It is
shown how this effect can be exploited to create and probe nuclear wave packets
in neutral ammonia using Lochfra{\ss}. Furthermore, imaging of a wave packet
tunneling through the barrier of a double-well potential in real time is
discussed.


  We study a dark matter model with one singlet complex scalar and two Higgs
doublets. The scalar potential respects a softly broken global symmetry, which
makes the imaginary part of the singlet become a pseudo-Nambu-Goldstone boson
acting as a dark matter candidate. The pseudo-Nambu-Goldstone nature of the
boson leads to the vanishing of its tree-level scattering amplitude off
nucleons at zero momentum transfer. Therefore, although the interaction
strength could be sufficiently large to yield a viable relic abundance via
thermal mechanism, direct detection is incapable of probing this candidate. We
further investigate the constraints from Higgs measurements, relic abundance
observation, and indirect detection.


  The asymmetric distribution of chiral objects with opposite chirality is of
great fundamental interests ranging from molecular biology to particle physics.
In quantum materials, chiral states can build on inversion-symmetry-breaking
lattice structures or emerge from spontaneous magnetic ordering induced by
competing interactions. Although the handedness of a chiral state can be
changed through external fields, a spontaneous chirality flipping has yet to be
discovered. In this letter, we present experimental evidence of chirality
flipping via changing temperature in a topological magnet EuAl$_4$, which
features orthogonal spin and charge density waves (SDW/CDW). Using circular
dichroism of Bragg peaks in the resonant magnetic x-ray scattering, we find
that the chirality of the helical SDW flips through a first order phase
transition with modified SDW wavelength. Intriguingly, we observe that the CDW
couples strongly with the SDW and displays a rare
commensurate-to-incommensurate transition at the chirality flipping
temperature. Combining with first principles calculations and angle resolved
photoemission spectroscopy, we establish the Fermi surface origin of the
helical SDW with intertwined spin, charge, and lattice degrees of freedom in
EuAl$_4$. Our results reveal an unprecedented spontaneous chirality flipping
and lays the groundwork for a new functional manipulation of chirality through
momentum dependent spin-charge-lattice interactions.


  The theory of resonant Auger decay of atoms in a high intensity coherent
X-ray pulse is presented. The theory includes the coupling between the ground
state and the resonance due to an intense X-ray pulse, taking into account the
decay of the resonance and the direct photoionization of the ground state, both
populating the final ionic states coherently. The theory also considers the
impact of the direct photoionization of the resonance state itself which
typically populates highly-excited ionic states. The combined action of the
resonant decay and of the direct ionization of the ground state in the field
induces a non-hermitian time-dependent coupling between the ground and the
'dressed' resonance stats. The impact of these competing processes on the total
electron yield and on the 2s$^2$2p$^{4}(^1\mathrm{D})$3p $^2$P spectator and
2s$^1$2p$^{6}$ $^2$S participator Auger decay spectra of the Ne 1s$\to$3p
resonance is investigated. The role of the direct photoionization of the ground
state and of the resonance increases dramatically with the field intensity.
This results in strong interference effects with distinct patterns in the
electron spectra, different for the participator and spectator final states.


  We report here on multi-frequency VLBA observations of three extragalactic
sources within 1 degree of the Galactic Center. These sources have been used as
astrometric reference sources for VLA and VLBA determinations of the proper
motion of Sagittarius A*, the compact nonthermal radio source in the Galactic
Center. Each source has a main component with a brightness temperature in
excess of 10^{7.5} K, confirming that the sources are active galactic nuclei.
The sources have simple structure that can be characterized by one or two
Gaussian components. The frequency dependence of the structure indicates that
the positions of Sgr A* determined by the VLA astrometry of Backer & Sramek
(1999) at 4.8 and 8.4 GHz should have an offset of \sim 2 mas. This offset is
in the same direction as the 5 mas shift measured by Backer & Sramek (1999).
The structure is unlikely to bias the 43 GHz VLBA results of Reid et al (1999).
Motions of components in the calibrator sources could lead to errors in the
proper motion of Sgr A* on the order of a few km s^{-1}.
  All three sources show frequency dependent structure consistent with
scattering which is significantly stronger than that of the Galactic scattering
model of Taylor & Cordes (1993) but significantly weaker than that of the
hyperstrong Galactic Center scattering. Combined with other observations, this
suggests the existence of a new component of Galactic scattering located
several kpc from the Galactic Center.


