  Properties of quantum states have disclosed new technologies, ranging from
quantum information to quantum metrology. Among them a recent research field is
quantum imaging, addressed to overcome limits of classical imaging by
exploiting spatial properties of quantum states of light . In particular
quantum correlations between twin beams represent a fundamental resource for
these studies. One of the most interesting proposed scheme exploits spatial
quantum correlations between parametric down conversion light beams for
realizing sub-shot-noise imaging of the weak absorbing objects, leading ideally
to a noise-free imaging. Here we present the first experimental realisation of
this scheme, showing its capability to reach a larger signal to noise ratio
(SNR) with respect to classical imaging methods. This work represents the
starting point of this quantum technology that can have relevant applications,
especially whenever there is a need of a low photon flux illumination (e.g. as
with certain biological samples).


  Eclipsing of the X-ray emitting region in active galactic nuclei (AGN) is a
potentially powerful probe to examine the AGN environment and absorber
properties. Here we study the eclipse data from the 2016 XMM-Newton observation
of NGC 6814 using a colour-colour analysis. Colours (i.e. hardness ratios) can
provide the advantage of better time-resolution over spectral analysis alone.
Colour-colour grids are constructed to examine the effects of different
parameters on the observed spectral variability during the eclipse. Consistent
with previous spectral analysis, the variations are dominated by changes in the
column density and covering fraction of the absorber. However, during maximum
eclipse the behaviour of the absorber changes. Just after ingress, the eclipse
is described by changes in column density and covering fraction, but prior to
egress, the variations are dominated by changes in column density alone.
Simulations are carried out to consider possible absorber geometries that might
produce this behaviour. The behaviour is inconsistent with a single,
homogeneous cloud, but simulations suggest that multiple clouds, perhaps
embedded in a highly ionised halo, could reproduce the results. In addition, we
determine the orbital covering factor (fraction of orbital path-length) based
on evidence of several eclipses in the 2016, 64-day Swift light curve. We
estimate that ~ 2-4 per cent of the orbit is covered by obscuring clouds and
that the distribution of clouds is not isotropic.


  Consider the random walk on the $n \times n$ upper triangular matrices with
ones on the diagonal and elements over $\mathbb{F}_p$ where we pick a row at
random and either add it or subtract it from the row directly above it. The
main result of this paper is to prove that the dependency of the mixing time on
$p$ is $p^2$. This is proven by combining super-character theory and comparison
theory arguments.


  We consider the production of ultrarelativistic positronium (Ps) in $\gamma A
\to Ps + A$ and $e A \to Ps + e A$ processes where $A$ is an atom or a nucleus
with charge $Ze$. For the photoproduction of para- and ortho-Ps and the
electroproduction of para-Ps we obtain the most complete description compared
with previous works. It includes high order $Z \alpha$ corrections and
polarization effects. The accuracy of the obtained cross sections is determined
by omitted terms of the order of the inverse Ps Lorentz factor squared. The
studied high order multi-photon electroproduction of ortho-Ps dominates for the
collision of electrons with heavy atoms over the bremsstrahlung production from
the electron via a virtual photon proposed by Holvik and Olsen. Our results
complete and correct the studies of those authors.


  Large-scale deep convolutional neural networks (CNNs) are widely used in
machine learning applications. While CNNs involve huge complexity, VLSI (ASIC
and FPGA) chips that deliver high-density integration of computational
resources are regarded as a promising platform for CNN's implementation. At
massive parallelism of computational units, however, the external memory
bandwidth, which is constrained by the pin count of the VLSI chip, becomes the
system bottleneck. Moreover, VLSI solutions are usually regarded as a lack of
the flexibility to be reconfigured for the various parameters of CNNs. This
paper presents CNN-MERP to address these issues. CNN-MERP incorporates an
efficient memory hierarchy that significantly reduces the bandwidth
requirements from multiple optimizations including on/off-chip data allocation,
data flow optimization and data reuse. The proposed 2-level reconfigurability
is utilized to enable fast and efficient reconfiguration, which is based on the
control logic and the multiboot feature of FPGA. As a result, an external
memory bandwidth requirement of 1.94MB/GFlop is achieved, which is 55% lower
than prior arts. Under limited DRAM bandwidth, a system throughput of
1244GFlop/s is achieved at the Vertex UltraScale platform, which is 5.48 times
higher than the state-of-the-art FPGA implementations.


  This review provides an overview of current research on the known
characteristics and motivations of offenders engaging in cyber-dependent
crimes. Due to the shifting dynamics of cybercriminal behaviour, and the
availability of prior reviews in 2013, this review focuses on original research
conducted from 2012 onwards, although some older studies that were not included
in prior reviews are also considered. As a basis for interpretation of results,
a limited quality assessment was also carried out on included studies through
examination of key indicators.


  We propose and investigate a semantics for "peer data exchange systems" where
different peers are related by data exchange constraints and trust
relationships. These two elements plus the data at the peers' sites and their
local integrity constraints are made compatible via a semantics that
characterizes sets of "solution instances" for the peers. They are the intended
-possibly virtual- instances for a peer that are obtained through a data repair
semantics that we introduce and investigate. The semantically correct answers
from a peer to a query, the so-called "peer consistent answers", are defined as
those answers that are invariant under all its different solution instances. We
show that solution instances can be specified as the models of logic programs
with a stable model semantics. The repair semantics is based on null values as
used in SQL databases, and is also of independent interest for repairs of
single databases with respect to integrity constraints.


  We give a model of dependent type theory with one univalent universe and
propositional truncation interpreting a type as a stack, generalising the
groupoid model of type theory. As an application, we show that countable choice
cannot be proved in dependent type theory with one univalent universe and
propositional truncation.


  We report the discovery of 652 star clusters, stellar groups and candidates
in the Milky Way with WISE. Most of the objects are projected close to Galactic
Plane and are embedded clusters. The present sample complements a similar study
(Paper I) which provided 437 star clusters and alike. We find evidence that
star formation processes span a wide range of sizes, from populous dense
clusters to small compact embedded ones, sparse stellar groups or in relative
isolation. The present list indicates multiple stellar generations during the
embedded phase, with giant molecular clouds collapsing into several clumps
composing an embedded cluster aggregate. We investigate the field star
decontaminated Colour Magnitude Diagrams and Radial Density Profiles of 9
cluster candidates in the list, and derive their parameters, confirming them as
embedded clusters.


  The entropy of network ensembles characterizes the amount of information
encoded in the network structure, and can be used to quantify network
complexity, and the relevance of given structural properties observed in real
network datasets with respect to a random hypothesis. In many real networks the
degrees of individual nodes are not fixed but change in time, while their
statistical properties, such as the degree distribution, are preserved. Here we
characterize the distribution of entropy of random networks with given degree
sequences, where each degree sequence is drawn randomly from a given degree
distribution. We show that the leading term of the entropy of scale-free
network ensembles depends only on the network size and average degree, and that
entropy is self-averaging, meaning that its relative variance vanishes in the
thermodynamic limit. We also characterize large fluctuations of entropy that
are fully determined by the average degree in the network. Finally, above a
certain threshold, large fluctuations of the average degree in the ensemble can
lead to condensation, meaning that a single node in a network of size~$N$ can
attract $O(N)$ links.


  Contemporary Large Language Models (LLMs) exhibit a high degree of code
generation and comprehension capability. A particularly promising area is their
ability to interpret code modules from unfamiliar libraries for solving
user-instructed tasks. Recent work has shown that large proprietary LLMs can
learn novel library usage in-context from demonstrations. These results raise
several open questions: whether demonstrations of library usage is required,
whether smaller (and more open) models also possess such capabilities, etc. In
this work, we take a broader approach by systematically evaluating a diverse
array of LLMs across three scenarios reflecting varying levels of domain
specialization to understand their abilities and limitations in generating code
based on libraries defined in-context. Our results show that even smaller
open-source LLMs like Llama-2 and StarCoder demonstrate an adept understanding
of novel code libraries based on specification presented in-context. Our
findings further reveal that LLMs exhibit a surprisingly high proficiency in
learning novel library modules even when provided with just natural language
descriptions or raw code implementations of the functions, which are often
cheaper to obtain than demonstrations. Overall, our results pave the way for
harnessing LLMs in more adaptable and dynamic coding environments.


  It is shown how to explicitly coarse-grain the microscopic dynamics of the
Vicsek model for self-propelled agents. The macroscopic transport equations are
derived by means of an Enskog-type kinetic theory. Expressions for all
transport coefficients at large particle speed are given. The phase transition
from a disordered to a flocking state is studied numerically and analytically.


  Let $f_{1}, \ldots, f_{k}$ be polynomials defining an algebraic set in affine
$n$-space over a finite field. Suppose $k>n$. We prove that there exists a
system of polynomials $g_{1}, \ldots, g_{n}$, each being a linear combination
with scalar coefficients of $f_{1}, \ldots, f_{k}$, defining the same algebraic
set. In particular, one reduces the number of equations without increasing the
total degree. We also have the corresponding result for systems of homogeneous
polynomials defining algebraic sets in projective spaces.


  The study of obstacle scattering for the Klein-Gordon equation in the
presence of long-range magnetic potentials is addressed. Previous results of
the authors are extended to the long-range case and the results the authors
previously proved for high-momenta long-range scattering for the Schr\"odinger
equation are brought to the relativistic scenario. It is shown that there are
important differences between relativistic and non-relativistic scattering
concerning long-range. In particular, it is proved that the electric potential
can be recovered without assuming the knowledge of the long-range part of the
magnetic potential, which has to be supposed in the non-relativistic case. The
electric potential and the magnetic field are recovered from the high momenta
limit of the scattering operator, as well as fluxes modulo $2 \pi $ around
handles of the obstacle. Moreover, it is proved that, for every $\hat{\mathbf
v} \in \mathbb{S}^2$, $ A_\infty(\hat{\mathbf v}) + A_\infty(-\hat{\mathbf v})$
can be reconstructed, where $A_\infty$ is the long-range part of the magnetic
potential. A a simple formula for the high momenta limit of the scattering
operator is given, in terms of magnetic fluxes over handles of the obstacle and
long-range magnetic fluxes at infinity, that are introduced in this paper. The
appearance of these long-range magnetic fluxes is a new effect in scattering
theory.


