  We present a unified approach to characterising fast-reaction limits of
systems of either two reaction-diffusion equations, or one reaction-diffusion
equation and one ordinary differential equation, on unbounded domains,
motivated by models of fast chemical reactions where either one or both
reactant(s) is/are mobile. For appropriate initial data, solutions of four
classes of problems each converge in the fast-reaction limit $k \to \infty$ to
a self-similar limit profile that has one of four forms, depending on how many
components diffuse and whether the spatial domain is a half or whole line. For
fixed $k$, long-time convergence to these same self-similar profiles is also
established, thanks to a scaling argument of Kamin. Our results generalise
earlier work of Hilhorst, van der Hout and Peletier to a much wider class of
problems, and provide a quantitative description of the penetration of one
substance into another in both the fast-reaction and long-time regimes.


  The thermodynamic formalism for dynamical systems with many degrees of
freedom is extended to deal with time averages and fluctuations of some
macroscopic quantity along typical orbits, and applied to coupled map lattices
exhibiting phase transitions. Thereby, it turns out that a seed of phase
transition is embedded as an anomalous distribution of unstable periodic
orbits, which appears as a so-called q-phase transition in the spatio-temporal
configuration space. This intimate relation between phase transitions and
q-phase transitions leads to one natural way of defining transitions and their
order in extended chaotic systems. Furthermore, a basis is obtained on which we
can treat locally introduced control parameters as macroscopic ``temperature''
in some cases involved with phase transitions.


  In Class-Incremental Learning (CIL) an image classification system is exposed
to new classes in each learning session and must be updated incrementally.
Methods approaching this problem have updated both the classification head and
the feature extractor body at each session of CIL. In this work, we develop a
baseline method, First Session Adaptation (FSA), that sheds light on the
efficacy of existing CIL approaches and allows us to assess the relative
performance contributions from head and body adaption. FSA adapts a pre-trained
neural network body only on the first learning session and fixes it thereafter;
a head based on linear discriminant analysis (LDA), is then placed on top of
the adapted body, allowing exact updates through CIL. FSA is replay-free
i.e.~it does not memorize examples from previous sessions of continual
learning. To empirically motivate FSA, we first consider a diverse selection of
22 image-classification datasets, evaluating different heads and body
adaptation techniques in high/low-shot offline settings. We find that the LDA
head performs well and supports CIL out-of-the-box. We also find that
Featurewise Layer Modulation (FiLM) adapters are highly effective in the
few-shot setting, and full-body adaption in the high-shot setting. Second, we
empirically investigate various CIL settings including high-shot CIL and
few-shot CIL, including settings that have previously been used in the
literature. We show that FSA significantly improves over the state-of-the-art
in 15 of the 16 settings considered. FSA with FiLM adapters is especially
performant in the few-shot setting. These results indicate that current
approaches to continuous body adaptation are not working as expected. Finally,
we propose a measure that can be applied to a set of unlabelled inputs which is
predictive of the benefits of body adaptation.


  Measuring the imprint of primordial gravitational waves in the cosmic
microwave background (CMB) polarisation field is one of the main goals in
modern cosmology. However, the so called $B$-mode polarisation can be generated
by different sources besides the primary one predicted by inflationary
theories, known as secondary $B$-mode signal. Among them, CMB lensing and
astrophysical foregrounds play an important role. Moreover, a partial sky
analysis leads to a leakage between $E$-modes and $B$-modes. In this article,
we use the well known Minkowski functionals (MF) statistics to study the
significance of this leakage in the CMB lensing $B$-mode signal. We find that
the MF can detect the $E$-to-$B$ leakage contamination, thus it should not be
neglected in future CMB data analysis.


  We shall give a new Schr\"odinger type uncertainty relation for a quantity
representing a quantum uncertainty, introduced by S.Luo in \cite{Luo1}. Our
result improves the Heisenberg uncertainty relation shown in \cite{Luo1} for a
mixed state.


  The property of the optimal signal ensembles of entanglement assisted channel
capacity is studied. A relationship between entanglement assisted channel
capacity and one-shot capacity of unassisted channel is obtained. The data
processing inequalities, convexity and additivity of the entanglement assisted
channel capacity are reformulated by simple methods.


  An elementary general overview of the neutrino physics and astrophysics is
given. We start by a historical account of the development of our understanding
of neutrinos and how they helped to unravel the structure of the Standard
Model. We discuss why it is so important to establish if neutrinos are massive
and we introduce the main scenarios to provide them a mass. The present bounds
and the positive indications in favor of non-zero neutrino masses are discussed
as well as the major role they play in astrophysics and cosmology.


  Cryptic crosswords, the dominant crossword variety in the UK, are a promising
target for advancing NLP systems that seek to process semantically complex,
highly compositional language. Cryptic clues read like fluent natural language
but are adversarially composed of two parts: a definition and a wordplay cipher
requiring character-level manipulations. Expert humans use creative
intelligence to solve cryptics, flexibly combining linguistic, world, and
domain knowledge. In this paper, we make two main contributions. First, we
present a dataset of cryptic clues as a challenging new benchmark for NLP
systems that seek to process compositional language in more creative,
human-like ways. After showing that three non-neural approaches and T5, a
state-of-the-art neural language model, do not achieve good performance, we
make our second main contribution: a novel curriculum approach, in which the
model is first fine-tuned on related tasks such as unscrambling words.We also
introduce a challenging data split, examine the meta-linguistic capabilities of
subword-tokenized models, and investigate model systematicity by perturbing the
wordplay part of clues, showing that T5 exhibits behavior partially consistent
with human solving strategies. Although our curricular approach considerably
improves on the T5 baseline, our best-performing model still fails to
generalize to the extent that humans can. Thus, cryptic crosswords remain an
unsolved challenge for NLP systems and a potential source of future innovation.


  We apply the technique of localization for vertex algebras to the
Segal-Sugawara construction of an ``internal'' action of the Virasoro algebra
on affine Kac-Moody algebras. The result is a lifting of twisted differential
operators from the moduli of curves to the moduli of curves with bundles, with
arbitrary decorations and complex twistings. This construction gives a uniform
approach to a collection of phenomena describing the geometry of the moduli
spaces of bundles over varying curves: the KZB equations and heat kernels on
non-abelian theta functions, their critical level limit giving the quadratic
parts of the Beilinson-Drinfeld quantization of the Hitchin system, and their
infinite level limit giving a Hamiltonian description of the isomonodromy
equations.


  Smith and Van den Bergh introduced the notion of finite F-representation type
as a characteristic $p$ analogue of the notion of finite representation type.
In this paper, we prove two finiteness properties of rings with finite
F-representation type. The first property states that if $R=\bigoplus_{n \ge
0}R_n$ is a Noetherian graded ring with finite (graded) F-representation type,
then for every non-zerodivisor $x \in R$, $R_x$ is generated by $1/x$ as a
$D_{R}$-module. The second one states that if $R$ is a Gorenstein ring with
finite F-representation type, then $H_I^n(R)$ has only finitely many associated
primes for any ideal $I$ of $R$ and any integer $n$. We also include a result
on the discreteness of F-jumping exponents of ideals of rings with finite
(graded) F-representation type as an appendix.


  We discuss intrinsic noise effects in stochastic multiplicative-noise partial
differential equations, which are qualitatively independent of the noise
interpretation (Ito vs. Stratonovich), in particular in the context of
noise-induced ordering phase transitions. We study a model which, contrary to
all cases known so far, exhibits such ordering transitions when the noise is
interpreted not only according to Stratonovich, but also to Ito. The main
feature of this model is the absence of a linear instability at the transition
point. The dynamical properties of the resulting noise-induced growth processes
are studied and compared in the two interpretations and with a reference
Ginzburg-Landau type model. A detailed discussion of new numerical algorithms
used in both interpretations is also presented.


  Optical near-field interactions between nanostructured matter, such as
quantum dots, result in unidirectional optical excitation transfer when energy
dissipation is induced. This results in versatile spatiotemporal dynamics of
the optical excitation, which can be controlled by engineering the dissipation
processes and exploited to realize intelligent capabilities such as solution
searching and decision making. Here we experimentally demonstrate the ability
to solve a decision making problem on the basis of optical excitation transfer
via near-field interactions by using colloidal quantum dots of different sizes,
formed on a geometry-controlled substrate. We characterize the energy transfer
behavior due to multiple control light patterns and experimentally demonstrate
the ability to solve the multi-armed bandit problem. Our work makes a decisive
step towards the practical design of nanophotonic systems capable of efficient
decision making, one of the most important intellectual attributes of the human
brain.


  This paper is motivated by the reconstruction problem on the sparse
stochastic block model. Mossel, et. al. proved that a reconstruction algorithm
that recovers an optimal fraction of the communities in the symmetric,
2-community case. The main contribution of their proof is to show that when the
signal to noise ratio is sufficiently large, in particular $\lambda^2d > C$,
the reconstruction accuracy for a broadcast process on a tree with or without
noise on the leaves is asymptotically the same. This paper will generalize
their results, including the main step, to a general class of the sparse
stochastic block model with any number of communities that are not necessarily
symmetric, proving that an algorithm closely related to Belief Propagation
recovers an optimal fraction of community labels.


  Methods for modelling the electrical conductivity of dense plasmas and liquid
metals, based upon the well-known Ziman formula, are reviewed from a general
perspective, and some earlier inconsistencies relating to its application to
finite temperature systems are resolved. A general formula for the conductivity
of a Lorentzian two-component plasma in thermal equilibrium is derived from the
Lenard-Balescu collision integral in which both energy and momentum exchange
between ions and electrons are accounted for. This formula is used as a basis
for some generalizations of the Ziman formula, which apply to plasmas of
arbitrary degeneracy over a much wider range of conditions. These formulae
implicitly include the collective motions of the ions, but neglect the
collective motions of the electrons. Detailed consideration of the latter shows
that they generally have a small effect on the conductivity. Conditions for the
validity of the Ziman formula are derived. The extension of the general theory
to arbitrarily low temperatures, where the ion dynamics become dominated by
collective effects, in which dynamical ion correlations need to be taken into
account, is shown to lead to the well-known Bloch formula. Consideration is
given to non-Lorentzian plasmas by explicitly accounting for electron-electron
collisions. Corrections to the Lorentzian model in the form of a power series
in 1/Z are derived.