  Many systems of physical and biological interest are characterized by
assemblies of phase oscillators whose interaction is mediated by a diffusing
chemical. The coupling effect results from the fact that the local
concentration of the mediating chemical affects both its production and
absorption by each oscillator. Since the chemical diffuses through the medium
in which the oscillators are embedded, the coupling among oscillators is
non-local: it considers all the oscillators depending on their relative spatial
distances. We considered a mathematical model for this coupling, when the
diffusion time is arbitrary with respect to the characteristic oscillator
periods, yielding a system of coupled nonlinear integro-differential equations
which can be solved using Green functions for appropriate boundary conditions.
In this paper we show numerical solutions of these equations for three finite
domains: a linear one-dimensional interval, a rectangular, and a circular
region, with absorbing boundary conditions. From the numerical solutions we
investigate phase and frequency synchronization of the oscillators, with
respect to changes in the coupling parameters for the three considered
geometries.


  We investigate the asymptotic behavior of solutions to a class of weighted
quasilinear elliptic equations which arise from the Euler--Lagrange equation
associated with the Caffarelli--Kohn--Nirenberg inequality. We obtain sharp
pointwise estimates which extend and improve previous results obtained in the
unweighted case. In particular, we show that we can refine the asymptotic
expansion at infinity by using a Kelvin-type transformation, which reduces the
problem to another elliptic-type problem near the origin. The application of
this transformation is straightforward in the linear case but more delicate in
the quasilinear case. In particular, it is necessary in this case to establish
some preliminary estimates before being able to apply the transformation.


  Superconducting qubits are one of the most mature platforms for quantum
computing, but significant performance improvements are still needed. To
improve the engineering of these systems, 3D full-wave computational
electromagnetics analyses are increasingly being used. Unfortunately, existing
analysis approaches often rely on full-wave simulations using eigenmode solvers
that are typically cumbersome, not robust, and computationally prohibitive if
devices with more than a few qubits are to be analyzed. To improve the
characterization of superconducting circuits while circumventing these
drawbacks, this work begins the development of an alternative framework that we
illustrate in the context of evaluating the qubit-qubit exchange coupling rate
between transmon qubits. This is a key design parameter that determines the
entanglement rate for fast multi-qubit gate performance and also affects
decoherence sources like qubit crosstalk. Our modeling framework uses a
field-based formalism in the context of macroscopic quantum electrodynamics,
which we use to show that the qubit-qubit exchange coupling rate can be related
to the electromagnetic dyadic Green's function linking the qubits together. We
further show how the quantity involving the dyadic Green's function can be
related to the impedance response of the system that can be efficiently
computed with classical computational electromagnetics tools. We demonstrate
the validity and efficacy of this approach by simulating four practical
multi-qubit superconducting circuits and evaluating their qubit-qubit exchange
coupling rates. We validate our results against a 3D numerical diagonalization
method and against experimental data where available. We also demonstrate the
impact of the qubit-qubit exchange coupling rate on qubit crosstalk by
simulating a multi-coupler device and identifying operating points where the
qubit crosstalk becomes zero.


  Spin-orbit interaction established itself as a major role player for emergent
phenomena in modern condensed matter including a topological insulator, spin
liquid and spin-dependent transports. However, its function is rather limited
to adding topological nature to each phases of matter. We prove by our spinor
line graph theory that a very strong spin-orbit interaction realized in 5d
pyrochlore electronic systems generates multiply degenerate perfect flat bands.
Unlike any of the previous flat bands, the electrons living there localize in
real space by destructively interfering with each other in a spin selective
manner ruled by the SU(2) gauge field. These electrons avoid the Coulomb
interaction by self-organizing their localized wave functions. This gives rise
to the trimerized charge ordering hand in hand with a stiff spin chirality,
which may explain the recently found exotic low-temperature insulating phase of
CsW2O6.


  A new multispectral Geostationary Operational Environmental Satellite (GOES)
imager product has been developed to assess downburst potential over the
western United States employing brightness temperature differences (BTD)
between band 3 (upper level water vapor), band 4 (longwave infrared window),
and split window band 5. Band 3 is intended to indicate mid to upper-level
moisture content and advection while band 5 indicates low-level moisture
content. Large BTDs between bands 3 and 5 imply a large relative humidity
gradient between the mid-troposphere and the surface, a condition favorable for
strong convective downdraft generation due to evaporational cooling of
precipitation in the deep sub-cloud layer. In addition, small BTDs between
bands 4 and 5 indicate a relatively dry surface layer with solar heating in
progress. This paper will outline the development of the GOES-West imager
microburst product and present case studies that feature example images,
outline potential operational use and assess performance of the algorithm.


  A new Italian edition of the Letters of Gerbert, the astronomer, scientist
and philosopher who become pope Silvester II, with their papal privileges has
been published in the occasion of the international year of astronomy. The
italian translation (1980) of Maria Giulia Panvini Carciotto (1949-1996), has
been co-edited by Costantino Sigismondi and Paolo Rossi. The volume, according
to the will of the relatives of Dr. Panvini Carciotto is available either in
press and as free e-book on the web indexed with the words "Gerberto
Episolario".