  Training large-scale CNNs that during inference can be run under Homomorphic
Encryption (HE) is challenging due to the need to use only polynomial
operations. This limits HE-based solutions adoption. We address this challenge
and pioneer in providing a novel training method for large polynomial CNNs such
as ResNet-152 and ConvNeXt models, and achieve promising accuracy on encrypted
samples on large-scale dataset such as ImageNet. Additionally, we provide
optimization insights regarding activation functions and skip-connection
latency impacts, enhancing HE-based evaluation efficiency. Finally, to
demonstrate the robustness of our method, we provide a polynomial adaptation of
the CLIP model for secure zero-shot prediction, unlocking unprecedented
capabilities at the intersection of HE and transfer learning.


  Non-Hermitian topological photonics is of great interest in bridging
topological matter with gain/dissipation engineering in optics. A key problem
in this direction is the interplay between the effective gauge potential and
the non-Hermiticity. Here we tackle this problem in a synthetic non-Hermitian
Hall ladder and experimentally observe antichiral edge currents (ACECs) of
photons, by tuning the locally uniform effective magnetic flux and the on-site
gain/loss. Such ACECs provide a topological method to probe the signatures of
the non-Hermitian skin effect (NHSE) from steady-state bulk dynamics. The
universality of this method is verified by its generalization to three
dimensions. This study paves a way to investigate exotic non-Hermitian
topological physics and has potential applications in topological photonics
engineering.


  We report on the local structure of the Martian subsolar Magnetic Pileup
Boundary (MPB) from minimum variance analysis of the magnetic field measured by
the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft for six orbits.
In particular, we detect a well defined current layer within the MPB and
provide a local estimate of its current density which results in a sunward Hall
electric force. This force accounts for the deflection of the solar wind ions
and the acceleration of electrons which carry the interplanetary magnetic field
through the MPB into the Magnetic Pileup Region. We find that the thickness of
the MPB current layer is of the order of both the upstream (magnetosheath)
solar wind proton inertial length and convective gyroradius. This study
provides a high resolution view of one of the components of the current system
around Mars reported in recent works.


  We study parabolic linear Weingarten surfaces in hyperbolic space
$\rlopezh^3$. In particular, we classify two family of parabolic surfaces:
surfaces with constant Gaussian curvature and surfaces that satisfy the
relation $a\kappa_1+b\kappa_2=c$, where $\kappa_i$ are the principal
curvatures, and $a,b$ and $c$ are constant.


  Contextual influences on language often exhibit substantial cross-lingual
regularities; for example, we are more verbose in situations that require finer
distinctions. However, these regularities are sometimes obscured by semantic
and syntactic differences. Using a newly-collected dataset of color reference
games in Mandarin Chinese (which we release to the public), we confirm that a
variety of constructions display the same sensitivity to contextual difficulty
in Chinese and English. We then show that a neural speaker agent trained on
bilingual data with a simple multitask learning approach displays more
human-like patterns of context dependence and is more pragmatically informative
than its monolingual Chinese counterpart. Moreover, this is not at the expense
of language-specific semantic understanding: the resulting speaker model learns
the different basic color term systems of English and Chinese (with noteworthy
cross-lingual influences), and it can identify synonyms between the two
languages using vector analogy operations on its output layer, despite having
no exposure to parallel data.


  We prove that the Gibbs measures $\rho$ for a class of Hamiltonian equations
written $\partial_t u = J (-\triangle u + V'(|u|^2)u)$ on the real line are
invariant under the flow of this equation in the sense that there exist random
variables $X(t)$ whose laws are $\rho$ (thus independent from $t$) and such
that $t\mapsto X(t)$ is a solution to the above equation. Besides, for all $t$,
$X(t)$ is almost surely not in $L^2$ which provides as a direct consequence the
existence of weak solutions for initial data not in $L^2$. The proof uses
Prokhorov's theorem, Skorohod's theorem, as in the strategy in \cite{burqtzv}
and Feynman-Kac's integrals.


  We discuss several new developments in the field of strange and heavy flavor
physics in high energy heavy ion collisions. As shown by many recent
theoretical works, heavy flavored particles give us a unique opportunity to
study the properties of systems created in these collisions. Two in particular
important aspects, the production of (multi) strange hypernuclei and the
properties of heavy flavor mesons, are at the core of several future facilities
and will be discussed in detail.


  Neutrinos can have naturally small Dirac masses if the Standard Model singlet
right-handed neutrinos are light composite fermions. Theories which produce
light composite fermions typically generate many of them, three of which can
marry the left-handed neutrinos with small Dirac masses. The rest can serve as
sterile states which can mix with the Standard Model neutrinos. We present
explicit models illustrating this idea.


  This paper provides theoretical insights into why and how deep learning can
generalize well, despite its large capacity, complexity, possible algorithmic
instability, nonrobustness, and sharp minima, responding to an open question in
the literature. We also discuss approaches to provide non-vacuous
generalization guarantees for deep learning. Based on theoretical observations,
we propose new open problems and discuss the limitations of our results.


  We present data of 10 penumbral microjets (PMJs) observed in H\alpha, Ca II
8542 \AA, and Fe I 6302 \AA line pair with the Swedish 1 m Solar Telescope
(SST) with CRISP and Ca II K with SST/CHROMIS in active region NOAA 12599 on
the 12th October 2016 at \mu=0.68. All four Stokes parameters of the Ca II 8542
\AA and Fe I 6302 \AA lines were observed and a series of test pixels was
inverted using the Stockholm inversion code. Our analysis revealed for the
first time that PMJs are visible in H\alpha, where they appear as dark features
with average line-of-sight (LOS) upflows of 1.1\pm0.6 km/s, matching the LOS
velocities from the inversions. Based on the H\alpha observations we extend the
previous average length and lifetime of PMJs to 2815\pm530 km and 163\pm25 s,
respectively. The plane-of-sky (POS) velocities of our PMJs of up to 17 km/s
tend to give increased velocities with distance travelled. Furthermore, two of
our PMJs with significant Stokes V signal indicate that the PMJs possess an
increased LOS magnetic field of up to 100 G compared to the local pre-/post-
PMJ magnetic field, which propagates as quickly as the PMJs' POS velocities.
Finally, we present evidence that PMJs display an on average 1 minute gradual
precursory brightening that only manifests itself in the cores of the Ca II
lines. We conclude that PMJs are not ordinary jets but likely are
manifestations of heat fronts that propagate at the local Alfven velocity.


  Deep learning enabled semantic communication has been studied to improve
communication efficiency while guaranteeing intelligent task performance.
Different from conventional communications systems, the resource allocation in
semantic communications no longer just pursues the bit transmission rate, but
focuses on how to better compress and transmit semantic to complete subsequent
intelligent tasks. This paper aims to appropriately allocate the bandwidth and
power for artificial intelligence (AI) task-oriented semantic communication and
proposes a joint compressiom ratio and resource allocation (CRRA) algorithm. We
first analyze the relationship between the AI task's performance and the
semantic information. Then, to optimize the AI task's perfomance under resource
constraints, a bandwidth and power allocation problem is formulated. The
problem is first separated into two subproblems due to the non-convexity. The
first subproblem is a compression ratio optimization problem with a given
resource allocation scheme, which is solved by a enumeration algorithm. The
second subproblem is to find the optimal resource allocation scheme, which is
transformed into a convex problem by successive convex approximation method,
and solved by a convex optimization method. The optimal semantic compression
ratio and resource allocation scheme are obtained by iteratively solving these
two subproblems. Simulation results show that the proposed algorithm can
efficiently improve the AI task's performance by up to 30\% comprared with
baselines.


  Advances in fluorescence microscopy enable acquisition of 3D image volumes
with better image quality and deeper penetration into tissue. Segmentation is a
required step to characterize and analyze biological structures in the images
and recent 3D segmentation using deep learning has achieved promising results.
One issue is that deep learning techniques require a large set of groundtruth
data which is impractical to annotate manually for large 3D microscopy volumes.
This paper describes a 3D deep learning nuclei segmentation method using
synthetic 3D volumes for training. A set of synthetic volumes and the
corresponding groundtruth are generated using spatially constrained
cycle-consistent adversarial networks. Segmentation results demonstrate that
our proposed method is capable of segmenting nuclei successfully for various
data sets.


  The problem of critical velocities in superfluids, that is the comprehension
of superfluidity breakdown by flow, has been long standing. One difficulty
stems from the existence of several breakdown mechanisms. A major advance has
come from the observation of single $2\pi$ phase slips, which arise from the
nucleation of quantised vortices, that is, their creation {\it ex nihilo}. The
statistical properties of the nucleation process in both the thermal regime and
the quantum regime are identified and analysed: vortex nucleation provides a
well-documented case of macroscopic quantum tunnelling (MQT). In particular, a
close scrutiny of the experimental data obtained on ultra-pure $^4$He reveals
the influence of damping on tunnelling, a rare occurrence where the effect of
the environment on MQT can be studied.


  We present the first results of our dedicated programme of automatised
classification of galaxies, stars and quasars in the mid-infrared all-sky data
from the WISE survey. We employ the Support Vector Machines (SVM) algorithm,
which defines a hyperplane separating different classes of sources in a
multidimensional space of arbitrarily chosen parameters. This approach consists
of four general steps: 1) selection of the training sample, 2) selection of the
optimal parameter space, 3) training of the classifier, 4) application to
target data. Here, as the training set, we use sources from a cross-correlation
of the WISE catalogue with the SDSS spectroscopic sample. The performance of
the SVM classifier was tested as a function of size of the training set,
dimension of the parameter space, WISE apparent magnitude and Galactic
extinction. We find that our classifier provides promising results already for
three classification parameters: magnitude, colour and differential aperture
magnitude. Completeness and purity levels as high as 95% are obtained for
quasars, while for galaxies and stars they vary between 80-95% depending on the
magnitude, deteriorating for fainter sources.