  Brain functional connectivity (FC) extracted from resting-state fMRI
(RS-fMRI) has become a popular approach for disease diagnosis, where
discriminating subjects with mild cognitive impairment (MCI) from normal
controls (NC) is still one of the most challenging problems. Dynamic functional
connectivity (dFC), consisting of time-varying spatiotemporal dynamics, may
characterize "chronnectome" diagnostic information for improving MCI
classification. However, most of the current dFC studies are based on detecting
discrete major brain status via spatial clustering, which ignores rich
spatiotemporal dynamics contained in such chronnectome. We propose Deep
Chronnectome Learning for exhaustively mining the comprehensive information,
especially the hidden higher-level features, i.e., the dFC time series that may
add critical diagnostic power for MCI classification. To this end, we devise a
new Fully-connected Bidirectional Long Short-Term Memory Network (Full-BiLSTM)
to effectively learn the periodic brain status changes using both past and
future information for each brief time segment and then fuse them to form the
final output. We have applied our method to a rigorously built large-scale
multi-site database (i.e., with 164 data from NCs and 330 from MCIs, which can
be further augmented by 25 folds). Our method outperforms other
state-of-the-art approaches with an accuracy of 73.6% under solid
cross-validations. We also made extensive comparisons among multiple variants
of LSTM models. The results suggest high feasibility of our method with
promising value also for other brain disorder diagnoses.


  Thoracic aortic aneurysm (TAA) is a fatal disease which potentially leads to
dissection or rupture through progressive enlargement of the aorta. It is
usually asymptomatic and screening recommendation are limited. The
gold-standard evaluation is performed by computed tomography angiography (CTA)
and radiologists time-consuming assessment. Scans for other indications could
help on this screening, however if acquired without contrast enhancement or
with low dose protocol, it can make the clinical evaluation difficult, besides
increasing the scans quantity for the radiologists. In this study, it was
selected 587 unique CT scans including control and TAA patients, acquired with
low and standard dose protocols, with or without contrast enhancement. A novel
segmentation model, DeepVox, exhibited dice score coefficients of 0.932 and
0.897 for development and test sets, respectively, with faster training speed
in comparison to models reported in the literature. The novel TAA
classification model, SAVE-CT, presented accuracies of 0.930 and 0.922 for
development and test sets, respectively, using only the binary segmentation
mask from DeepVox as input, without hand-engineered features. These two models
together are a potential approach for TAA screening, as they can handle
variable number of slices as input, handling thoracic and thoracoabdominal
sequences, in a fully automated contrast- and dose-independent evaluation. This
may assist to decrease TAA mortality and prioritize the evaluation queue of
patients for radiologists.


  Many Stated Preference studies conducted in developing countries provide a
low willingness to pay (WTP) for a wide range of goods and services. However,
recent studies in these countries indicate that this may partly be a result of
the choice of payment vehicle, not the preference for the good. Thus, low WTP
may not indicate a low welfare effect for public projects in developing
countries. We argue that in a setting where 1) there is imperfect
substitutability between money and other measures of wealth (e.g. labor), and
2) institutions are perceived to be corrupt, including payment vehicles that
are currently available to the individual and less pron to corruption may be
needed to obtain valid welfare estimates. Otherwise, we risk underestimating
the welfare benefit of projects. We demonstrate this through a rural household
contingent valuation (CV) survey designed to elicit the value of access to
reliable irrigation water in Ethiopia. Of the total average annual WTP for
access to reliable irrigation service, cash contribution comprises only 24.41
%. The implication is that socially desirable projects might be rejected based
on cost-benefit analysis as a result of welfare gain underestimation due to
mismatch of payment vehicles choice in valuation study.


  In this paper,we develop a local-to-global and measure-theoretical approach
to understand datasets. The idea is to take network models with restricted
domains as local charts of datasets. We develop the mathematical foundations
for these structures, and show in experiments how it can be used to find fuzzy
domains and to improve accuracy in data classification problems.


  In this article, we investigate the convergence rate of the discrete-time
Clark--Ocone formula provided by Akahori--Amaba--Okuma [1]. In that paper, they
mainly focus on the $L_{2}$-convergence rate of the first-order error estimate
related to the tracking error of the delta hedge in mathematical finance. Here,
as two extensions, we estimate "the higher order error" for Wiener functionals
with an integrability index $2$ and "an arbitrary differentiability index."


  Stable derivators provide an enhancement of triangulated categories as is
indicated by the existence of canonical triangulations. In this paper we show
that exact morphisms of stable derivators induce exact functors of canonical
triangulations, and similarly for arbitrary natural transformations. This
2-categorical refinement also provides a uniqueness statement concerning
canonical triangulations.
  These results rely on a more careful study of morphisms of derivators and
this study is of independent interest. We analyze the interaction of morphisms
of derivators with limits, colimits, and Kan extensions, including a discussion
of invariance and closure properties of the class of Kan extensions preserved
by a fixed morphism.


  This paper considers endogenous selection models, in particular nonparametric
ones. Estimating the unconditional law of the outcomes is possible when one
uses instrumental variables. Using a selection equation which is additively
separable in a one dimensional unobservable has the sometimes undesirable
property of instrument monotonicity. We present models which allow for
nonmonotonicity and are based on nonparametric random coefficients indices. We
discuss their nonparametric identification and apply these results to inference
on nonlinear statistics such as the Gini index in surveys when the nonresponse
is not missing at random.


  This paper is devoted to reconcile the tension between theoretic expectation
from naturalness and the present LHC limits on superpartner mass bounds. We
argue that in SUSY models of direct gauge mediation the focusing phenomenon
appears, which dramatically reduces the fine tuning associated to 126 GeV Higgs
boson. This type of model is highly predictive in mass spectrum, with multi-TeV
third generation, $A_t$ term of order 1 TeV, gluino mass above LHC mass bound,
and light neutralinos and charginos beneath 1 TeV.


  For a completely regular space $X$ and a non-vanishing self-adjoint closed
subalgebra $H$ of $C_B(X)$ which separates points from closed sets in $X$ we
construct the Gelfand spectrum $\mathfrak{sp}(H)$ of $H$ as an open subspace of
the compactification of $X$ generated by $H$. The simple construction of
$\mathfrak{sp}(H)$ enables easier examination of its properties. We illustrate
this by an example showing that the space $\mathfrak{sp}(H)$ is separable
metrizable if and only if $H$ is countably generated.


  We address the question of the appearence of ordinary quantum mechanics in
the context of noncommutative quantum mechanics. We obtain the noncommutative
extension of the Hu-Paz-Zhang master equation for a Brownian particle linearly
coupled to a bath of harmonic oscillators. We consider the particular case of
an Ohmic regime.


  We present the results of five years (2005-2009) of MAGIC observations of the
BL Lac object PG 1553+113 at very high energies (VHEs, E > 100 GeV). Power law
fits of the individual years are compatible with a steady mean photon index
\Gamma = 4.27 $\pm$ 0.14. In the last three years of data, the flux level above
150 GeV shows a clear variability (probability of constant flux < 0.001%). The
flux variations are modest, lying in the range from 4% to 11% of the Crab
Nebula flux. Simultaneous optical data also show only modest variability that
seems to be correlated with VHE gamma ray variability. We also performed a
temporal analysis of (all available) simultaneous Fermi/LAT data of PG 1553+113
above 1 GeV, which reveals hints of variability in the 2008-2009 sample.
Finally, we present a combination of the mean spectrum measured at very high
energies with archival data available for other wavelengths. The mean spectral
energy distribution can be modeled with a one-zone Synchrotron Self Compton
(SSC) model, which gives the main physical parameters governing the VHE
emission in the blazar jet.


  Let K be a field of positive characteristic p and KG the group algebra of a
group G. It is known that, if KG is Lie nilpotent, then its upper (or lower)
Lie nilpotency index is at most |G'|+1, where |G'| is the order of the
commutator subgroup. Previously we determined the groups G for which the
upper/lower nilpotency index is maximal or the upper nilpotency index is
`almost maximal' (that is, of the next highest possible value, namely |G'|-p
+2). Here we determine the groups for which the lower nilpotency index is
`almost maximal'.


  In this paper we have developed a two dimensional (2D) analytical model for
surface potential and drain current for a long channel Dual Material Gate (DMG)
Silicon-on-Insulator (SOI) Tunneling Field Effect Transistor (TFET). This model
includes the effect of drain voltage, gate metal work function, oxide thickness
and silicon film thickness, without assuming a fully depleted channel. The
proposed model also includes the effect of charge accumulation at the interface
of the two gates and the variation in the tunneling volume with the applied
gate voltage. The accuracy of the model is tested using two-dimensional
numerical simulations. In comparison to the conventional TFET, the proposed
model predicts that a DMGTFET provides a higher ON-state current (ION), a
better ON-state to OFF-state current (ION/IOFF) ratio and a better
sub-threshold slope (SS).


  Nonlocally coupled oscillators with a phase lag self-organize into various
patterns such as global synchronization, the twisted state, and the chimera
state. In this paper, we consider nonlocally coupled oscillators that move on a
ring by randomly exchanging their positions with the neighbors, and investigate
the combined effects of phase lag and mobility on the collective phase
dynamics. Spanning the whole range of phase lag and mobility, we show that
mobility promotes synchronization for an attractive coupling, while it destroys
coherence for a repulsive coupling. The transition behaviors are discussed in
terms of the timescales of synchronization and diffusion of the oscillators. We
also find a novel spatiotemporal pattern at the border between coherent and
incoherent states.


  A mixture of two types of super-paramagnetic colloidal particles with long
range dipolar interaction is confined by gravity to a flat interface of a
hanging water droplet. The particles are observed by video microscopy and the
dipolar interaction strength is controlled via an external magnetic field. The
system is a model system to study the glass transition in 2D, and it exhibits
partial clustering of the small particles. This clustering is strongly
dependent on the relative concentration $\xi$ of big and small particles.
However, changing the interaction strength $\Gamma$ reveals that the clustering
does not depend on the interaction strength. The partial clustering scenario is
quantified using Minkowski functionals and partial structure factors. Evidence
that partial clustering prevents global crystallization is discussed.