  We present a Fermionic Cellular Automaton model which describes massless
Dirac fermion in 1+1 dimension coupled with local, number preserving
interaction. The diagonalization of the two particle sector shows that specific
values of the total momentum and of the coupling constant allows for the
formation of bound states. Furthermore, we present a classification of the
local number-preserving interactions that are invariant under the isotropy
group of the cellular automaton which simulates the Weyl equation.


  As we begin to reach the limits of classical computing, quantum computing has
emerged as a technology that has captured the imagination of the scientific
world. While for many years, the ability to execute quantum algorithms was only
a theoretical possibility, recent advances in hardware mean that quantum
computing devices now exist that can carry out quantum computation on a limited
scale. Thus it is now a real possibility, and of central importance at this
time, to assess the potential impact of quantum computers on real problems of
interest. One of the earliest and most compelling applications for quantum
computers is Feynman's idea of simulating quantum systems with many degrees of
freedom. Such systems are found across chemistry, physics, and materials
science. The particular way in which quantum computing extends classical
computing means that one cannot expect arbitrary simulations to be sped up by a
quantum computer, thus one must carefully identify areas where quantum
advantage may be achieved. In this review, we briefly describe central problems
in chemistry and materials science, in areas of electronic structure, quantum
statistical mechanics, and quantum dynamics, that are of potential interest for
solution on a quantum computer. We then take a detailed snapshot of current
progress in quantum algorithms for ground-state, dynamics, and thermal state
simulation, and analyze their strengths and weaknesses for future developments.


  If $\mathcal{H}$ denotes a Hilbert space of analytic functions on a region
$\Omega \subseteq \mathbb{C}^d$, then the weak product is defined by
$$\mathcal{H}\odot\mathcal{H}=\left\{h=\sum_{n=1}^\infty f_n g_n :
\sum_{n=1}^\infty \|f_n\|_{\mathcal{H}}\|g_n\|_{\mathcal{H}} <\infty\right\}.$$
We prove that if $\mathcal{H}$ is a first order holomorphic Besov Hilbert space
on the unit ball of $\mathbb{C}^d$, then the multiplier algebras of
$\mathcal{H}$ and of $\mathcal{H}\odot\mathcal{H}$ coincide.


  Alon and F\"{u}redi (1993) showed that the number of hyperplanes required to
cover $\{0,1\}^n\setminus \{0\}$ without covering $0$ is $n$. We initiate the
study of such exact hyperplane covers of the hypercube for other subsets of the
hypercube. In particular, we provide exact solutions for covering $\{0,1\}^n$
while missing up to four points and give asymptotic bounds in the general case.
Several interesting questions are left open.


  In this paper, geometric characterizations of conformally flat and radially
flat hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times
\mathbb{R}$ are given by means of their extrinsic geometry. Under suitable
conditions on the shape operator, we classify conformally flat hypersurfaces in
terms of rotation hypersurfaces. In addition, a close relation between radially
flat hypersurfaces and semi-parallel hypersurfaces is established. These
results lead to geometric descriptions of hypersurfaces with special intrinsic
structures, such as Einstein metrics, Ricci solitons and hypersurfaces with
constant scalar curvature.


  Dark Matter (DM) comprising particles in the mass range of a few MeV to GeV
is waiting to be explored, given the many theoretical models accommodating
cosmological abundance. We hereby propose an experiment with the LHC proton
beam of 7 TeV striking onto the beam dump target, emitting neutrinos and
possibly, Dark Matter candidates. This experiment would also permit to observe
signatures involving elastic and inelastic processes involving DM candidates,
electrons and strongly interacting particles present in nuclei of the dump
target. There will be residual neutrino background present in each of these
signatures, hence the proposed experimental detector sub-systems would be such
that they would involve as final states, elastically or inelasticity scattered,
standard model particles. The bump or the excess in the tail of the kinematic
distributions will eventually give us glimpse of presence of new particles
which could possibly be Dark Matter candidates. Given the parameters of the LHC
machine, the sensitivity of such an experiment is unique in the energy region
it is supposed to exploit.


  This study proposes a tractable stochastic choice model to identify
motivations for prosocial behavior, and to explore alternative motivations of
deliberate randomization beyond ex-ante fairness concerns. To represent social
preferences, we employ an additively perturbed utility model consisting of the
sum of expected utility and a nonlinear cost function, where the utility
function is purely selfish while the cost function depends on social
preferences. Using the cost function, we study stochastic choice patterns to
distinguish between stochastic inequity-averse behavior and stochastic
shame-mitigating behavior. Moreover, we discuss how our model can complement
recent experimental evidence of ex-post and ex-ante fairness concerns.