  Training segmentation models for medical images continues to be challenging
due to the limited availability of data annotations. Segment Anything Model
(SAM) is a foundation model that is intended to segment user-defined objects of
interest in an interactive manner. While the performance on natural images is
impressive, medical image domains pose their own set of challenges. Here, we
perform an extensive evaluation of SAM's ability to segment medical images on a
collection of 19 medical imaging datasets from various modalities and
anatomies. We report the following findings: (1) SAM's performance based on
single prompts highly varies depending on the dataset and the task, from
IoU=0.1135 for spine MRI to IoU=0.8650 for hip X-ray. (2) Segmentation
performance appears to be better for well-circumscribed objects with prompts
with less ambiguity and poorer in various other scenarios such as the
segmentation of brain tumors. (3) SAM performs notably better with box prompts
than with point prompts. (4) SAM outperforms similar methods RITM, SimpleClick,
and FocalClick in almost all single-point prompt settings. (5) When
multiple-point prompts are provided iteratively, SAM's performance generally
improves only slightly while other methods' performance improves to the level
that surpasses SAM's point-based performance. We also provide several
illustrations for SAM's performance on all tested datasets, iterative
segmentation, and SAM's behavior given prompt ambiguity. We conclude that SAM
shows impressive zero-shot segmentation performance for certain medical imaging
datasets, but moderate to poor performance for others. SAM has the potential to
make a significant impact in automated medical image segmentation in medical
imaging, but appropriate care needs to be applied when using it.


  Interactive lenses are useful tools for supporting the analysis of data in
different ways. Most existing lenses are designed for 2D visualization and are
operated using standard mouse and keyboard interaction. On the other hand,
research on virtual lenses for novel 3D immersive visualization environments is
scarce. Our work aims to narrow this gap in the literature. We focus
particularly on the interaction with lenses. Inspired by natural interaction
with magnifying glasses in the real world, our lenses are designed as graspable
tools that can be created and removed as needed, manipulated and parameterized
depending on the task, and even combined to flexibly create new views on the
data. We implemented our ideas in a system for the visual analysis of 3D sonar
data. Informal user feedback from more than a hundred people suggests that the
designed lens interaction is easy to use for the task of finding a hidden wreck
in sonar data.


  In order to study the running coupling in four-flavour QCD, we review the
set-up of the Schr\"odinger functional (SF) with staggered quarks. Staggered
quarks require lattices which, in the usual counting, have even spatial lattice
extent $L/a$ while the time extent $T/a$ must be odd. Setting $T=L$ is
therefore only possible up to ${\rm O}(a)$, which introduces different cutoff
effects already in the pure gauge theory. We re-define the SF such as to cope
with this situation and determine the corresponding classical background field.
A perturbative calculation yields the coefficient of the pure gauge ${\rm
O}(a)$ boundary counterterm to one-loop order.


  The non-proper value set of a nonsingular polynomial map from $\C^2$ into
itself, if non-empty, must be a curve with one point at infinity.


  We present an example of SUSY SU(6) GUT, which predicts an excellent value
for $\al_s(M_Z)(\simeq 0.119)$, in comparison with the value
$\al_s^0(M_Z)\simeq 0.126$ of minimal SUSY SU(5). A crucial role is played by
the vectorlike multiplets from the matter sector, whose masses lie below the
GUT scale. For a realistic pattern of fermion masses, the adjoint scalar of
SU(6) has VEV along the $SU(4)\times SU(2)\times U(1)$ direction. This also
offers a natural resolution of the doublet-triplet (DT) splitting through the
pseudo Goldstone Boson mechanism.


  We describe a detailed study on the properties of alkali atoms in extrasolar
giant planets, and specifically focus on their role in generating the
atmospheric free electron densities, as well as their impact on the transit
depth observations. We focus our study on the case of HD 209458 b, and we show
that photoionization produces a large electron density in the middle atmosphere
that is about two orders of magnitude larger than the density anticipated from
thermal ionization. Our purely photochemical calculations though result in a
much larger transit depth for K than observed for this planet. This result does
not change even if the roles of molecular chemistry and excited state chemistry
are considered for the alkali atoms. In contrast, the model results for the
case of exoplanet XO-2 b are in good agreement with the available observations.
Given these results we discuss other possible scenarios, such as changes in the
elemental abundances, changes in the temperature profiles, and the possible
presence of clouds, which could potentially explain the observed HD 209458 b
alkali properties. We find that most of these scenarios can not explain the
observations, with the exception of a heterogeneous source (i.e. clouds or
aerosols) under specific conditions, but we also note the discrepancies among
the available observations.


  In this paper we show that on a general sextic hypersurface $X\subset \bf
P^4$, a rank 2 vector bundle $E$ splits if and only if $h^1(E(n))=0$ for any $n
\in \bf Z$. We get thus a characterization of complete intersection curves in
$X$


  Beyond Bose and Fermi statistics, there still exist various kinds of
generalized quantum statistics. Two ways to approach generalized quantum
statistics: (1) in quantum mechanics, generalize the permutation symmetry of
the wave function and (2) in statistical mechanics, generalize the maximum
occupation number of quantum statistics. The connection between these two
approaches, however, is obscure. In this paper, we suggest a unified framework
to describe various kinds of generalized quantum statistics. We first provide a
general formula of canonical partition functions of ideal $N$-particle gases
obeying various kinds of generalized quantum statistics. Then we reveal the
connection between the permutation phase of the wave function and the maximum
occupation number, through constructing a method to obtain the permutation
phase and the maximum occupation number from the canonical partition function.
In our scheme, the permutation phase of wave functions is generalized to a
matrix phase, rather than a number. It is commonly accepted that different
kinds of statistics are distinguished by the maximum number. We show that the
maximum occupation number is not sufficient to distinguish different kinds of
generalized quantum statistics. As examples, we discuss a series of generalized
quantum statistics in the unified framework, giving the corresponding canonical
partition functions, maximum occupation numbers, and the permutation phase of
wave functions. Especially, we propose three new kinds of generalized quantum
statistics which seem to be the missing pieces in the puzzle. The mathematical
basis of the scheme are the mathematical theory of the invariant matrix, the
Schur-Weyl duality, the symmetric function, and the representation theory of
the permutation group and the unitary group. The result in this paper builds a
bridge between the statistical mechanics and such mathematical theories.


  We consider the problem of consistently matching multiple sets of elements to
each other, which is a common task in fields such as computer vision. To solve
the underlying NP-hard objective, existing methods often relax or approximate
it, but end up with unsatisfying empirical performance due to a misaligned
objective. We propose a coordinate update algorithm that directly optimizes the
target objective. By using pairwise alignment information to build an
undirected graph and initializing the permutation matrices along the edges of
its Maximum Spanning Tree, our algorithm successfully avoids bad local optima.
Theoretically, with high probability our algorithm guarantees an optimal
solution under reasonable noise assumptions. Empirically, our algorithm
consistently and significantly outperforms existing methods on several
benchmark tasks on real datasets.


  We present a method for the propagation of partially coherent radiation using
coherent mode decomposition and wavefront propagation. The radiation field is
decomposed into a sum of independent coherent modes. Each mode is then
propagated separately using conventional wavefront propagation techniques. The
summation of these modes in the plane of observation gives the coherence
properties of the propagated radiation. As an example, we analyze propagation
of partially coherent radiation transmitted through a single circular aperture.


  Modern weather and climate models share a common heritage, and often even
components, however they are used in different ways to answer fundamentally
different questions. As such, attempts to emulate them using machine learning
should reflect this. While the use of machine learning to emulate weather
forecast models is a relatively new endeavour there is a rich history of
climate model emulation. This is primarily because while weather modelling is
an initial condition problem which intimately depends on the current state of
the atmosphere, climate modelling is predominantly a boundary condition
problem. In order to emulate the response of the climate to different drivers
therefore, representation of the full dynamical evolution of the atmosphere is
neither necessary, or in many cases, desirable. Climate scientists are
typically interested in different questions also. Indeed emulating the
steady-state climate response has been possible for many years and provides
significant speed increases that allow solving inverse problems for e.g.
parameter estimation. Nevertheless, the large datasets, non-linear
relationships and limited training data make Climate a domain which is rich in
interesting machine learning challenges.
  Here I seek to set out the current state of climate model emulation and
demonstrate how, despite some challenges, recent advances in machine learning
provide new opportunities for creating useful statistical models of the
climate.


  We explore the photon population dynamics in two coupled circuit QED systems.
For a sufficiently weak inter-cavity photon hopping, as the photon-cavity
coupling increases, the dynamics undergoes double transitions first from a
delocalized to a localized phase and then from the localized to another
delocalized phase. The latter delocalized phase is distinguished from the
former one; instead of oscillating between the two cavities, the photons
rapidly quasi-equilibrate over the two cavities. These intrigues are attributed
to an interplay between two qualitatively distinctive nonlinear behaviors of
the circuit QED systems in the utrastrong coupling regime, whose distinction
has been widely overlooked.


  Existing color sampling based alpha matting methods use the compositing
equation to estimate alpha at a pixel from pairs of foreground (F) and
background (B) samples. The quality of the matte depends on the selected (F,B)
pairs. In this paper, the matting problem is reinterpreted as a sparse coding
of pixel features, wherein the sum of the codes gives the estimate of the alpha
matte from a set of unpaired F and B samples. A non-parametric probabilistic
segmentation provides a certainty measure on the pixel belonging to foreground
or background, based on which a dictionary is formed for use in sparse coding.
By removing the restriction to conform to (F,B) pairs, this method allows for
better alpha estimation from multiple F and B samples. The same framework is
extended to videos, where the requirement of temporal coherence is handled
effectively. Here, the dictionary is formed by samples from multiple frames. A
multi-frame graph model, as opposed to a single image as for image matting, is
proposed that can be solved efficiently in closed form. Quantitative and
qualitative evaluations on a benchmark dataset are provided to show that the
proposed method outperforms current state-of-the-art in image and video
matting.