  In this paper we prove the connectedness of symplectic ball packings in the
complement of a spherical Lagrangian, S^2 or RP^2, in symplectic manifolds that
are rational or ruled. Via a symplectic cutting construction this is a natural
extension of McDuff's connectedness of ball packings in other settings and this
result has applications to several different questions: smooth knotting and
unknottedness results for spherical Lagrangians, the transitivity of the action
of the symplectic Torelli group, classifying Lagrangian isotopy classes in the
presence of knotting, and detecting Floer-theoretically essential Lagrangian
tori in the del Pezzo surfaces.


  A novel polarized reflectarray is designed, fabricated, and experimentally
characterized to show its flexibility and efficiency to control wave generation
and focusing of orbital angular momentum (OAM) vortices with desirable OAM
modes in the microwave frequency regime. In order to rigorously study the
generation and focusing of OAM, a versatile analytical theory is proposed to
theoretically study the compensation phase of reflectarray. Two prototypes of
microwave reflectarrays are fabricated and experimentally characterized at 12
GHz, one for generation and one for focusing of OAM-carrying beams. Compared
with the OAM-generating reflectarray, the reflectarray for focusing OAM vortex
can significantly reduce the beam diameter, and this can further improve the
transmission efficiency of the OAM vortex beams. We also show that the
numerical and experimental results agree very well. The proposed design method
and reflectarrays may spur the development of new efficient approaches to
generate and focus OAM vortex waves for applications to microwave wireless
communications.


  Motivated by distributed statistical learning over uncertain communication
networks, we study distributed stochastic optimization by networked nodes to
cooperatively minimize a sum of convex cost functions. The network is modeled
by a sequence of time-varying random digraphs with each node representing a
local optimizer and each edge representing a communication link. We consider
the distributed subgradient optimization algorithm with noisy measurements of
local cost functions' subgradients, additive and multiplicative noises among
information exchanging between each pair of nodes. By stochastic Lyapunov
method, convex analysis, algebraic graph theory and martingale convergence
theory, we prove that if the local subgradient functions grow linearly and the
sequence of digraphs is conditionally balanced and uniformly conditionally
jointly connected, then proper algorithm step sizes can be designed so that all
nodes' states converge to the global optimal solution almost surely.


  We report a systematic study on Edelstein magnetoresistance (Edelstein MR) in
Co25Fe75/Cu/Bi2O3 heterostructures with a strong spin-orbit interaction at the
Cu/Bi2O3 interface. We succeed in observing a significant dependence of the
Edelstein MR on both Cu layer thickness and temperature, and also develop a
general analytical model considering distinct bulk and interface contributions
on spin relaxation. Our analysis, based on the above model, quantitatively
illustrates a unique property of the spin transport near the Rashba interface,
revealing a prominent role of the spin relaxation process by determining the
ratios of the spin relaxation inside and outside the interface. We further find
the characteristic spin transport is unaffected by temperature. Our results
provide an essential tool for exploring the transport in a system with
spin-momentum-locked two-dimensional states.


  The rapid expansion of large foundation models within the pre-training and
fine-tuning framework has underscored that larger models often yield better
results. However, the scaling up of large foundation models has led to soaring
costs in fine-tuning and parameter storage, rendering extensive adaptations
impractical. This challenge has sparked the development of parameter-efficient
fine-tuning (PEFT), which focuses on optimizing a select subset of parameters
while keeping the rest fixed, significantly lowering computational and storage
overheads. While recent years have witnessed a significant success in PEFT, a
deep understanding of the fundamental principles behind these methods remains
unexplored. To this end, here we take the first step to unify all approaches by
dissecting them from a decomposition perspective. We initiate a comprehensive
mathematical analysis of these methods, allowing us to delve deeply into their
underlying mechanisms, and we explore the reasons behind the variations in
performance among different techniques. Furthermore, inspired by our
theoretical analysis, we introduce two novel PEFT methods alongside a simple
yet effective framework designed to enhance the performance of PEFT techniques
across various applications. Our empirical validations, conducted across
multiple datasets, demonstrate the efficacy of these methods, showcasing both
theoretical validity and practical performance improvements under the guidance
of our analytical findings. We believe our work will deepen researchers'
understanding of PEFT and other techniques, prompting further contemplation and
advancing the research across the whole community.


  We calculate the topological boundary modes found for quantum wire for a
quantum ring. For the symmetric ring we find analytical solutions for two
quasi-particles identifiable as the Majorana states and for asymmetric ring, we
have also find approximate solution. By turning on a small field at time zero,
we find a field induced oscillation of the Majorana states that was initially
localized. The range of validity of our solution, the relation between the
period of oscillation and the coin parameter and field strength, and the
encoding of a message of the on/off of the field using the Majorana states are
discussed. Our results suggest ways to reduce decoherence for small systems,
thereby providing a good candidate for quantum memory and computing as the
Majorana qubit is topologically protected.


  An explicit and computable error estimator for the $hp$ version of the
virtual element method (VEM), together with lower and upper bounds with respect
to the exact energy error, is presented. Such error estimator is employed to
provide $hp$ adaptive mesh refinements for very general polygonal meshes. In
addition, a novel VEM $hp$ Cl\'ement quasi-interpolant, instrumental for the a
posteriori error analysis, is introduced. The performances of the adaptive
method are validated by a number of numerical experiments.


  The recent observation of quantum oscillations in underdoped high-Tc
superconductors, combined with their negative Hall coefficient at low
temperature, reveals that the Fermi surface of hole-doped cuprates includes a
small electron pocket. This strongly suggests that the large hole Fermi surface
characteristic of the overdoped regime undergoes a reconstruction caused by the
onset of some order which breaks translational symmetry. Here we consider the
possibility that this order is "stripe" order, a form of charge / spin
modulation observed most clearly in materials like Eu-doped and Nd-doped LSCO.
In these materials, the onset of stripe order is indeed the cause of
Fermi-surface reconstruction. We identify the critical doping where this
reconstruction occurs and show that the temperature dependence of transport
coefficients at that doping is typical of metals at a quantum critical point.
We discuss how the pseudogap phase may be a fluctuating precursor of the
stripe-ordered phase.


  This paper is proposing some physics problems from a book, De Motu Gravium
Naturaliter Descendentium, written by Evangelista Torricelli, with the aim of
showing how physics was taught in a university, that of Pisa, in the 17th
century.


  We explore the asymptotic behavior of the centroids of random polygons
constructed from regular polygons with vertices on the unit circle by extending
the rays so that their lengths form a random permutation of the first (n)
integers. Surprisingly, this question has connections to diverse mathematical
contexts, including random matrix theory and discrete Fourier transforms.
Through rigorous analysis, we establish that the sequence of the suitably
rescaled centroids converges to a circularly-symmetric complex normal
distribution with variance (\frac{1}{12}). This result is a manifestation of
central limit behavior in a setting involving sums of heavily dependent random
variables.


  Previous methods on estimating detailed human depth often require supervised
training with `ground truth' depth data. This paper presents a self-supervised
method that can be trained on YouTube videos without known depth, which makes
training data collection simple and improves the generalization of the learned
network. The self-supervised learning is achieved by minimizing a
photo-consistency loss, which is evaluated between a video frame and its
neighboring frames warped according to the estimated depth and the 3D non-rigid
motion of the human body. To solve this non-rigid motion, we first estimate a
rough SMPL model at each video frame and compute the non-rigid body motion
accordingly, which enables self-supervised learning on estimating the shape
details. Experiments demonstrate that our method enjoys better generalization
and performs much better on data in the wild.


  Extracting point correspondences from two or more views of a scene is a
fundamental computer vision problem with particular importance for relative
camera pose estimation and structure-from-motion. Existing local feature
matching approaches, trained with correspondence supervision on large-scale
datasets, obtain highly-accurate matches on the test sets. However, they do not
generalise well to new datasets with different characteristics to those they
were trained on, unlike classic feature extractors. Instead, they require
finetuning, which assumes that ground-truth correspondences or ground-truth
camera poses and 3D structure are available. We relax this assumption by
removing the requirement of 3D structure, e.g., depth maps or point clouds, and
only require camera pose information, which can be obtained from odometry. We
do so by replacing correspondence losses with epipolar losses, which encourage
putative matches to lie on the associated epipolar line. While weaker than
correspondence supervision, we observe that this cue is sufficient for
finetuning existing models on new data. We then further relax the assumption of
known camera poses by using pose estimates in a novel bootstrapping approach.
We evaluate on highly challenging datasets, including an indoor drone dataset
and an outdoor smartphone camera dataset, and obtain state-of-the-art results
without strong supervision.


  In recent years, the fusion of high spatial resolution multispectral image
(HR-MSI) and low spatial resolution hyperspectral image (LR-HSI) has been
recognized as an effective method for HSI super-resolution (HSI-SR). However,
both HSI and MSI may be acquired under extreme conditions such as night or
poorly illuminating scenarios, which may cause different exposure levels,
thereby seriously downgrading the yielded HSISR. In contrast to most existing
methods based on respective low-light enhancements (LLIE) of MSI and HSI
followed by their fusion, a deep Unfolding HSI Super-Resolution with Automatic
Exposure Correction (UHSR-AEC) is proposed, that can effectively generate a
high-quality fused HSI-SR (in texture and features) even under very imbalanced
exposures, thanks to the correlation between LLIE and HSI-SR taken into
account. Extensive experiments are provided to demonstrate the state-of-the-art
overall performance of the proposed UHSR-AEC, including comparison with some
benchmark peer methods.


  Using high-resolution numerical simulations, we investigate mass- and
luminosity-normalized specific frequencies (T_N and S_N, respectively) of
globular cluster systems (GCSs) in order to understand the origin of the
observed U-shaped relation between S_N and V-band magnitude (M_V) of their host
galaxies.
  We adopt a biased GC formation scenario in which GC formation is truncated in
galaxy halos that are virialized at a later redshift, z_trun. T_N is derived
for galaxies with GCs today and converted into S_N for reasonable galaxy
mass-to-light-ratios (M/L). We find that T_N depends on halo mass (M_h) in the
sense that T_N can be larger in more massive halos with M_h > 10^9 M_sun, if
z_trun is as high as 15. We however find that the dependence is too weak to
explain the observed S_N-M_V relation and the wide range of S_N in low-mass
early-type galaxies with -20.5 < M_V < -16.0 mag for a reasonable constant M/L.
The M_V-dependence of S_N for the low-mass galaxies can be well reproduced, if
the mass-to-light-ratio M_h/L_V \propto M_h^{\alpha}, where \alpha is as steep
as -1. Based on these results, we propose that the origin of the observed
U-shaped S_N-M_V relation of GCSs can be understood in terms of the bimodality
in the dependence of M_h/L_V on M_h of their host galaxies. We also suggest
that the observed large dispersionin S_N in low-mass galaxies is due partly to
the large dispersion in T_N.


  When an infectious disease strikes a population, the number of newly reported
cases is often the only available information that one can obtain during early
stages of the outbreak. An important goal of early outbreak analysis is to
obtain a reliable estimate for the basic reproduction number, $R_{0}$, from the
limited information available. We present a novel method that enables us to
make a reliable real-time estimate of the reproduction number at a much earlier
stage compared to other available methods. Our method takes into account the
possibility that a disease has a wide distribution of infectious period and
that the degree distribution of the contact network is heterogeneous. We
validate our analytical framework with numerical simulations.


  Analogies have had and continue to have an important role in the development
of theoretical physics. They may start from similarities of physical concepts
followed by similarities in the mathematical formalization or it may be a
purely mathematical aspect to suggest the development of analogous physical
concepts. More often a subtle non obvious interplay between these levels is
involved. In this paper I will discuss two cases sufficiently intricate to
illustrate some ways of how analogies work. The first topic is the introduction
of spontaneous symmetry breaking in particle physics. The second one is the use
of the renormalization group in the theory of critical phenomena and its
statistical interpretation.


  A simple and efficient quantum non-demolition measurement (QND) scheme is
proposed in which the arrival of a signal photon is detected without affecting
the qubit state. The proposed QND scheme functions even if the ancillary photon
is replaced with weak light composed of vacuum and one-photon states. Although
the detection scheme is designed for entanglement sharing applications, it is
also suitable for general purification of a single photon state.


  Visual-Inertial odometry (VIO) is known to suffer from drifting especially
over long-term runs. In this paper, we present GVINS, a non-linear optimization
based system that tightly fuses GNSS raw measurements with visual and inertial
information for real-time and drift-free state estimation. Our system aims to
provide accurate global 6-DoF estimation under complex indoor-outdoor
environment where GNSS signals may be intermittent or even totally unavailable.
To connect global measurements with local states, a coarse-to-fine
initialization procedure is proposed to efficiently calibrate the
transformation online and initialize GNSS states from only a short window of
measurements. The GNSS code pseudorange and Doppler shift measurements, along
with visual and inertial information, are then modelled and used to constrain
the system states in a factor graph framework. For complex and GNSS-unfriendly
areas, the degenerate cases are discussed and carefully handled to ensure
robustness. Thanks to the tightly-coupled multi-sensor approach and system
design, our system fully exploits the merits of three types of sensors and is
capable to seamlessly cope with the transition between indoor and outdoor
environments, where satellites are lost and reacquired. We extensively evaluate
the proposed system by both simulation and real-world experiments, and the
result demonstrates that our system substantially eliminates the drift of VIO
and preserves the local accuracy in spite of noisy GNSS measurements. The
challenging indoor-outdoor and urban driving experiments verify the
availability and robustness of GVINS in complex environments. In addition,
experiments also show that our system can gain from even a single satellite
while conventional GNSS algorithms need four at least.


  Although high-resistivity, low-loss silicon is an excellent material for THz
transmission optics, its high refractive index necessitates antireflection
treatment. We fabricated a wide-bandwidth, two-layer antireflection treatment
by cutting subwavelength structures into the silicon surface using multi-depth
deep reactive ion etching (DRIE). A wafer with this treatment on both sides has
<-20 dB (<1%) reflectance over 190-310 GHz. We also demonstrated that bonding
wafers introduces no reflection features above the -20 dB level, reproducing
previous work. Together these developments immediately enable construction of
wide-bandwidth silicon vacuum windows and represent two important steps toward
gradient-index silicon optics with integral broadband antireflection treatment.


  The origin of interband electron pairing responsible for enhancing
superconductivity and the factors controlling its strength were examined. We
show that the interband electron pairing is a natural consequence of breaking
down the Born-Oppenheimer approximation during the electron-phonon
interactions. Its strength is determined by the pair-state excitations around
the Fermi surfaces that take place to form a superconducting state. Fermi
surfaces favorable for the pairing were found and its implications were
discussed.


  Generalization beyond the training distribution is a core challenge in
machine learning. The common practice of mixing and shuffling examples when
training neural networks may not be optimal in this regard. We show that
partitioning the data into well-chosen, non-i.i.d. subsets treated as multiple
training environments can guide the learning of models with better
out-of-distribution generalization. We describe a training procedure to capture
the patterns that are stable across environments while discarding spurious
ones. The method makes a step beyond correlation-based learning: the choice of
the partitioning allows injecting information about the task that cannot be
otherwise recovered from the joint distribution of the training data. We
demonstrate multiple use cases with the task of visual question answering,
which is notorious for dataset biases. We obtain significant improvements on
VQA-CP, using environments built from prior knowledge, existing meta data, or
unsupervised clustering. We also get improvements on GQA using annotations of
"equivalent questions", and on multi-dataset training (VQA v2 / Visual Genome)
by treating them as distinct environments.


  The instantaneous contributions to the 3PN gravitational wave luminosity from
the inspiral phase of a binary system of compact objects moving in a quasi
elliptical orbit is computed using the multipolar post-Minkowskian wave
generation formalism. The necessary inputs for this calculation include the 3PN
accurate mass quadrupole moment for general orbits and the mass octupole and
current quadrupole moments at 2PN. Using the recently obtained 3PN
quasi-Keplerian representation of elliptical orbits the flux is averaged over
the binary's orbit. Supplementing this by the important hereditary
contributions arising from tails, tails-of-tails and tails squared terms
calculated in a previous paper, the complete 3PN energy flux is obtained. The
final result presented in this paper would be needed for the construction of
ready-to-use templates for binaries moving on non-circular orbits, a plausible
class of sources not only for the space based detectors like LISA but also for
the ground based ones.


  We perform parametric tests of the consistency of the standard $w$CDM model
in the framework of general relativity by carefully separating information
between the geometry and growth of structure. We replace each late-universe
parameter that describes the behavior of dark energy with two parameters: one
describing geometrical information in cosmological probes, and the other
controlling the growth of structure. We use data from all principal
cosmological probes: of these, Type Ia supernovae, baryon acoustic
oscillations, and the peak locations in the cosmic microwave background angular
power spectrum constrain the geometry, while the redshift space distortions,
weak gravitational lensing and the abundance of galaxy clusters constrain both
geometry and growth. Both geometry and growth separately favor the $\Lambda$CDM
cosmology with the matter density relative to critical $\Omega_M\simeq 0.3$.
When the equation of state is allowed to vary separately for probes of growth
and geometry, we find again a good agreement with the $\Lambda$CDM value
($w\simeq -1$), with the major exception of redshift-space distortions which
favor less growth than in $\Lambda$CDM at 3-$\sigma$ confidence, favoring the
equation of state $w^{\rm grow}\simeq -0.8$. The anomalous growth favored by
redshift space distortions has been noted earlier, and is common to all
redshift space distortion data sets, but may well be caused by systematics, or
be explained by the sum of the neutrino masses higher than that expected from
the simplest mass hierarchies, $m_\nu \simeq 0.45$ eV. On the whole, the
constraints are tight even in the new, larger parameter space due to impressive
complementarity of different cosmological probes.


  We describe the E-infinity algebra structure on the complex of singular
cochains of a topological space, in the context of sheaf theory. As a first
application, for any algebraic variety we define a weight filtration compatible
with its E-infinity structure. This naturally extends the theory of mixed Hodge
structures in rational homotopy to p-adic homotopy theory. The spectral
sequence associated to the weight filtration gives a new family of
multiplicative algebraic invariants of the varieties for any coefficient ring,
carrying Steenrod operations. As a second application, we promote Deligne's
intersection complex computing intersection cohomology, to a sheaf carrying
E-infinity structures. This allows for a natural interpretation of the Steenrod
operations defined on the intersection cohomology of any topological
pseudomanifold.


  We recently introduced a method to approximate functions of Hermitian Matrix
Product Operators or Tensor Trains that are of the form $\mathsf{Tr} f(A)$.
Functions of this type occur in several applications, most notably in quantum
physics. In this work we aim at extending the theoretical understanding of our
method by showing several properties of our algorithm that can be used to
detect and correct errors in its results. Most importantly, we show that there
exists a more computationally efficient version of our algorithm for certain
inputs. To illustrate the usefulness of our finding, we prove that several
classes of spin Hamiltonians in quantum physics fall into this input category.
We finally support our findings with numerical results obtained for an example
from quantum physics.


  We found the analytical solution to the problem of the skin effect for
Maxwell plasma with the use of the kinetic equation, where the frequency of
electron collisions is constant. We use the specular reflection of electrons
from the surface as a boundary condition. The behavior of an impedance near to
a plasma resonance is considered. We consider limiting cases of skin effect.


  We classify super-symmetric solutions of the minimal $N=2$ gauged Euclidean
supergravity in four dimensions. The solutions with anti-self-dual Maxwell
field give rise to anti-self-dual Einstein metrics given in terms of solutions
to the $SU(\infty)$ Toda equation and more general three-dimensional
Einstein--Weyl structures. Euclidean Kastor--Traschen metrics are also
characterised by the existence of a certain super covariantly constant spinor.


  We study arithmetic inequalities for multiplicative,
sub(super)-multiplicative, sub(super)-homogeneous functions. Applications for
the classical arithmetic functions are pointed out.