  We propose a new sampling algorithm combining two quite powerful ideas in the
Markov chain Monte Carlo literature -- adaptive Metropolis sampler and
two-stage Metropolis-Hastings sampler. The proposed sampling method will be
particularly very useful for high-dimensional posterior sampling in Bayesian
models with expensive likelihoods. In the first stage of the proposed
algorithm, an adaptive proposal is used based on the previously sampled states
and the corresponding acceptance probability is computed based on an
approximated inexpensive target density. The true expensive target density is
evaluated while computing the second stage acceptance probability only if the
proposal is accepted in the first stage. The adaptive nature of the algorithm
guarantees faster convergence of the chain and very good mixing properties. On
the other hand, the two-stage approach helps in rejecting the bad proposals in
the inexpensive first stage, making the algorithm computationally efficient. As
the proposals are dependent on the previous states the chain loses its Markov
property, but we prove that it retains the desired ergodicity property. The
performance of the proposed algorithm is compared with the existing algorithms
in two simulated and two real data examples.


  We study the projective behavior, mainly with respect to osculating spaces
and secant varieties, of Lagrangian Grassmannians and Spinor varieties. We
prove that these varieties have osculating dimension smaller than expected.
Furthermore, we give numerical conditions ensuring the non secant defectivity
of Lagrangian Grassmannians in their Pl\"ucker embedding and of Spinor
varieties in both their Pl\"ucker and Spinor embeddings.


  Language has been useful in extending the vision encoder to data from diverse
distributions without empirical discovery in training domains. However, as the
image description is mostly at coarse-grained level and ignores visual details,
the resulted embeddings are still ineffective in overcoming complexity of
domains at inference time. We present a self-supervision framework WIDIn,
Wording Images for Domain-Invariant representation, to disentangle
discriminative visual representation, by only leveraging data in a single
domain and without any test prior. Specifically, for each image, we first
estimate the language embedding with fine-grained alignment, which can be
consequently used to adaptively identify and then remove domain-specific
counterpart from the raw visual embedding. WIDIn can be applied to both
pretrained vision-language models like CLIP, and separately trained uni-modal
models like MoCo and BERT. Experimental studies on three domain generalization
datasets demonstrate the effectiveness of our approach.


  We introduce the first cut-free nested sequent systems for first-order modal
logics that admit increasing, decreasing, constant, and empty domains along
with so-called general path conditions and seriality. We obtain such systems by
means of two devices: 'reachability rules' and 'structural refinement'.
Regarding the former device, we introduce reachability rules as special logical
rules parameterized with formal grammars (viz. types of semi-Thue systems) that
operate by propagating formulae and/or checking if data exists along certain
paths within a nested sequent, where paths are encoded as strings generated by
a parameterizing grammar. Regarding the latter device, structural refinement is
a relatively new methodology used to extract nested sequent systems from
labeled systems (which are ultimately obtained from a semantics) by means of
eliminating structural/relational rules, introducing reachability rules, and
then carrying out a notational translation. We therefore demonstrate how this
method can be extended to the setting of first-order modal logics, and expose
how reachability rules naturally arise from applying this method.


  We characterize the set of planar locally finite Cayley graphs, and give a
finite representation of these graphs by a special kind of finite state
automata called labeling schemes. As a result, we are able to enumerate and
describe all planar locally finite Cayley graphs of a given degree. This
analysis allows us to solve the problem of decision of the locally finite
planarity for a word-problem-decidable presentation.
  Keywords: vertex-transitive, Cayley graph, planar graph, tiling, labeling
scheme


  Three-dimension will be a characteristic of future user interfaces, although
we are just starting to gain an understanding of how users can navigate and
share information within a virtual 3D environment. Three-dimensional graphical
user interfaces (3D-GUI) raise many issues of design, metaphor and usability.
This research is devoted to designing a 3D-GUI as a front-end tool for a file
management system, in this case, for Microsoft Windows\c{opyright} Explorer; as
well as evaluating the efficiency of a 3D application. The software design was
implemented by extending the Half-Life 3D engine. This extension provides a
directory traversal and basic file management functions, like cut, copy, paste,
delete, and so on. This paper shows the design and implementation of a
real-world application that contains an efficient 3D-GUI.


  Our subject of study is strong approximation of stochastic differential
equations (SDEs) with respect to the supremum error criterion, and we seek
approximations that are strongly asymptotically optimal in specific classes of
approximations. We hereby focus on two principal types of classes, namely, the
classes of approximations that are based only on the evaluation of the initial
value and on at most finitely many sequential evaluations of the driving
Brownian motion on average and the classes of approximations that are based
only on the evaluation of the initial value and on finitely many evaluations of
the driving Brownian motion at equidistant sites. For SDEs with globally
Lipschitz continuous coefficients, M\"uller-Gronbach [Ann. Appl. Probab. 12
(2002), no. 2, 664-690] showed that specific Euler-Maruyama schemes relating to
adaptive and to equidistant time discretizations perform strongly
asymptotically optimal in these classes. In the present article, we generalize
these results to a significantly wider class of SDEs, such as ones with
super-linearly growing coefficients. More precisely, we prove strong asymptotic
optimality for specific coefficient-modified Euler-Maruyama schemes relating to
adaptive and to equidistant time discretizations under rather mild assumptions
on the underlying SDE. To illustrate our findings, we present two exemplary
applications - namely, Euler-Maruyama schemes and tamed Euler schemes - and
thereby analyze the SDE associated with the Heston-$3/2$-model originating from
mathematical finance.


  We present the first polynomial time algorithm for the f vertex fault
tolerant spanner problem, which achieves almost optimal spanner size. Our
algorithm for constructing f vertex fault tolerant spanner takes $O(k\cdot
n\cdot m^2 \cdot W)$ time, where W is the maximum edge weight, and constructs a
spanner of size $O(n^{1+1/k}f^{1-1/k}\cdot (\log n)^{1-1/k})$. Our spanner has
almost optimal size and is at most a $\log n$ factor away from the upper bound
on the worst-case size. Prior to this work, no other polynomial time algorithm
was known for constructing f vertex fault tolerant spanner with optimal size.
  Our algorithm is based on first greedily constructing a hitting set for the
collection of paths of weight at most $k \cdot w(u,v)$ between the endpoints u
and v of an edge (u,v) and then using this set to decide whether the edge (u,v)
needs to be added to the growing spanner.


  We report a design and experimental realization of a three-dimensional (3D)
acoustic double-zero-index medium (DZIM), whose effective mass density and
compressibility are nearly zero simultaneously. The DZIM is constructed from a
cubic lattice of three orthogonally-aligned metal rods in air. The combination
of lattice symmetry and accidental degeneracy yields a four-fold degenerate
point with conical dispersion at the Brillouin zone center, where the material
becomes a 3D DZIM. Though occupying a finite volume, the 3D DZIM maintains the
wave properties of a "void space," and enables rich applications. For
demonstration, we fabricate an acoustic "periscope" by placing the designed 3D
DZIM inside a 3D bending waveguide, and observe the unusual wave tunneling
effect through this waveguide with undisturbed planar wavefront. Our findings
establish a practical route to realize 3D DZIM as an effective acoustic "void
space," which offers unprecedented opportunities for advanced sound
manipulation.


  We examine the percolation model in $\mathbb{Z}^d$ by an approach involving
lattice animals, in which their relevant characteristic is
surface-area-to-volume ratio. Two critical exponents are introduced. The first
is related to the growth rate in size of the number of lattice animals up to
translation whose surface-area-to-volume ratio is marginally greater than
$1/p_c -1$. The second describes how unusually large clusters form in the
percolation model at parameter values slightly below $p_c$. Certain
inequalities on the pair of exponents cannot be satisfied, while others imply
the continuity of the percolation probability. The first exponent is related to
one of a more conventional nature, that of correlation size.
  In this paper, the central aspects of the approach are described, and the
proofs of the main results are presented. The report located at math.PR/0402026
gives complete proofs of all of the assertions.


  In recent years, deep learning methods have shown impressive results for
camera-based remote physiological signal estimation, clearly surpassing
traditional methods. However, the performance and generalization ability of
Deep Neural Networks heavily depends on rich training data truly representing
different factors of variation encountered in real applications. Unfortunately,
many current remote photoplethysmography (rPPG) datasets lack diversity,
particularly in darker skin tones, leading to biased performance of existing
rPPG approaches. To mitigate this bias, we introduce PhysFlow, a novel method
for augmenting skin diversity in remote heart rate estimation using conditional
normalizing flows. PhysFlow adopts end-to-end training optimization, enabling
simultaneous training of supervised rPPG approaches on both original and
generated data. Additionally, we condition our model using CIELAB color space
skin features directly extracted from the facial videos without the need for
skin-tone labels. We validate PhysFlow on publicly available datasets,
UCLA-rPPG and MMPD, demonstrating reduced heart rate error, particularly in
dark skin tones. Furthermore, we demonstrate its versatility and adaptability
across different data-driven rPPG methods.


  We present the discovery and characterisation of two transiting planets
observed by \textit{TESS} in the light curves of the young and bright (V=9.67)
star HD73583 (TOI-560). We perform an intensive spectroscopic and photometric
space- and ground-based follow-up in order to confirm and characterise the
system. We found that HD73583 is a young ($\sim 500$~Myr) active star with a
rotational period of $12.08 \pm 0.11 $\,d, and a mass and radius of $ 0.73 \pm
0.02 M_\odot$ and $0.65 \pm 0.02 R_\odot$, respectively. HD73583 b
($P_b=6.3980420 _{ - 0.0000062 }^{+0.0000067}$ d) has a mass and radius of
$10.2 _{-3.1}^{+3.4} M_\oplus$ and$2.79 \pm 0.10 R_\oplus$, respectively, that
gives a density of $2.58 _{-0.81}^{ 0.95} {\rm g\,cm^{-3}}$. HD73583 c ($P_c=
18.87974 _{-0.00074 }^{+0.00086}$) has a mass and radius of $9.7_{-1.7} ^
{+1.8} M_\oplus$ and $2.39_{-0.09}^{+0.10} R_\oplus$, respectively, this
translates to a density of $3.88 _{-0.80}^{+0.91} {\rm g\,cm^{-3}}$. Both
planets are consistent with worlds made of a solid core surrounded by a
volatile envelope. Because of their youth and host star brightness, they both
are excellent candidates to perform transmission spectroscopy studies. We
expect ongoing atmospheric mass-loss for both planets caused by stellar
irradiation. We estimate that the detection of evaporating signatures on H and
He would be challenging, but doable with present and future instruments.