  The task of table structure recognition aims to recognize the internal
structure of a table, which is a key step to make machines understand tables.
Currently, there are lots of studies on this task for different file formats
such as ASCII text and HTML. It also attracts lots of attention to recognize
the table structures in PDF files. However, it is hard for the existing methods
to accurately recognize the structure of complicated tables in PDF files. The
complicated tables contain spanning cells which occupy at least two columns or
rows. To address the issue, we propose a novel graph neural network for
recognizing the table structure in PDF files, named GraphTSR. Specifically, it
takes table cells as input, and then recognizes the table structures by
predicting relations among cells. Moreover, to evaluate the task better, we
construct a large-scale table structure recognition dataset from scientific
papers, named SciTSR, which contains 15,000 tables from PDF files and their
corresponding structure labels. Extensive experiments demonstrate that our
proposed model is highly effective for complicated tables and outperforms
state-of-the-art baselines over a benchmark dataset and our new constructed
dataset.


  Artificial intelligence (AI), particularly machine learning and deep learning
models, has significantly impacted bioinformatics research by offering powerful
tools for analyzing complex biological data. However, the lack of
interpretability and transparency of these models presents challenges in
leveraging these models for deeper biological insights and for generating
testable hypotheses. Explainable AI (XAI) has emerged as a promising solution
to enhance the transparency and interpretability of AI models in
bioinformatics. This review provides a comprehensive analysis of various XAI
techniques and their applications across various bioinformatics domains
including DNA, RNA, and protein sequence analysis, structural analysis, gene
expression and genome analysis, and bioimaging analysis. We introduce the most
pertinent machine learning and XAI methods, then discuss their diverse
applications and address the current limitations of available XAI tools. By
offering insights into XAI's potential and challenges, this review aims to
facilitate its practical implementation in bioinformatics research and help
researchers navigate the landscape of XAI tools.


  Let the matrix operator $L = D\partial_{xx} + q(x)A_0$, with $D = diag(1,
\nu)$, $\nu \neq 1$, $q \in L^{\infty} (0, $\pi$)$, and $A_0$ is a Jordan block
of order 1. We analyze the boundary null controllability for system $y_t - Ly =
0$. When $ \nu \notin \mathbb{Q} ^*_+ $ and $q(x) = 1$, $x $\in$ (0, $\pi$)$,
there exists a family of root vectors of $(L * , D(L *)) $ forming a Riesz
basis, moreover, F. Ammar Khodja, A.Benabdallah, M.Gonzalez-Burgos, L.Teresa,
show the existence of a minimal time of control depending on condensation of
eigenvalues of $(L^* , D(L^*))$. But there exists $q \in L^{\infty} (0, $\pi$)$
such that the family of eigenfunctions of $(L^* , D(L^*))$ is complete but it
is not a Riesz basis. In this framework new phenomena arise : simultaneous
condensation of eigenvalues and eigenfunctions. We prove the existence of a
minimal time $T_0 \in [0, +\infty]$ depending on the condensation of
eigenvalues and associated eigenfunctions of $(L^* , D(L^*))$, such that the
corresponding system is null controllable at any time $T > T_0$ and is not if
$T < T_0$.


  The transitions $B_{s,d}\rightarrow \ell^+\ell^-$ (for $\ell=e, \mu, \tau$),
although extremely suppressed within the SM, are exceptionally clean channels
particularly sensitive to New Physics contributions. So far only the branching
ratio for the process $B_{s}\rightarrow \mu^+\mu^-$ has been measured
experimentally and, although the results are in agreement with the SM
prediction, there is still room for NP effects. Here we provide an overview of
the theoretical status of rare decays. We present strategies that can allow us
to discriminate between different NP scenarios. Finally, we include a
discussion of the effects of nontrivial new CP violating phases on the
observables associated with $B_{s}\rightarrow \mu^+\mu^-$.


  Deep learning models have demonstrated remarkable capabilities in learning
complex patterns and concepts from training data. However, recent findings
indicate that these models tend to rely heavily on simple and easily
discernible features present in the background of images rather than the main
concepts or objects they are intended to classify. This phenomenon poses a
challenge to image classifiers as the crucial elements of interest in images
may be overshadowed. In this paper, we propose a novel approach to address this
issue and improve the learning of main concepts by image classifiers. Our
central idea revolves around concurrently guiding the model's attention toward
the foreground during the classification task. By emphasizing the foreground,
which encapsulates the primary objects of interest, we aim to shift the focus
of the model away from the dominant influence of the background. To accomplish
this, we introduce a mechanism that encourages the model to allocate sufficient
attention to the foreground. We investigate various strategies, including
modifying the loss function or incorporating additional architectural
components, to enable the classifier to effectively capture the primary concept
within an image. Additionally, we explore the impact of different foreground
attention mechanisms on model performance and provide insights into their
effectiveness. Through extensive experimentation on benchmark datasets, we
demonstrate the efficacy of our proposed approach in improving the
classification accuracy of image classifiers. Our findings highlight the
importance of foreground attention in enhancing model understanding and
representation of the main concepts within images. The results of this study
contribute to advancing the field of image classification and provide valuable
insights for developing more robust and accurate deep-learning models.


  We consider an online version of the robust Principle Component Analysis
(PCA), which arises naturally in time-varying source separations such as video
foreground-background separation. This paper proposes a compressive online
robust PCA with prior information for recursively separating a sequences of
frames into sparse and low-rank components from a small set of measurements. In
contrast to conventional batch-based PCA, which processes all the frames
directly, the proposed method processes measurements taken from each frame.
Moreover, this method can efficiently incorporate multiple prior information,
namely previous reconstructed frames, to improve the separation and thereafter,
update the prior information for the next frame. We utilize multiple prior
information by solving $n\text{-}\ell_{1}$ minimization for incorporating the
previous sparse components and using incremental singular value decomposition
($\mathrm{SVD}$) for exploiting the previous low-rank components. We also
establish theoretical bounds on the number of measurements required to
guarantee successful separation under assumptions of static or slowly-changing
low-rank components. Using numerical experiments, we evaluate our bounds and
the performance of the proposed algorithm. In addition, we apply the proposed
algorithm to online video foreground and background separation from compressive
measurements. Experimental results show that the proposed method outperforms
the existing methods.


  Design automation in general, and in particular logic synthesis, can play a
key role in enabling the design of application-specific Binarized Neural
Networks (BNN). This paper presents the hardware design and synthesis of a
purely combinational BNN for ultra-low power near-sensor processing. We
leverage the major opportunities raised by BNN models, which consist mostly of
logical bit-wise operations and integer counting and comparisons, for pushing
ultra-low power deep learning circuits close to the sensor and coupling it with
binarized mixed-signal image sensor data. We analyze area, power and energy
metrics of BNNs synthesized as combinational networks. Our synthesis results in
GlobalFoundries 22nm SOI technology shows a silicon area of 2.61mm2 for
implementing a combinational BNN with 32x32 binary input sensor receptive field
and weight parameters fixed at design time. This is 2.2x smaller than a
synthesized network with re-configurable parameters. With respect to other
comparable techniques for deep learning near-sensor processing, our approach
features a 10x higher energy efficiency.


  The case of motion of a generalized two-field gyrostat found by V.V.Sokolov
and A.V.Tsiganov is known as a Liouville integrable Hamiltonian system with
three degrees of freedom. We find a set of points at which the momentum map has
rank 1. This set consists of special periodic motions which correspond to the
singular points of a bifurcation diagram on an iso-energetic surface. For such
motions the phase variables can be expressed in terms of algebraic functions of
a single auxiliary variable. These algebraic functions satisfy a differential
equation integrable in elliptic functions of time. It is shown that the
corresponding points in the three-dimensional space of the constants of the
integrals belong to the intersection of two sheets of the discriminant surface
of the Lax curve.


  The problem of branched transportation aims to describe the movement of
masses when, due to concavity effects, they have the interest to travel
together as much as possible, because the cost for a path of length


  It has been shown that there is a potential ambiguity in the asteroseismic
determination of the location of internal structures in a pulsating star. We
show how, in the case of high-order non-radial acoustic modes, it is possible
to remove this ambiguity by considering modes of different degree. To support
our conclusions we have investigated the seismic signatures of sharp density
variations in the structure of quasi-homogeneous models.


  The non-perturbative superpotential can be effectively calculated in
$M$-theory compactification to three dimensions on a Calabi-Yau four-fold $X$.
For certain $X$, the superpotential is identically zero, while for other $X$, a
non-perturbative superpotential is generated. Using $F$-theory, these results
carry over to certain Type IIB and heterotic string compactifications to four
dimensions with $N=1$ supersymmetry. In the heterotic string case, the
non-perturbative superpotential can be interpreted as coming from space-time
and world-sheet instantons; in many simple cases contributions come only from
finitely many values of the instanton numbers.


  We establish the consistency of K-medoids in the context of metric spaces. We
start by proving that K-medoids is asymptotically equivalent to K-means
restricted to the support of the underlying distribution under general
conditions, including a wide selection of loss functions. This asymptotic
equivalence, in turn, enables us to apply the work of Parna (1986) on the
consistency of K-means. This general approach applies also to non-metric
settings where only an ordering of the dissimilarities is available. We
consider two types of ordinal information: one where all quadruple comparisons
are available; and one where only triple comparisons are available. We provide
some numerical experiments to illustrate our theory.


  This paper develops entropy stable (ES) adaptive moving mesh schemes for the
2D and 3D special relativistic hydrodynamic (RHD) equations. They are built on
the ES finite volume approximation of the RHD equations in curvilinear
coordinates, the discrete geometric conservation laws, and the mesh adaptation
implemented by iteratively solving the Euler-Lagrange equations of the mesh
adaption functional in the computational domain with suitably chosen monitor
functions. First, a sufficient condition is proved for the two-point entropy
conservative (EC) flux, by mimicking the derivation of the continuous entropy
identity in curvilinear coordinates and using the discrete geometric
conservation laws given by the conservative metrics method. Based on such
sufficient condition, the EC fluxes for the RHD equations in curvilinear
coordinates are derived and the second-order accurate semi-discrete EC schemes
are developed to satisfy the entropy identity for the given convex entropy
pair. Next, the semi-discrete ES schemes satisfying the entropy inequality are
proposed by adding a suitable dissipation term to the EC scheme and utilizing
linear reconstruction with the minmod limiter in the scaled entropy variables
in order to suppress the numerical oscillations of the above EC scheme. Then,
the semi-discrete ES schemes are integrated in time by using the second-order
strong stability preserving explicit Runge-Kutta schemes. Finally, several
numerical results show that our 2D and 3D ES adaptive moving mesh schemes
effectively capture the localized structures, such as sharp transitions or
discontinuities, and are more efficient than their counterparts on uniform
mesh.


  The present nearly exponential growth of the cumulative installation power of
wind and photovoltaic power plants is very promising in the context of a rapid
reduction of the emission of CO2, which can lead to a swift mitigation climate
change if this growth behavior is maintained in the future. In this review we
identify a set of ten limiting factors that can restrain, or halt back, an
exponential growth of these variable renewable power plants (VREs) in the
future. If the exponential growth slows down to a linear growth, such a case
would extent considerably the time to reduce the CO2 emissions and the related
mitigation of climate change. A scenario that would result to a much higher
risk of a future continuation of the economic grow and thrive of the global
economy and human society. We argue that if these limiting factors are
adequately addressed to an exponential expansion VRE power plants is feasible
and can result in the nearly complete avoidance of CO2 emissions as related to
energy generation and consumption in 2030.


  We present elemental abundances for multiple HII regions in Leo A and GR 8
obtained from long slit optical spectroscopy of these two nearby low luminosity
dwarf irregular galaxies. As expected from their luminosities, and in agreement
with previous observations, the derived oxygen abundances are extremely low in
both galaxies. High signal-to-noise ratio observations of a planetary nebula in
Leo A yield 12 + log(O/H) = 7.30 +/- 0.05; "semi-empirical" calculations of the
oxygen abundance in four HII regions in Leo A indicate 12 + log(O/H) = 7.38 +/-
0.10. These results confirm that Leo A has one of the lowest ISM metal
abundances of known nearby galaxies. Based on results from two HII regions with
high signal-to-noise measurements of the weak [O III] 4363 line, the mean
oxygen abundance of GR 8 is 12 + log(O/H) = 7.65 +/- 0.06; using "empirical"
and "semi-empirical" methods, similar abundances are derived for 6 other GR 8
HII regions. Similar to previous results in other low metallicity galaxies, the
mean log(N/O) = -1.53 +/- 0.09 for Leo A and -1.51 +/- 0.07 for GR 8. There is
no evidence of significant variations in either O/H or N/O in the HII regions.
The metallicity-luminosity relation for nearby (D < 5 Mpc) dwarf irregular
galaxies with measured oxygen abundances has a mean correlation of 12 +
log(O/H) = 5.67 - 0.151 M_B with a dispersion in oxygen about the relationship
of 0.21. These observations confirm that gas-rich low luminosity galaxies have
extremely low elemental abundances in the ionized gas-phase of their
interstellar media. Although Leo A has one of the lowest metal abundances of
known nearby galaxies, detection of tracers of an older stellar population
indicate that it is not a newly formed galaxy as has been proposed for some
other similarly low metallicity star forming galaxies.


  We propose a new bivariate symmetric copula with positive and negative
dependence properties. The main features of the proposed copula are its simple
mathematical structure, wider dependence range compared to FGM copula and its
generalizations, and no lower and upper tail dependence. The maximum range of
Spearman's Rho of the proposed copula is [-0.5866,0.5866], which improves the
dependence range of the FGM copula and its various generalizations. A new
bivariate Rayleigh distribution is developed using the proposed copula, and
some statistical properties have been studied. A real data set is analyzed to
illustrate the proposed bivariate distribution's relevance in practical
contexts.


  We propose an interferometry experiment for the detection of axion-like
particles (ALPs). As in ordinary photon-regeneration (light shining through a
wall) experiments, a laser beam traverses a region permeated by a magnetic
field, where photons are converted to ALPs via the Primakoff process, resulting
in a slight power loss and phase shift. The beam is then combined with a
reference beam that originates from the same source. The detection of a change
in the output intensity would signal the presence of ALPs (or possibly other
particles that couple to the photon in a similar way). Because only one stage
of conversion is needed, the signal is of ${\cal O}(g^2_{a\gamma \gamma})$, as
opposed to ${\cal O}(g^4_{a\gamma \gamma})$ for photon-regeneration
experiments, where $g_{a\gamma \gamma}$ is the coupling between ALPs and
photons. This improvement over photon-regeneration is nullified by the presence
of shot noise, which however can be reduced by the use of squeezed light,
resulting in an improvement in the sensitivity to $g_{a\gamma\gamma}$ over
ordinary photon-regeneration experiments by an order of $10^{1/2}$ assuming
$10{\rm dB}$ noise suppression. Additionally, our setup can incorporate
straightforwardly optical delay lines or Fabry-Perot cavities, boosting the
signal by a factor of $n\sim10^3$, where $n$ is the number of times the laser
beam is folded. This way, we can constrain $g_{a\gamma\gamma}$ better by yet
another factor of $n^{1/2}\sim 10^{1.5}$, as compared to the $n^{1/4}$ boost
that would be achieved in photon-regeneration experiments.


  A chatbot is perceived as more humanlike and likeable if it includes some
jokes in its output. But most existing joke generators were not designed to be
integrated into chatbots. This paper presents Witscript, a novel joke
generation system that can improvise original, contextually relevant jokes,
such as humorous responses during a conversation. The system is based on joke
writing algorithms created by an expert comedy writer. Witscript employs
well-known tools of natural language processing to extract keywords from a
topic sentence and, using wordplay, to link those keywords and related words to
create a punch line. Then a pretrained neural network language model that has
been fine-tuned on a dataset of TV show monologue jokes is used to complete the
joke response by filling the gap between the topic sentence and the punch line.
A method of internal scoring filters out jokes that don't meet a preset
standard of quality. Human evaluators judged Witscript's responses to input
sentences to be jokes more than 40% of the time. This is evidence that
Witscript represents an important next step toward giving a chatbot a humanlike
sense of humor.


  We study the thermodynamic phase transition in the rainbow Schwarzschild
black hole where the metric depends on the energy of the test particle.
Identifying the black hole temperature with the energy from the modified
dispersion relation, we obtain the modified entropy and thermodynamic energy
along with the modified local temperature in the cavity to provide well defined
black hole states. It is found that apart from the conventional critical
temperature related to Hawking-Page phase transition there appears an
additional critical temperature which is of relevance to the existence of a
locally stable tiny black hole; however, the off-shell free energy tells us
that this black hole should eventually tunnel into the stable large black hole.
Finally, we discuss the reason why the temperature near the horizon is finite
in the rainbow black hole by employing the running gravitational coupling
constant, whereas it is divergent near the horizon in the ordinary
Schwarzschild black hole.


  We study the asymptotic properties of four-simplex amplitudes for various
four-dimensional spin foam models. We investigate the semi-classical limit of
the Ooguri, Euclidean and Lorentzian EPRL models using coherent states for the
boundary data. For some classes of geometrical boundary data, the asymptotic
formulae are given, in all three cases, by simple functions of the Regge action
for the four-simplex geometry.


  We prove and apply two theorems: First, a quantitative, scale-free unique
continuation estimate for functions in a spectral subspace of a Schr\"odinger
operator on a bounded or unbounded domain, second, a perturbation and lifting
estimate for edges of the essential spectrum of a self-adjoint operator under a
semi-definite perturbation. These two results are combined to obtain lower and
upper Lipschitz bounds on the function parametrizing locally a chosen edge of
the essential spectrum of a Schr\"odinger operator in dependence of a coupling
constant. Analogous estimates for eigenvalues, possibly in gaps of the
essential spectrum, are exhibited as well.


  We have detected coherent oscillations (``dwarf nova oscillations'') in
Hubble Space Telescope spectra of the dwarf nova OY Car. The oscillations were
seen towards the end of a superoutburst of OY Car. The oscillations are
extraordinary compared to the many other examples in the literature for two
reasons. First, their amplitude is large, with a peak-to-peak variation of 8 to
20% of the total flux over the range 1100 to 2500A. However, most remarkably we
find that there are two components present simultaneously. Both have periods
close to 18sec (equivalent to 4800 cycles/day) but they are separated by
57.7+/-0.5 cycles/day. The lower frequency component of the pair has a strong
second harmonic while its companion, which has about twice its amplitude, does
not. The oscillation spectra appear hotter than the mean spectrum and
approximately follow the continuum distribution of a black-body with a
temperature in the range 30,000 to 50,000K.
  We tentatively suggest that the weaker non-sinusoidal component could
represent the rotation of the white dwarf, although we have been unable to
recover any such signal in quiescent data.


  The structure of ecological interactions is commonly understood through
analyses of interaction networks. However, these analyses may be sensitive to
sampling biases in both the interactors (the nodes of the network) and
interactions (the links between nodes). These issues may affect the accuracy of
empirically constructed ecological networks. We explore the properties of
sampled ecological networks by simulating large-scale ecological networks with
predetermined topologies, and sampling them with different mathematical
procedures. Several types of modular networks were generated, intended to
represent a wide variety of communities that vary in size and types of
ecological interactions. We sampled these networks with different sampling
designs that may be encountered in field experiments. The observed networks
generated by each sampling process were analyzed with respect to number and
size of components. We show that the sampling effort needed to estimate
underlying network properties depends both on the sampling design and on
network topology. Networks with random or scale-free modules require more
complete sampling compared to networks whose modules are nested or bipartite.
Overall, the structure of nested modules was the easiest to detect, regardless
of sampling design. Sampling according to species degree was consistently found
to be the most accurate strategy to estimate network structure. Conversely,
sampling according to module results in an accurate view of certain modules,
but fails to provide a global picture of the underlying network. We recommend
that these findings are incorporated into the design of projects aiming to
characterize large networks of species interactions in the field, to reduce
sampling biases. The software scripts developed to construct and sample
networks are provided for further explorations of network structure and
comparisons to real interaction data.


  Machine learning (ML) and artificial intelligence (AI) have recently made a
significant impact on improving the operations of wireless networks and
establishing intelligence at the edge. In return, rare efforts were made to
explore how adapting, optimizing, and arranging wireless networks can
contribute to implementing ML/AI at the edge. This article aims to address this
void by setting a vision on how wireless networking researchers can leverage
their expertise to return the favor to edge learning. It will review the
enabling technologies, summarize the inaugural works on this path, and shed
light on different directions to establish a comprehensive framework for mobile
edge learning (MEL).