  Shape restrictions on functional regression coefficients such as
non-negativity, monotonicity, convexity or concavity are often available in the
form of a prior knowledge or required to maintain a structural consistency in
functional regression models. A new estimation method is developed in
shape-constrained functional regression models using Bernstein polynomials.
Specifically, estimation approaches from nonparametric regression are extended
to functional data, properly accounting for shape-constraints in a large class
of functional regression models such as scalar-on-function regression (SOFR),
function-on-scalar regression (FOSR), and function-on-function regression
(FOFR). Theoretical results establish the asymptotic consistency of the
constrained estimators under standard regularity conditions. A projection based
approach provides point-wise asymptotic confidence intervals for the
constrained estimators. A bootstrap test is developed facilitating testing of
the shape constraints. Numerical analysis using simulations illustrate
improvement in efficiency of the estimators from the use of the proposed method
under shape constraints. Two applications include i) modeling a drug effect in
a mental health study via shape-restricted FOSR and ii) modeling
subject-specific quantile functions of accelerometry-estimated physical
activity in the Baltimore Longitudinal Study of Aging (BLSA) as outcomes via
shape-restricted quantile-function on scalar regression (QFOSR). R software
implementation and illustration of the proposed estimation method and the test
is provided.


  Vision is a major component in several digital technologies and tools used in
agriculture. The object detector, You Look Only Once (YOLO), has gained
popularity in agriculture in a relatively short span due to its
state-of-the-art performance. YOLO offers real-time detection with good
accuracy and is implemented in various agricultural tasks, including
monitoring, surveillance, sensing, automation, and robotics. The research and
application of YOLO in agriculture are accelerating rapidly but are fragmented
and multidisciplinary. Moreover, the performance characteristics (i.e.,
accuracy, speed, computation) of the object detector influence the rate of
technology implementation and adoption in agriculture. Thus, the study aims to
collect extensive literature to document and critically evaluate the advances
and application of YOLO for agricultural object recognition. First, we
conducted a bibliometric review of 257 articles to understand the scholarly
landscape of YOLO in agricultural domain. Secondly, we conducted a systematic
review of 30 articles to identify current knowledge, gaps, and modifications in
YOLO for specific agricultural tasks. The study critically assesses and
summarizes the information on YOLO's end-to-end learning approach, including
data acquisition, processing, network modification, integration, and
deployment. We also discussed task-specific YOLO algorithm modification and
integration to meet the agricultural object or environment-specific challenges.
In general, YOLO-integrated digital tools and technologies show the potential
for real-time, automated monitoring, surveillance, and object handling to
reduce labor, production cost, and environmental impact while maximizing
resource efficiency. The study provides detailed documentation and
significantly advances the existing knowledge on applying YOLO in agriculture,
which can greatly benefit the scientific community.


  We consider complete graphs with edge weights and/or node weights taking
values in some set. In the first part of this paper, we show that a large
number of graphs are completely determined, up to isomorphism, by the
distribution of their sub-triangles. In the second part, we propose graph
representations in terms of one-dimensional distributions (e.g., distribution
of the node weights, sum of adjacent weights, etc.). For the case when the
weights of the graph are real-valued vectors, we show that all graphs, except
for a set of measure zero, are uniquely determined, up to isomorphism, from
these distributions. The motivating application for this paper is the problem
of browsing through large sets of graphs.


  Autonomous UAV path planning for 3D reconstruction has been actively studied
in various applications for high-quality 3D models. However, most existing
works have adopted explore-then-exploit, prior-based or exploration-based
strategies, demonstrating inefficiency with repeated flight and low autonomy.
In this paper, we propose PredRecon, a prediction-boosted planning framework
that can autonomously generate paths for high 3D reconstruction quality. We
obtain inspiration from humans can roughly infer the complete construction
structure from partial observation. Hence, we devise a surface prediction
module (SPM) to predict the coarse complete surfaces of the target from the
current partial reconstruction. Then, the uncovered surfaces are produced by
online volumetric mapping waiting for observation by UAV. Lastly, a
hierarchical planner plans motions for 3D reconstruction, which sequentially
finds efficient global coverage paths, plans local paths for maximizing the
performance of Multi-View Stereo (MVS), and generates smooth trajectories for
image-pose pairs acquisition. We conduct benchmarks in the realistic simulator,
which validates the performance of PredRecon compared with the classical and
state-of-the-art methods. The open-source code is released at
https://github.com/HKUST-Aerial-Robotics/PredRecon.


  Localization and dephasing of conduction electrons in a low carrier density
ferromagnet due to scattering on magnetic fluctuations is considered. We claim
the existence of the "mobility edge", which separates the states with fast
diffusion and the states with slow diffusion; the latter is determined by the
dephasing time. When the "mobility edge" crosses the Fermi energy a large and
sharp change of conductivity is observed. The theory provides an explanation
for the observed temperature dependence of conductivity in ferromagnetic
semiconductors and manganite pyrochlores.


  "Net neutrality" often refers to the policy dictating that an Internet
service provider (ISP) cannot charge content providers (CPs) for delivering
their content to consumers. Many past quantitative models designed to determine
whether net neutrality is a good idea have been rather equivocal in their
conclusions. Here we propose a very simple two-sided market model, in which the
types of the consumers and the CPs are {\em power-law distributed} --- a kind
of distribution known to often arise precisely in connection with
Internet-related phenomena. We derive mostly analytical, closed-form results
for several regimes: (a) Net neutrality, (b) social optimum, (c) maximum
revenue by the ISP, or (d) maximum ISP revenue under quality differentiation.
One unexpected conclusion is that (a) and (b) will differ significantly, unless
average CP productivity is very high.


  We propose a modified moment matching algorithm to avoid catastrophic
failures for sources with a low signal to noise ratio (SNR). The proposed
modifications include a method to eliminate non-physical negative pixel values
and a forced single iteration with an initial guess derived from co-add
measurements when iterative methods are unstable. We correct for all biases in
measurements introduced by the method. We find that the proposed modifications
allow the algorithm to avoid catastrophic failures in nearly 100\% of the
cases, especially at low signal to noise ratio. Additionally, with a reasonable
guess from co-add measurements, the algorithm measures the flux, centroid,
size, shape and ellipticity with bias statistically consistent with zero. We
show the proposed method allows us to measure sources seven times fainter than
traditional methods when applied to images obtained from WIYN-ODI. We also
present a scheme to find uncertainties in measurements when using the new
method to measure astronomical sources.


  Large language models (LLMs) have significantly advanced audio processing
through audio codecs that convert audio into discrete tokens, enabling the
application of language modelling techniques to audio data. However,
traditional codecs often operate at high bitrates or within narrow domains such
as speech and lack the semantic clues required for efficient language
modelling. Addressing these challenges, we introduce SemantiCodec, a novel
codec designed to compress audio into fewer than a hundred tokens per second
across diverse audio types, including speech, general audio, and music, without
compromising quality. SemantiCodec features a dual-encoder architecture: a
semantic encoder using a self-supervised AudioMAE, discretized using k-means
clustering on extensive audio data, and an acoustic encoder to capture the
remaining details. The semantic and acoustic encoder outputs are used to
reconstruct audio via a diffusion-model-based decoder. SemantiCodec is
presented in three variants with token rates of 25, 50, and 100 per second,
supporting a range of ultra-low bit rates between 0.31 kbps and 1.43 kbps.
Experimental results demonstrate that SemantiCodec significantly outperforms
the state-of-the-art Descript codec on reconstruction quality. Our results also
suggest that SemantiCodec contains significantly richer semantic information
than all evaluated audio codecs, even at significantly lower bitrates. Our code
and demos are available at https://haoheliu.github.io/SemantiCodec/.


  Convolutional Neural Networks (CNNs) are well-known for their vulnerability
to adversarial attacks, posing significant security concerns. In response to
these threats, various defense methods have emerged to bolster the model's
robustness. However, most existing methods either focus on learning from
adversarial perturbations, leading to overfitting to the adversarial examples,
or aim to eliminate such perturbations during inference, inevitably increasing
computational burdens. Conversely, clean training, which strengthens the
model's robustness by relying solely on clean examples, can address the
aforementioned issues. In this paper, we align with this methodological stream
and enhance its generalizability to unknown adversarial examples. This
enhancement is achieved by scrutinizing the behavior of latent features within
the network. Recognizing that a correct prediction relies on the correctness of
the latent feature's pattern, we introduce a novel and effective Feature
Pattern Consistency Constraint (FPCC) method to reinforce the latent feature's
capacity to maintain the correct feature pattern. Specifically, we propose
Spatial-wise Feature Modification and Channel-wise Feature Selection to enhance
latent features. Subsequently, we employ the Pattern Consistency Loss to
constrain the similarity between the feature pattern of the latent features and
the correct feature pattern. Our experiments demonstrate that the FPCC method
empowers latent features to uphold correct feature patterns even in the face of
adversarial examples, resulting in inherent adversarial robustness surpassing
state-of-the-art models.


  We discuss neutrino masses in the framework of a minimal extension of the
minimal supersymmetric standard model (MSSM) consisting of an additional single
right-handed neutrino superfield $N$ with a heavy Majorana mass $M$, which
induces a single light see-saw mass $m_{\nu_3}$ leaving two neutrinos massless
at tree-level. This trivial extension to the MSSM may account for the
atomospheric neutrino data via $\nu_{\mu}\to \nu_{\tau}$ oscillations by
assuming a near maximal mixing angle $\theta_{23}\sim \pi/4$ and taking $\Delta
m_{23}^2 \sim m_{\nu_3}^2 \sim 2.5\times 10^{-3} eV^2$. In order to account for
the solar neutrino data we appeal to one-loop radiative corrections involving
internal loops of SUSY particles, which we show can naturally generate an
additional light neutrino mass $m_{\nu_{2}}\sim 10^{-5} eV$ again with near
maximal mixing angle $\theta_{12}\sim \pi/4$. The resulting scheme corresponds
to so-called ``bi-maximal'' neutrino mixing involving ``just-so'' solar
oscillations.