  Here we use pristine graphene samples in order to analyze how the Raman peaks
intensity, measured at 2.4 eV and 1.96 eV excitation energy, changes with the
amount of doping. The use of pristine graphene allows investigating the
intensity dependence close to the Dirac point. We show that the G peak
intensity is independent on the doping, while the 2D peak intensity strongly
decreases for increasing doping. Analyzing this dependence in the framework of
a fully resonant process, we found that the total electron-phonon scattering
rate is ~40 meV at 2.4 eV.


  We demonstrate that 60 keV electron irradiation drives the diffusion of
threefold coordinated Si dopants in graphene by one lattice site at a time.
First principles simulations reveal that each step is caused by an electron
impact on a C atom next to the dopant. Although the atomic motion happens below
our experimental time resolution, stochastic analysis of 38 such lattice jumps
reveals a probability for their occurrence in a good agreement with the
simulations. Conversions from three- to fourfold coordinated dopant structures
and the subsequent reverse process are significantly less likely than the
direct bond inversion. Our results thus provide a model of non-destructive and
atomically precise structural modification and detection for two-dimensional
materials.


  This paper is concerned with several not-quantum aspects of black holes, with
emphasis on theoretical and mathematical issues related to numerical modeling
of black hole space-times. Part of the material has a review character, but
some new results or proposals are also presented. We review the experimental
evidence for existence of black holes. We propose a definition of black hole
region for any theory governed by a symmetric hyperbolic system of equations.
Our definition reproduces the usual one for gravity, and leads to the one
associated with the Unruh metric in the case of Euler equations. We review the
global conditions which have been used in the Scri-based definition of a black
hole and point out the deficiencies of the Scri approach. Various results on
the structure of horizons and apparent horizons are presented, and a new proof
of semi-convexity of horizons based on a variational principle is given. Recent
results on the classification of stationary singularity-free vacuum solutions
are reviewed. Two new frameworks for discussing black holes are proposed: a
"naive approach", based on coordinate systems, and a "quasi-local approach",
based on timelike boundaries satisfying a null convexity condition. Some
properties of the resulting black holes are established, including an area
theorem, topology theorems, and an approximation theorem for the location of
the horizon.


  Let $S\subseteq V(G)$ and $\pi_{G}(S)$ denote the maximum number $t$ of
edge-disjoint paths $P_{1},P_{2},\ldots,P_{t}$ in a graph $G$ such that
$V(P_{i})\cap V(P_{j})=S$ for any $i,j\in\{1,2,\ldots,t\}$ and $i\neq j$. If
$S=V(G)$, then $\pi_{G}(S)$ is the maximum number of edge-disjoint spanning
paths in $G$. It is proved [Graphs Combin., 37 (2021) 2521-2533] that deciding
whether $\pi_G(S)\geq r$ is NP-complete for a given $S\subseteq V(G)$. For an
integer $r$ with $2\leq r\leq n$, the $r$-path connectivity of a graph $G$ is
defined as $\pi_{r}(G)=$min$\{\pi_{G}(S)|S\subseteq V(G)$ and $|S|=r\}$, which
is a generalization of tree connectivity. In this paper, we study the $3$-path
connectivity of the $k$-dimensional data center network with $n$-port switches
$D_{k,n}$ which has significate role in the cloud computing, and prove that
$\pi_{3}(D_{k,n})=\lfloor\frac{2n+3k}{4}\rfloor$ with $k\geq 1$ and $n\geq 6$.


  The lack of interpretability is an inevitable problem when using neural
network models in real applications. In this paper, an explainable neural
network based on generalized additive models with structured interactions
(GAMI-Net) is proposed to pursue a good balance between prediction accuracy and
model interpretability. GAMI-Net is a disentangled feedforward network with
multiple additive subnetworks; each subnetwork consists of multiple hidden
layers and is designed for capturing one main effect or one pairwise
interaction. Three interpretability aspects are further considered, including
a) sparsity, to select the most significant effects for parsimonious
representations; b) heredity, a pairwise interaction could only be included
when at least one of its parent main effects exists; and c) marginal clarity,
to make main effects and pairwise interactions mutually distinguishable. An
adaptive training algorithm is developed, where main effects are first trained
and then pairwise interactions are fitted to the residuals. Numerical
experiments on both synthetic functions and real-world datasets show that the
proposed model enjoys superior interpretability and it maintains competitive
prediction accuracy in comparison to the explainable boosting machine and other
classic machine learning models.


  We introduce OmniPrint, a synthetic data generator of isolated printed
characters, geared toward machine learning research. It draws inspiration from
famous datasets such as MNIST, SVHN and Omniglot, but offers the capability of
generating a wide variety of printed characters from various languages, fonts
and styles, with customized distortions. We include 935 fonts from 27 scripts
and many types of distortions. As a proof of concept, we show various use
cases, including an example of meta-learning dataset designed for the upcoming
MetaDL NeurIPS 2021 competition. OmniPrint is available at
https://github.com/SunHaozhe/OmniPrint.


  Spectra of the magnetic white dwarf binary AM Her were obtained with the Far
Ultraviolet Spectroscopic Explorer (FUSE) during three consecutive spacecraft
orbits. These observations were split into 19 spectra of about 5 min duration
(0.025P binary phase) partially covering the binary orbit. We report the
phase-related changes in the far ultraviolet continuum light curve and the
emission lines, noting particularly the behavior of O VI. We discuss the fluxes
and velocities of the narrow and broad O VI emissions. We find the FUV light
curve has maximum amplitude at ~1000A, although at shorter wavelengths the
continuum may be strongly affected by overlapping Lyman lines. Weak, narrow
Lyman absorption lines are present. Their velocities don't appear to vary over
the observed orbital phases, and their mean value is consistent with the
systemic velocity.


  A method to determine the state of a single quantized cavity mode is
proposed. By adiabatic passage, the quantum state of the field is transfered
completely onto an internal Zeeman sub-manifold of an atom. Utilizing a method
of Newton and Young, we can determine this angular momentum state uniquely, by
a finite number of magnetic dipole measurements with Stern-Gerlach analyzers.
An example illustrates the influence of dissipation.


  We present a catalog of 316 trans-Neptunian bodies detected by the Dark
Energy Survey (DES). These objects include 245 discoveries by DES (139 not
previously published) detected in $\approx 60,000$ exposures from the first
four seasons of the survey ("Y4" data). The survey covers a contiguous 5000
deg$^2$ of the southern sky in the $grizY$ optical/NIR filter set, with a
typical TNO in this part of the sky being targeted by $25-30$ Y4 exposures. We
describe the processes for detection of transient sources and the linkage into
TNO orbits, which are made challenging by the absence of the few-hour repeat
observations employed by TNO-optimized surveys. We also describe the procedures
for determining detection efficiencies vs. magnitude and estimating rates of
false-positive linkages. This work presents all TNOs which were detected on
$\ge 6$ unique nights in the Y4 data and pass a "sub-threshold confirmation"
test wherein we demand the the object be detectable in a stack of the
individual images in which the orbit indicates an object should be present, but
was not detected. This eliminates false positives and yields TNO detections
complete to $r\lesssim 23.3$ mag with virtually no dependence on orbital
properties for bound TNOs at distance $30\,{\rm AU}<d<2500\,{\rm AU}.$ The
final DES TNO catalog is expected to yield $>0.3$ mag more depth, and arcs of
$>4$ years for nearly all detections.


  When identifying electrical, mechanical, or biological systems, parametric
continuous-time identification methods can lead to interpretable and
parsimonious models when the model structure aligns with the physical
properties of the system. Traditional linear system identification may not
consider the most parsimonious model when relying solely on unfactored transfer
functions, which typically result from standard direct approaches. This paper
presents a novel identification method that delivers additive models for both
open and closed-loop setups. The estimators that are derived are shown to be
generically consistent, and can admit the identification of marginally stable
additive systems. Numerical simulations show the efficacy of the proposed
approach, and its performance in identifying a modal representation of a
flexible beam is verified using experimental data.


  This research introduces a novel approach, MBO-NB, that leverages Migrating
Birds Optimization (MBO) coupled with Naive Bayes as an internal classifier to
address feature selection challenges in text classification having large number
of features. Focusing on computational efficiency, we preprocess raw data using
the Information Gain algorithm, strategically reducing the feature count from
an average of 62221 to 2089. Our experiments demonstrate MBO-NB's superior
effectiveness in feature reduction compared to other existing techniques,
emphasizing an increased classification accuracy. The successful integration of
Naive Bayes within MBO presents a well-rounded solution. In individual
comparisons with Particle Swarm Optimization (PSO), MBO-NB consistently
outperforms by an average of 6.9% across four setups. This research offers
valuable insights into enhancing feature selection methods, providing a
scalable and effective solution for text classification


  A word automaton recognizing a language $L$ is good for games (GFG) if its
composition with any game with winning condition $L$ preserves the game's
winner. While all deterministic automata are GFG, some nondeterministic
automata are not. There are various other properties that are used in the
literature for defining that a nondeterministic automaton is GFG, including
"history-deterministic", "compliant with some letter game", "good for trees",
and "good for composition with other automata". The equivalence of these
properties has not been formally shown.
  We generalize all of these definitions to alternating automata and show their
equivalence. We further show that alternating GFG automata are as expressive as
deterministic automata with the same acceptance conditions and indices. We then
show that alternating GFG automata over finite words, and weak automata over
infinite words, are not more succinct than deterministic automata, and that
determinizing B\"uchi and co-B\"uchi alternating GFG automata involves a
$2^{\Theta(n)}$ state blow-up. We leave open the question of whether
alternating GFG automata of stronger acceptance conditions allow for
doubly-exponential succinctness compared to deterministic automata.


  Upcoming Sunyaev-Zel'dovich surveys are expected to return ~10^4 intermediate
mass clusters at high redshift. Their average masses must be known to same
accuracy as desired for the dark energy properties. Internal to the surveys,
the CMB potentially provides a source for lensing mass measurements whose
distance is precisely known and behind all clusters. We develop statistical
mass estimators from 6 quadratic combinations of CMB temperature and
polarization fields that can simultaneously recover large-scale structure and
cluster mass profiles. The performance of these estimators on idealized NFW
clusters suggests that surveys with a ~1' beam and 10uK' noise in
uncontaminated temperature maps can make a ~10sigma detection, or equivalently
a ~10% mass measurement for each 10^3 set of clusters. With internal or
external acoustic scale E-polarization measurements, the ET cross correlation
estimator can provide a stringent test for contaminants on a first detection at
\~1/3 the significance. For surveys that reach below 3muK', the EB cross
correlation estimator should provide the most precise measurements and
potentially the strongest control over contaminants.


  In this paper we consider the effect of the direct ionizing stellar radiation
field on the evolution of protoplanetary discs subject to photoevaporative
winds. We suggest that models which combine viscous evolution with
photoevaporation of the disc (e.g. Clarke, Gendrin & Sotomayor 2001)
incorrectly neglect the direct field after the inner disc has drained, at late
times in the evolution. We construct models of the photoevaporative wind
produced by the direct field, first using simple analytic arguments and later
using detailed numerical hydrodynamics. We find that the wind produced by the
direct field at late times is much larger than has previously been assumed, and
we show that the mass-loss rate scales as $R_{in}^{1/2}$ (where $R_{in}$ is the
radius of the instantaneous inner disc edge). We suggest that this result has
important consequences for theories of disc evolution, and go on to consider
the effects of this result on disc evolution in detail in a companion paper
(Alexander, Clarke & Pringle 2006b).


  Cloth-changing person re-identification (CC-ReID) aims to retrieve specific
pedestrians in a cloth-changing scenario. Its main challenge is to disentangle
the clothing-related and clothing-unrelated features. Most existing approaches
force the model to learn clothing-unrelated features by changing the color of
the clothes. However, due to the lack of ground truth, these methods inevitably
introduce noise, which destroys the discriminative features and leads to an
uncontrollable disentanglement process. In this paper, we propose a new person
re-identification network called features reconstruction disentanglement ReID
(FRD-ReID), which can controllably decouple the clothing-unrelated and
clothing-related features. Specifically, we first introduce the human parsing
mask as the ground truth of the reconstruction process. At the same time, we
propose the far away attention (FAA) mechanism and the person contour attention
(PCA) mechanism for clothing-unrelated features and pedestrian contour features
to improve the feature reconstruction efficiency. In the testing phase, we
directly discard the clothing-related features for inference,which leads to a
controllable disentanglement process. We conducted extensive experiments on the
PRCC, LTCC, and Vc-Clothes datasets and demonstrated that our method
outperforms existing state-of-the-art methods.


  For a polynomial $P$ of degree greater than one, we show the existence of
patterns of the form $(x,x+t,x+P(t))$ with a gap estimate on $t$ in positive
density subsets of the reals. This is an extension of an earlier result of
Bourgain. Our proof is a combination of Bourgain's approach and more recent
methods that were originally developed for the study of the bilinear Hilbert
transform along curves.


  This paper concerns the estimation of the regression function at a given
point in nonparametric heteroscedastic models with Gaussian noise or with noise
having unknown distribution. In the two cases an asymptotically efficient
kernel estimator is constructed for the minimax absolute error risk.


  Assessing processes is one of the best ways for an organization to start a
software process improvement program. An alternative for organizations seeking
for lighter assessments methods is to perform self-assessments, which can be
carried out by an organization to assess its own process. In this context, the
question that arises is which software process self-assessment methods exist
and which kind of support they provide? To answer this question, a mapping
study on software process self-assessment methods was performed. As result, a
total of 33 methods were identified and analyzed, synthesizing information on
their measurement framework, process reference model and assessment process. We
observed that most self-assessment methods are based on consolidated models,
such as CMMI or ISO/IEC 15504 with a trend to develop self-assessment methods
specifically for SMEs. In general, they use simplified assessment processes,
focusing on data collection and analysis. Most of the methods propose to
collect data through questionnaires that are answered by managers or other team
members related to the process being assessed. However, we noted a lack of
information on how most of the assessment methods (AMs) have been developed and
validated, which leaves their validity questionable. The results of our study
may help practitioners, interested in conducting software process
self-assessments, to choose a self-assessment method. This research is also
relevant for researchers, as it provides a better understanding of the existing
self-assessment methods and their strengths and weaknesses.


  This paper proposes to correct the rolling shutter (RS) distorted images by
estimating the distortion flow from the global shutter (GS) to RS directly.
Existing methods usually perform correction using the undistortion flow from
the RS to GS. They initially predict the flow from consecutive RS frames,
subsequently rescaling it as the displacement fields from the RS frame to the
underlying GS image using time-dependent scaling factors. Following this,
RS-aware forward warping is employed to convert the RS image into its GS
counterpart. Nevertheless, this strategy is prone to two shortcomings. First,
the undistortion flow estimation is rendered inaccurate by merely linear
scaling the flow, due to the complex non-linear motion nature. Second, RS-aware
forward warping often results in unavoidable artifacts. To address these
limitations, we introduce a new framework that directly estimates the
distortion flow and rectifies the RS image with the backward warping operation.
More specifically, we first propose a global correlation-based flow attention
mechanism to estimate the initial distortion flow and GS feature jointly, which
are then refined by the following coarse-to-fine decoder layers. Additionally,
a multi-distortion flow prediction strategy is integrated to mitigate the issue
of inaccurate flow estimation further. Experimental results validate the
effectiveness of the proposed method, which outperforms state-of-the-art
approaches on various benchmarks while maintaining high efficiency. The project
is available at \url{https://github.com/ljzycmd/DFRSC}.


  Our objective is to study the observability and unique continuation property
of the adjoint of a linearized compressible fluid structure interaction model
in a 2D channel. Concerning the structure we will consider a damped
Euler-Bernoulli beam located on a portion of the boundary. In the present
article we establish an observability inequality for the adjoint of the
linearized fluid structure interaction problem under consideration which in
principle is equivalent with the null controllability of the linearized system.
As a corollary of the derived observability inequality we also obtain a unique
continuation property for the adjoint problem.


  Exploration tasks are essential to many emerging robotics applications,
ranging from search and rescue to space exploration. The planning problem for
exploration requires determining the best locations for future measurements
that will enhance the fidelity of the map, for example, by reducing its total
entropy. A widely-studied technique involves computing the Mutual Information
(MI) between the current map and future measurements, and utilizing this MI
metric to decide the locations for future measurements. However, computing MI
for reasonably-sized maps is slow and power hungry, which has been a bottleneck
towards fast and efficient robotic exploration. In this paper, we introduce a
new hardware accelerator architecture for MI computation that features a
low-latency, energy-efficient MI compute core and an optimized memory subsystem
that provides sufficient bandwidth to keep the cores fully utilized. The core
employs interleaving to counter the recursive algorithm, and workload balancing
and numerical approximations to reduce latency and energy consumption. We
demonstrate this optimized architecture with a Field-Programmable Gate Array
(FPGA) implementation, which can compute MI for all cells in an entire
201-by-201 occupancy grid ({\em e.g.}, representing a 20.1m-by-20.1m map at
0.1m resolution) in 1.55 ms while consuming 1.7 mJ of energy, thus finally
rendering MI computation for the whole map real time and at a fraction of the
energy cost of traditional compute platforms. For comparison, this particular
FPGA implementation running on the Xilinx Zynq-7000 platform is two orders of
magnitude faster and consumes three orders of magnitude less energy per MI map
compute, when compared to a baseline GPU implementation running on an NVIDIA
GeForce GTX 980 platform. The improvements are more pronounced when compared to
CPU implementations of equivalent algorithms.


  Physics-informed neural networks (PINNs) are revolutionizing science and
engineering practice by bringing together the power of deep learning to bear on
scientific computation. In forward modeling problems, PINNs are meshless
partial differential equation (PDE) solvers that can handle irregular,
high-dimensional physical domains. Naturally, the neural architecture
hyperparameters have a large impact on the efficiency and accuracy of the PINN
solver. However, this remains an open and challenging problem because of the
large search space and the difficulty of identifying a proper search objective
for PDEs. Here, we propose Auto-PINN, the first systematic, automated
hyperparameter optimization approach for PINNs, which employs Neural
Architecture Search (NAS) techniques to PINN design. Auto-PINN avoids manually
or exhaustively searching the hyperparameter space associated with PINNs. A
comprehensive set of pre-experiments using standard PDE benchmarks allows us to
probe the structure-performance relationship in PINNs. We find that the
different hyperparameters can be decoupled, and that the training loss function
of PINNs is a good search objective. Comparison experiments with baseline
methods demonstrate that Auto-PINN produces neural architectures with superior
stability and accuracy over alternative baselines.


  It has been understood that short range interactions can reduce the
classification of topological superconductors in all dimensions. In this paper
we demonstrate by explicit calculations that when the topological phase
transition between two distinct phases in the noninteracting limit is gapped
out by interaction, the bulk fermion Green's function $G(i\omega)$ at the
"transition" approaches zero as $G(i\omega) \sim \omega$ at certain momentum
$\vec{k}$ in the Brillouin zone.


  We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov
(NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is
studied using the GH polynomials and then the Lax pair is found. In particulr,
when $N=3,4,5$, one can get the Gold-fish model. The smooth rational solutions
of the NV equation are also constructed via the extended Moutard transformation
and the GH polynomials. The asymptotic behavior is discussed and then the
smooth rational solution of the Liouville equation is obtained.


  In this work we study the 3D Navier-Stokes equations, under the action of an
external force and with the fractional Laplacian operator $(-\Delta)^{\alpha}$
in the diffusion term, from the point of view of variable Lebesgue spaces.
Based on decay estimates of the fractional heat kernel we prove the existence
and uniqueness of mild solutions on this functional setting. Thus, in a first
theorem we obtain an unique local-in-time solution in the space $L^{p(\cdot)}
\left( [0,T], L^{q} (\mathbb{R}^3) \right)$. As a bi-product, in a second
theorem we prove the existence of an unique global-in-time solution in the
mixed-space $\mathcal{L}^{p(\cdot)}_{\frac{3}{2\alpha
-1}}(\mathbb{R}^3,L^\infty([0,T[))$.