  We explain the use of quantum process calculus to describe and analyse linear
optical quantum computing (LOQC). The main idea is to define two processes, one
modelling a linear optical system and the other expressing a specification, and
prove that they are behaviourally equivalent. We extend the theory of
behavioural equivalence in the process calculus Communicating Quantum Processes
(CQP) to include multiple particles (namely photons) as information carriers,
described by Fock states or number states. We summarise the theory in this
paper, including the crucial result that equivalence is a congruence, meaning
that it is preserved by embedding in any context. In previous work, we have
used quantum process calculus to model LOQC but without verifying models
against specifications. In this paper, for the first time, we are able to carry
out verification. We illustrate this approach by describing and verifying two
models of an LOQC CNOT gate.


  In this paper, we investigate the quantization of the output of a binary
input discrete memoryless channel that maximizing the mutual information
between the input and the quantized output under an entropy-constrained of the
quantized output. A polynomial time algorithm is introduced that can find the
truly global optimal quantizer. These results hold for binary input channels
with an arbitrary number of quantized output. Finally, we extend these results
to binary input continuous output channels and show a sufficient condition such
that a single threshold quantizer is an optimal quantizer. Both theoretical
results and numerical results are provided to justify our techniques.


  This paper is devoted to the study of operator-valued Triebel-Lizorkin
spaces. We develop some Fourier multiplier theorems for square functions as our
main tool, and then study the operator-valued Triebel-Lizorkin spaces on
$\mathbb{R}^d$. As in the classical case, we connect these spaces with
operator-valued local Hardy spaces via Bessel potentials. We show the lifting
theorem, and get interpolation results for these spaces. We obtain
Littlewood-Paley type, as well as the Lusin type square function
characterizations in the general way. Finally, we establish smooth atomic
decompositions for the operator-valued Triebel-Lizorkin spaces. These atomic
decompositions play a key role in our recent study of mapping properties of
pseudo-differential operators with operator-valued symbols.


  Sparse direct linear solvers are at the computational core of domain
decomposition preconditioners and therefore have a strong impact on their
performance. In this paper, we consider the Fast and Robust Overlapping Schwarz
(FROSch) solver framework of the Trilinos software library, which contains a
parallel implementations of the GDSW domain decomposition preconditioner. We
compare three different sparse direct solvers used to solve the subdomain
problems in FROSch. The preconditioner is applied to different model problems;
linear elasticity and more complex fully-coupled deformation diffusion-boundary
value problems from chemo-mechanics. We employ FROSch in fully algebraic mode,
and therefore, we do not expect numerical scalability. Strong scalability is
studied from 64 to 4096 cores, where good scaling results are obtained up to
1728 cores. The increasing size of the coarse problem increases the solution
time for all sparse direct solvers.


  We consider the effect of hard core repulsion in the baryon-baryon
interaction at short distance to the properties of a neutron star. We obtain
that, even with hyperons in the interior of a neutron star, the neutron star
mass can be as large as $\sim 2 M_\odot$.


  I will describe some of the events that led to the creation of General
Atomic, a research and development organization founded in San Diego in 1956.


  The standard approach to the long term evolution of pulsar wind nebulae
(PWNe) is based on one-zone models treating the nebula as a uniform system. In
particular for the late phase of evolved systems, many of the generally used
prescriptions are based on educated guesses for which a proper assessment
lacks. Using an advanced radiative code we evaluate the systematic impact of
various parameters, like the properties of the supernova ejecta, of the inner
pulsar, as well of the ambient medium, upon the extent of the reverberation
phase of PWNe. We investigate how different prescriptions shift the starting
time of the reverberation phase, how this affects the amount of the
compression, and how much of this can be ascribable to the radiation processes.
Some critical aspects are the description of the reverse shock evolution, the
efficiency by which at later times material from the ejecta accretes onto the
swept-up shell around the PWN, and finally the density, velocity and pressure
profiles in the surrounding supernova remnant. We have explicitly treated the
cases of the Crab Nebula, and of J1834.9--0846, taken to be representatives of
the more and the less energetic pulsars, respectively. Especially for the
latter object the prediction of large compression factors is confirmed, even
larger in the presence of radiative losses, also confirming our former
prediction of periods of super-efficiency during the reverberation phase of
some PWNe.


  In solids, the response of the lattice to photo-excitation is often described
by the inertial evolution on an impulsively modified potential energy surface
which leads to coherent motion. However, it remains unknown if vibrational
coherence is sustained through a phase transition, during which coupling
between modes can be strong and may lead to rapid loss of coherence. Here we
use coherent phonon spectroscopy to track lattice coherence in the structural
phase transition of V$_2$O$_3$. In both the low and high symmetry phases unique
coherent phonon modes are generated at low fluence. However, coherence is lost
when driving between the low and high symmetry phases. Our results suggest
non-inertial dynamics dominate during phase transition due to disorder and
multi-mode coupling.


  Detecting leaks in Water Distribution Networks (WDN) using sensors has become
crucial towards an efficient management of water resources. The leak detection
methods that use this data rely on the correctness of the acquired data.
However, this assumption is often violated in practice. Consequently, leak
detection under sensor faults is a problem of practical importance. This
relates to the more general problem of simultaneous detectability in sensor and
process faults for a class of systems modelled as a network, by exploiting the
redundancies available through the topological relationship between the
sensors. This paper hence aims at i) modeling WDN as graphs containing both
systems and sensors faults ii) providing theoretical joint detectability
results for such graphs and iii) applying these results to the scenario of leak
identification under sensor faults conditions on real data issued from a rural
WDN.


  The most stringent constraint on the so-called effective electron neutrino
mass from the present neutrinoless double beta decay experiments is |M_{ee}| <
0.2 eV, while the planned next generation experiment GENIUS is anticipated to
reach a considerably more stringent limit |M_{ee}|< 0.001 eV. We investigate
the constraints these bounds set on the neutrino masses and mixings of
neutrinos in four-neutrino models where there exists a sterile neutrino along
with the three ordinary neutrinos. We find that the GENIUS experiment would be
sensitive to the electron neutrino masses down to the limit m_{\nu_e}\lsim
0.024 eV in such a scenario.


  The crushing demand for wireless data services will soon exceed the
capability of the current homogeneous cellular architecture. An emerging
solution is to overlay small-cell networks with the macro-cell networks. In
this paper, we propose an amplitude space sharing (ASS) method among the
macro-cell user and small-cell users. By transmit layer design and data-rate
optimization, the signals and interferences are promised to be separable at
each receiver and the network sum-rate is maximized. The Han-Koboyashi coding
is employed and optimal power allocation is derived for the one small-cell
scenario, and a simple ASS transmission scheme is developed for the multiple
small-cells scenarios. Simulation results show great superiority over other
interference management schemes.


  The Steiner Tree problem is a classical problem in combinatorial
optimization: the goal is to connect a set $T$ of terminals in a graph $G$ by a
tree of minimum size. Karpinski and Zelikovsky (1996) studied the
$\delta$-dense version of {\sc Steiner Tree}, where each terminal has at least
$\delta |V(G)\setminus T|$ neighbours outside $T$, for a fixed $\delta > 0$.
They gave a PTAS for this problem.
  We study a generalization of pairwise $\delta$-dense {\sc Steiner Forest},
which asks for a minimum-size forest in $G$ in which the nodes in each terminal
set $T_1,\dots,T_k$ are connected, and every terminal in $T_i$ has at least
$\delta |T_j|$ neighbours in $T_j$, and at least $\delta|S|$ nodes in $S =
V(G)\setminus (T_1\cup\dots\cup T_k)$, for each $i, j$ in $\{1,\dots, k\}$ with
$i\neq j$. Our first result is a polynomial-time approximation scheme for all
$\delta > 1/2$. Then, we show a $(\frac{13}{12}+\varepsilon)$-approximation
algorithm for $\delta = 1/2$ and any $\varepsilon > 0$. We also consider the
$\delta$-dense Group Steiner Tree problem as defined by Hauptmann and show that
the problem is $\mathsf{APX}$-hard.


  In numerical simulations studying preheating in the classical approximation
there is the problem how to derive the classical initial conditions from the
quantum vacuum fluctuations. In past treatments, the initial conditions often
put an energy density into the classical field of order of the cutoff, leading
to a divergent temperature after thermalization. We suggest a solution to the
problem which follows naturally from a Hartree ensemble approximation,
introduced recently as an improvement over the standard Hartree approximation.
We study the effects on particle numbers of the various treatments, within the
context of `tachyonic preheating' in 1+1 dimensional $\phi^4$ theory.


  Using numerical simulations, we observe phase locking, Arnold tongues, and
Devil's staircases for vortex lattices driven at varying angles with respect to
an underlying superconducting periodic pinning array. This rich structure
should be observalble in transport measurments. The transverse $V(I)$ curves
have a Devil's staircase structure, with plateaus occurring near the driving
angles along symmetry directions of the pinning array. Each of the plateaus
corresponds to a different dyanmical phase with a distinctive vortex structure
and flow pattern.


  The experiment reported in this article addresses manufacturer claims of
fluorocarbon leader material strength versus experimental tests of leaders
strength. Breaking strength of fishing line is the most common specification
when marketing fishing line. In this study, eight leaders rated near 15 pounds
by their manufacturers were tested. Each leader was tested with a knot in the
line and without a knot in the line. The strongest leader tested without a knot
was Cabela's Seaguar fluorocarbon and the weakest leader tested without a knot
was Cabela's Premier leader. The highest strength of leaders with a knot was
the Ande Monofilament Fluorocarbon and the lowest breaking strength of leaders
with a knot was the Seaguar Grand Max Fluorocarbon. Few published studies
actually test the breaking strength of a leader to determine the accuracy of
manufacturers' claims. Tensile strengths are also reported.


  We present a full dynamical model of the Fornax dwarf spheroidal galaxy
obtained with the spherically symmetric Schwarzschild orbit superposition
method applied to the largest kinematic data set presently available. We
modelled the total mass content of the dwarf with the mass-to-light ratio
$\Upsilon$ varying with radius and found that Fornax is with high probability
embedded in a massive and extended dark matter halo. We estimated the total
mass contained within 1$\,$kpc to be $M(<1\,$kpc$)=1.25^{+0.06}_{-0.13} \times
10^8\,$M$_{\odot}$. The data are consistent with the constant mass-to-light
ratio, i.e. the mass-follows-light model, only at 3$\sigma$ level, but still
require a high value of $\Upsilon \approx 11.2\,$M$_{\odot}/$L$_{\odot}$. Our
results are in general agreement with previous estimates of the dynamical mass
profile of Fornax. As the Schwarzschild method does not require any assumptions
on the orbital anisotropy of the stars, we obtained a profile of the anisotropy
parameter $\beta$ as an output of our modelling. The derived anisotropy is
close to zero in the centre of the galaxy and decreases with radius, but
remains consistent with isotropic orbits at all radii at 1$\sigma$ confidence
level.


  Collecting high-quality labeled data for model training is notoriously
time-consuming and labor-intensive for various NLP tasks. While copious
solutions, such as active learning for small language models (SLMs) and
prevalent in-context learning in the era of large language models (LLMs), have
been proposed and alleviate the labeling burden to some extent, their
performances are still subject to human intervention. It is still underexplored
how to reduce the annotation cost in the LLMs era. To bridge this, we
revolutionize traditional active learning and propose an innovative
collaborative learning framework FreeAL to interactively distill and filter the
task-specific knowledge from LLMs. During collaborative training, an LLM serves
as an active annotator inculcating its coarse-grained knowledge, while a
downstream SLM is incurred as a student to filter out high-quality in-context
samples to feedback LLM for the subsequent label refinery. Extensive
experiments on eight benchmark datasets demonstrate that FreeAL largely
enhances the zero-shot performances for both SLM and LLM without any human
supervision. The code is available at https://github.com/Justherozen/FreeAL .


  We determine the abelianizations of the following three kinds of graded Lie
algebras in certain stable ranges: derivations of the free associative algebra,
derivations of the free Lie algebra and symplectic derivations of the free
associative algebra. In each case, we consider both the whole derivation Lie
algebra and its ideal consisting of derivations with positive degrees. As an
application of the last case, and by making use of a theorem of Kontsevich, we
obtain a new proof of the vanishing theorem of Harer concerning the top
rational cohomology group of the mapping class group with respect to its
virtual cohomological dimension.


  We consider autonomous conservative dynamical systems which are constrained
with the condition that the total energy of the system has a specified value.
We prove a theorem which provides the quadratic first integrals (QFIs),
time-dependent and autonomous, of these systems in terms of the symmetries
(conformal Killing vectors and conformal Killing tensors) of the kinetic
metric. It is proved that there are three types of QFIs and for each type we
give explicit formulae for their computation. It is also shown that when the
autonomous QFIs are considered, then we recover the known results of previous
works. For zero potential function, we have the case of constrained geodesics
and obtain formulae to compute their QFIs. The theorem is applied in two cases.
In the first case, we determine potentials which admit the second of the three
types of QFIs. We recover a superintegrable potential of the Ermakov type and a
new integrable potential whose trajectories for zero energy and zero QFI are
circles. In the second case, we integrate the constrained geodesic equations
for a family of two-dimensional conformally flat metrics.


  We consider two saturated Fell bundles over a countable discrete group, whose
unit fibers are $\sigma$-unital $C^*$-algebras. Then by taking the reduced
cross-sectional $C^*$-algebras, we get two inclusions of $C^*$-algebras. We
suppose that they are strongly Morita equivalent as inclusions of
$C^*$-algebras. Also, we suppose that one of the inclusions of $C^*$-algebras
is irreducible, that is, the relative commutant of one of the unit fiber
algebras, which is a $\sigma$-unital $C^*$-algebra, in the multiplier
$C^*$-algebra of the reduced cross-sectional $C^*$-algebra is trivial. We show
that the two saturated Fell bundles are then equivalent up to some automorphism
of the group.


  We perform a systematic numerical study of the effects of the particle-size
ratio $R \ge 1$ on the properties of jammed binary mixtures. We find that
changing $R$ does not qualitatively affect the critical scaling of the pressure
and coordination number with the compression near the jamming transition, but
the critical volume fraction at the jamming transition varies with $R$.
Moreover, the static structure factor (density correlation) $S(k)$ strongly
depends on $R$ and shows distinct long wave-length behaviors between large and
small particles. Thus the previously reported behavior of $S(k)\sim k$ in the
long wave-length limit is only a special case in the $R\to 1$ limit, and cannot
be simply generalized to jammed systems with $R>1$.


  We present a formalism based on the functional Schr\"odinger equation to
analyse time-dependent tunneling in quantum field theory at the semi-classical
level. The full problem is reduced step by step to a finite dimensional quantum
mechanical setup and solved using the WKB approximation. As an example, we
consider tunneling from a homogeneous oscillating initial state in scalar
quantum field theory.


  Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so
contains a \textit{universal $R$-matrix} in the tensor product algebra which
satisfies the Yang-Baxter equation. Applying the vector representation $\pi$,
which acts on the vector module $V$, to one side of a universal $R$-matrix
gives a Lax operator. In this paper a Lax operator is constructed for the
$C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to
find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$
where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included
here as an example.


  We present a V-I color-magnitude diagram for a region 1'-2' from the center
of M32 based on Hubble Space Telescope WFPC2 images. The broad color-luminosity
distribution of red giants shows that the stellar population comprises stars
with a wide range in metallicity. This distribution cannot be explained by a
spread in age. The blue side of the giant branch rises to M_I ~ -4.0 and can be
fitted with isochrones having [Fe/H] ~ -1.5. The red side consists of a heavily
populated and dominant sequence that tops out at M_I ~ -3.2, and extends beyond
V-I=4. This sequence can be fitted with isochrones with -0.2 < [Fe/H] < +0.1,
for ages running from 15 Gyr to 5 Gyr respectively. We do not find the
optically bright asymptotic giant branch stars seen in previous ground-based
work and argue that the majority of them were artifacts of crowding. Our
results are consistent with the presence of the infrared-luminous giants found
in ground-based studies, though their existence cannot be directly confirmed by
our data. There is little evidence for an extended or even a red horizontal
branch, but we find a strong clump on the giant branch itself. If the age
spread is not extreme, the distribution of metallicities in M32 is considerably
narrower than that of the closed-box model of chemical evolution, and also
appears somewhat narrower than that of the solar neighborhood. Overall, the M32
HST color-magnitude diagram is consistent with the average luminosity-weighted
age of 8.5 Gyr and [Fe/H] = -0.25 inferred from integrated spectral indices.


  Integral representation for harmonic function in the ring is constructed in
this work.
  We prove the existence and uniqueness of solutions of the Cauchy problem for
the Laplace equation in the ring. Integral representation for the solution of
the Cauchy problem was found.


  This paper presents a method for real-time estimation of 2-dimensional
direction of arrival (2D-DOA) of one or more sound sources using a nonlinear
array of three microphones. 2D-DOA is estimated employing frame-level time
difference of arrival (TDOA) measurements. Unlike conventional methods, which
infer location parameters from TDOAs using a theoretical model, we propose a
more practical approach based on supervised learning. The proposed model
employs nearest neighbor search (NNS) applied to a spherical Fibonacci lattice
consisting of TDOA to 2D-DOA mappings learned directly in the field. Filtering
and clustering post-processors are also introduced for improved source
detection and localization robustness.


  While the pandemic highlighted the critical role technology plays in
children's lives, not all Australian children have reliable access to
technology. This situation exacerbates educational disadvantage for children
who are already amongst our nation's most vulnerable. In this research project,
we carried out a pilot project with three schools in Western Australia,
conducting a series of workshops and interviews with students, parents, school
staff members, and teachers. Drawing on rich empirical material, we identify
key barriers and enablers for digitally inclusive online learning at the
individual, interpersonal, organizational, and infrastructural levels. Of
particular importance is that technology is only part of this story - an array
of social, environmental, and skills "infrastructure" is needed to facilitate
inclusive online learning. Building on this finding, we ran a Digital Inclusion
Studio to address this holistic set of issues with strongly positive feedback
from participants. We conclude with a set of recommendations for stakeholders
(parents, schools, government agencies) who wish to support more digitally
inclusive learning.


  New criterion of regularity for representation of canonical commutation
relations algebra is given on the basis of concept of an analytical vector.


  We present evidence that PG1159 stars could harbour He--rich envelopes
substantially thinner than those predicted by current evolutionary models with
current estimates of mass loss, which may be attributable to an extensive
mass--loss episode during the born--again AGB phase. Specifically, we show that
the models with thin He--rich envelopes predict remarkably large magnitudes of
the rates of period change of the trapped and untrapped modes observed in the
pulsating star PG 1159$-$035. This is a consequence of the much shorter
evolutionary timescale of the models with thin He--rich envelopes during the
low--gravity PG1159 regime. Our findings are particularly interesting in view
of the suggestion of an evolutionary link between the helium--deficient PG1159
star H1504+65 and the recently discovered white dwarfs with almost pure carbon
atmospheres.


  We study the problem of communication over a compound quantum channel in the
presence of entanglement. Classically such channels are modeled as a collection
of conditional probability distributions wherein neither the sender nor the
receiver is aware of the channel being used for transmission, except for the
fact that it belongs to this collection. We provide near optimal achievability
and converse bounds for this problem in the one-shot quantum setting in terms
of quantum hypothesis testing divergence. We also consider the case of informed
sender, showing a one-shot achievability result that converges appropriately in
the asymptotic and i.i.d. setting. Our achievability proof is similar in spirit
to its classical counterpart. To arrive at our result, we use the technique of
position-based decoding along with a new approach for constructing a union of
two projectors, which can be of independent interest. We give another
application of the union of projectors to the problem of testing composite
quantum hypotheses.


  Potts statistical models have become a popular and promising way to analyze
mutational covariation in protein Multiple Sequence Alignments (MSAs) in order
to understand protein structure, function and fitness. But the statistical
limitations of these models, which can have millions of parameters and are fit
to MSAs of only thousands or hundreds of effective sequences using a procedure
known as inverse Ising inference, are incompletely understood. In this work we
predict how model quality degrades as a function of the number of sequences
$N$, sequence length $L$, amino-acid alphabet size $q$, and the degree of
conservation of the MSA, in different applications of the Potts models: In
"fitness" predictions of individual protein sequences, in predictions of the
effects of single-point mutations, in "double mutant cycle" predictions of
epistasis, and in 3-d contact prediction in protein structure. We show how as
MSA depth $N$ decreases an "overfitting" effect occurs such that sequences in
the training MSA have overestimated fitness, and we predict the magnitude of
this effect and discuss how regularization can help correct for it, use a
regularization procedure motivated by statistical analysis of the effects of
finite sampling. We find that as $N$ decreases the quality of point-mutation
effect predictions degrade least, fitness and epistasis predictions degrade
more rapidly, and contact predictions are most affected. However, overfitting
becomes negligible for MSA depths of more than a few thousand effective
sequences, as often used in practice, and regularization becomes less
necessary. We discuss the implications of these results for users of Potts
covariation analysis.


  3C 400.2 belongs to the mixed morphology supernova remnant class, showing
center-filled X-ray and shell-like radio morphology. We present a study of 3C
400.2 with archival Suzaku and Fermi-LAT observations. We find recombining
plasma (RP) in the Suzaku spectra of north-east and south-east regions. The
spectra of these regions are well described by two-component thermal plasma
models: The hard component is in RP, while the soft component is in collisional
ionization equilibrium (CIE) conditions. The RP has enhanced abundances
indicating that the X-ray emission has an ejecta origin, while the CIE has
solar abundances associated with the interstellar material. The X-ray spectra
of north-west and south-west regions are best fitted by a two-component thermal
plasma model: an ionizing and a CIE plasma. We have detected GeV gamma-ray
emission from 3C 400.2 at the level of $\sim$5$\sigma$ assuming a point-like
source model with a power-law (PL) type spectrum. We have also detected a new
GeV source at the level of $\sim$13$\sigma$ assuming a Gaussian extension model
with a PL type spectrum in the neighborhood of the SNR. We report the analysis
results of 3C 400.2 and the new extended gamma-ray source and discuss the
nature of gamma-ray emission of 3C 400.2 in the context of existing NANTEN CO
data, DRAO HI data, and the Suzaku X-ray analysis results.


  The model of Expansive Nondecelerative Universe exploiting the Vaidya metrics
is used as a tool for unification of gravitation and strong interactions. The
proposed approach stems from the capability to localize the energy of
gravitational field and enables to reach a certain level in unifying the
general theory of relativity and quantum chromodynamics. A relationship between
the energy binding quarks and gravitational energy of virtual black holes is
rationalized.


  Melting of rhombohedral boron subnitride B13N2 has been studied in situ at
pressures to 8 GPa using synchrotron X-ray diffraction and electrical
resistivity measurements. It has been found that above 2.6 GPa B13N2 melts
incongruently, and the melting curve exhibits positive slope of 31(3) K/GPa
that points to a lower density of the melt as compared to the solid phase.


  Freeman Dyson has questioned whether any conceivable experiment in the real
universe can detect a single graviton. If not, is it meaningful to talk about
gravitons as physical entities? We attempt to answer Dyson's question and find
it is possible concoct an idealized thought experiment capable of detecting one
graviton; however, when anything remotely resembling realistic physics is taken
into account, detection becomes impossible, indicating that Dyson's conjecture
is very likely true. We also point out several mistakes in the literature
dealing with graviton detection and production.


  We consider the Maxwell-London electrodynamics of three dimensional
superconductors in p-wave pairing states with nodal points or lines in the
energy gap. The current-velocity relation is then nonlinear in the applied
field, cubic for point nodes and quadratic for lines. We obtain explicit
angular and depth dependent expressions for measurable quantities such as the
transverse magnetic moment, and associated torque. These dependences are
different for point and line nodes and can be used to distinguish between
different order parameters. We discuss the experimental feasibility of this
method, and bring forth its advantages, as well as limitations that might be
present.


  Multi-radio multi-channel (MR-MC) networks contribute significant enhancement
in the network throughput by exploiting multiple radio interfaces and
non-overlapping channels. While throughput optimization is one of the main
targets in allocating resource in MR-MC networks, recently, the network energy
efficiency is becoming a more and more important concern. Although turning on
more radios and exploiting more channels for communication is always beneficial
to network capacity, they may not be necessarily desirable from an energy
efficiency perspective. The relationship between these two often conflicting
objectives has not been well-studied in many existing works. In this paper, we
investigate the problem of optimizing energy efficiency under full capacity
operation in MR-MC networks and analyze the optimal choices of numbers of
radios and channels. We provide detailed problem formulation and solution
procedures. In particular, for homogeneous commodity networks, we derive a
theoretical upper bound of the optimal energy efficiency and analyze the
conditions under which such optimality can be achieved. Numerical results
demonstrate that the achieved optimal energy efficiency is close to the
theoretical upper bound.


  In this paper we present a numerical comparison of various mass-conservative
discretizations for the time-dependent Gross-Pitaevskii equation. We have three
main objectives. First, we want to clarify how purely mass-conservative methods
perform compared to methods that are additionally energy-conservative or
symplectic. Second, we shall compare the accuracy of energy-conservative and
symplectic methods among each other. Third, we will investigate if a linearized
energy-conserving method suffers from a loss of accuracy compared to an
approach which requires to solve a full nonlinear problem in each time-step. In
order to obtain a representative comparison, our numerical experiments cover
different physically relevant test cases, such as traveling solitons,
stationary multi-solitons, Bose-Einstein condensates in an optical lattice and
vortex pattern in a rapidly rotating superfluid. We shall also consider a
computationally severe test case involving a pseudo Mott insulator. Our space
discretization is based on finite elements throughout the paper. We will also
give special attention to long time behavior and possible coupling conditions
between time-step sizes and mesh sizes. The main observation of this paper is
that mass conservation alone will not lead to a competitive method in complex
settings. Furthermore, energy-conserving and symplectic methods are both
reliable and accurate, yet, the energy-conservative schemes achieve a visibly
higher accuracy in our test cases. Finally, the scheme that performs best
throughout our experiments is an energy-conserving relaxation scheme with
linear time-stepping proposed by C. Besse (SINUM,42(3):934--952,2004).


  Accurately and efficiently extracting building footprints from a wide range
of remote sensed imagery remains a challenge due to their complex structure,
variety of scales and diverse appearances. Existing convolutional neural
network (CNN)-based building extraction methods are complained that they cannot
detect the tiny buildings because the spatial information of CNN feature maps
are lost during repeated pooling operations of the CNN, and the large buildings
still have inaccurate segmentation edges. Moreover, features extracted by a CNN
are always partial which restricted by the size of the respective field, and
large-scale buildings with low texture are always discontinuous and holey when
extracted. This paper proposes a novel multi attending path neural network
(MAP-Net) for accurately extracting multiscale building footprints and precise
boundaries. MAP-Net learns spatial localization-preserved multiscale features
through a multi-parallel path in which each stage is gradually generated to
extract high-level semantic features with fixed resolution. Then, an attention
module adaptively squeezes channel-wise features from each path for
optimization, and a pyramid spatial pooling module captures global dependency
for refining discontinuous building footprints. Experimental results show that
MAP-Net outperforms state-of-the-art (SOTA) algorithms in boundary localization
accuracy as well as continuity of large buildings. Specifically, our method
achieved 0.68\%, 1.74\%, 1.46\% precision, and 1.50\%, 1.53\%, 0.82\% IoU score
improvement without increasing computational complexity compared with the
latest HRNetv2 on the Urban 3D, Deep Globe and WHU datasets, respectively. The
TensorFlow implementation is available at https://github.com/lehaifeng/MAPNet.


  Nanoparticles of high refractive index materials can possess strong magnetic
polarizabilities and give rise to artificial magnetism in the optical spectral
range. While the response of individual dielectric or metal spherical particles
can be described analytically via multipole decomposition in the Mie series,
the influence of substrates, in many cases present in experimental
observations, requires different approaches. Here, the comprehensive numerical
studies of the influence of a substrate on the spectral response of high- index
dielectric nanoparticles were performed. In particular, glass, perfect electric
conductor, gold, and hyperbolic metamaterial substrates were investigated.
Optical properties of nanoparticles were characterized via scattering
cross-section spectra, electric field profiles, and induced electric and
magnetic moments. The presence of substrates was shown to introduce significant
impact on particle's magnetic resonances and resonant scattering
cross-sections. Variation of substrate material provides an additional degree
of freedom in tailoring properties of emission of magnetic multipoles,
important in many applications.


  The Orr-Sommerfeld equation is a spectral problem which is known to play an
important role in hydrodynamic stability. For an appropriate operator
theoretical realization of the equation, we will determine the essential
spectrum, and calculate an enclosure of the set of all eigenvalues by
elementary analytical means.


  We propose a definition of varieties over the field with one element. These
have extensions of scalars to the ring of integers which are varieties in the
usual sense. We show that toric varieties can be defined over the field with
one element. We also discuss zeta functions for such objects. We give a motivic
interpretation of the image of the J-homomorphism defined by Adams. ~ ~ ~ ~


  Making use of infinite projected entangled pair states, we investigate the
ground state phase diagram of the nearest-neighbor spin-1 bilinear-biquadratic
Heisenberg model on the triangular lattice. In agreement with previous studies,
we find the ferromagnetic, 120 degree magnetically ordered, ferroquadrupolar
and antiferroquadrupolar phases, and confirm that all corresponding phase
transitions are first order. Moreover, we provide an accurate estimate of the
location of the ferroquadrupolar to 120 degree magnetically ordered phase
transition, thereby fully establishing the phase diagram. Also, we do not
encounter any signs of the existence of a quantum paramagnetic phase. In
particular, contrary to the equivalent square lattice model, we demonstrate
that on the triangular lattice the one-dimensional Haldane phase does not reach
all the way up to the two-dimensional limit. Finally, we investigate the
possibility of an intermediate partially-magnetic partially-quadrupolar phase
close to $\theta = \pi/2$, and we show that, also contrary to the square
lattice case, this phase is not present on the triangular lattice.