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In this paper we prove formal glueing along an arbitrary closed substack $Z$
of an arbitrary Artin stack $X$ (locally of finite type over a field $k$), for
the stacks of (almost) perfect complexes , and of $G$-bundles on $X$ (for $G$ a
smooth affine algebraic $k$-group scheme). By iterating this result, we get a
decomposition of these stacks along an arbitrary nonlinear flag of closed
substacks in $X$. By taking points over the base field, we deduce from this
both a formal glueing, and a flag-related decomposition formula for the
corresponding symmetric monoidal derived $\infty$-categories of (almost)
perfect modules. When $X$ is a quasi-compact and quasi-separated scheme, we
also prove a localization theorem for almost perfect complexes on $X$, which
parallels Thomason's localization results for perfect complexes. This is one of
the main ingredients we need to provide a global characterization of the
category of almost perfect complexes on the punctured formal neighbourhood. We
then extend all of the previous results - i.e. the formal glueing and
flag-decomposition formulas - to the case when $X$ is a derived Artin stack
(locally almost of finite type over a field $k$), for the derived versions of
the stacks of (almost) perfect modules, and of $G$-bundles on $X$. We close the
paper by highlighting some expected progress in the subject matter of this
paper, related to a Geometric Langlands program for higher dimensional
varieties. In an Appendix (for $X$ a variety), we give a precise comparison
between our formal glueing results and the rigid-analytic approach of
Ben-Bassat and Temkin.
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{\it We first give a geometrical description of the action of the parity
operator ($\hat{P}$) on non relativistic spin ${{1}\over{2}}$ Pauli spinors in
terms of bundle theory. The relevant bundle, $SU(2)\odot \Z_2\to O(3)$, is a
non trivial extension of the universal covering group $SU(2)\to SO(3)$.
$\hat{P}$ is the non relativistic limit of the corresponding Dirac matrix
operator ${\cal P}=i\gamma_0$ and obeys $\hat{P}^2=-1$. Then, from the direct
product of O(3) by $\Z_2$, naturally induced by the structure of the galilean
group, we identify, in its double cover, the time reversal operator ($\hat{T}$)
acting on spinors, and its product with $\hat{P}$. Both, $\hat{P}$ and
$\hat{T}$, generate the group $\Z_4 \times \Z_2$. As in the case of parity,
$\hat{T}$ is the non relativistic limit of the corresponding Dirac matrix
operator ${\cal T}=\gamma^3 \gamma^1$, and obeys $\hat{T}^2=-1$.}
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We discuss how tensor polarizations of gravitational waves can suffer Landau
damping in the presence of velocity birefringence, when parity symmetry is
explicitly broken. In particular, we analyze the role of the Nieh-Yan and
Chern-Simons terms in modified theories of gravity, showing how the
gravitational perturbation in collisionless media can be characterized by a
subluminal phase velocity, circumventing the well-known results of General
Relativity and allowing for the appearance of the kinematic damping. We
investigate in detail the connection between the thermodynamic properties of
the medium, such as temperature and mass of the particles interacting with the
gravitational wave, and the parameters ruling the parity violating terms of the
models. In this respect, we outline how the dispersion relations can give rise
in each model to different regions of the wavenumber space, where the phase
velocity is subluminal, superluminal or does not exist. Quantitative estimates
on the considered models indicate that the phenomenon of Landau damping is not
detectable given the sensitivity of present-day instruments.
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In this article, we discuss a couple of nonlinear Galerkin method (NLG) in
finite element set up for viscoelastic fluid flow, mainly equations of motion
arising in the flow of 2D Oldroyd model. We obtain improved error estimate in
$L^{\infty}(\bL^2)$ norm, which is optimal in nature, for linear finite element
approximation, in view of the error estimate available in literature, in
$L^2(\bH^1)$ norm.
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We re-investigate the magnetically frustrated, {\it
diamond-lattice-antiferromagnet} spinels FeAl$_2$O$_4$ and MnAl$_2$O$_4$ using
magnetization measurements and diffuse scattering of polarized neutrons. In
FeAl$_2$O$_4$, macroscopic measurements evidence a "cusp" in zero field-cooled
susceptibility around 13~K. Dynamic magnetic susceptibility and {\it memory
effect} experiments provide results that do not conform with a canonical
spin-glass scenario in this material. Through polarized neutron scattering
studies, absence of long-range magnetic order down to 4~K is confirmed in
FeAl$_2$O$_4$. By modeling the powder averaged differential magnetic neutron
scattering cross-section, we estimate that the spin-spin correlations in this
compound extend up to the third nearest-neighbour shell. The estimated value of
the Land\'{e} $g$ factor points towards orbital contributions from Fe$^{2+}$.
This is also supported by a Curie-Weiss analysis of the magnetic
susceptibility. MnAl$_2$O$_4$, on the contrary, undergoes a magnetic phase
transition into a long-range ordered state below $\approx$ 40~K, which is
confirmed by macroscopic measurements and polarized neutron diffraction.
However, the polarized neutron studies reveal the existence of prominent
spin-fluctuations co-existing with long-range antiferromagnetic order. The
magnetic diffuse intensity suggests a similar short range order as in
FeAl$_2$O$_4$. Results of the present work supports the importance of spin-spin
correlations in understanding magnetic response of frustrated magnets like
$A$-site spinels which have predominant short-range spin correlations
reminiscent of the "spin liquid" state.
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Compressed sensing is a recent set of mathematical results showing that
sparse signals can be exactly reconstructed from a small number of linear
measurements. Interestingly, for ideal sparse signals with no measurement
noise, random measurements allow perfect reconstruction while measurements
based on principal component analysis (PCA) or independent component analysis
(ICA) do not. At the same time, for other signal and noise distributions, PCA
and ICA can significantly outperform random projections in terms of enabling
reconstruction from a small number of measurements. In this paper we ask: given
the distribution of signals we wish to measure, what are the optimal set of
linear projections for compressed sensing? We consider the problem of finding a
small number of linear projections that are maximally informative about the
signal. Formally, we use the InfoMax criterion and seek to maximize the mutual
information between the signal, x, and the (possibly noisy) projection y=Wx. We
show that in general the optimal projections are not the principal components
of the data nor random projections, but rather a seemingly novel set of
projections that capture what is still uncertain about the signal, given the
knowledge of distribution. We present analytic solutions for certain special
cases including natural images. In particular, for natural images, the
near-optimal projections are bandwise random, i.e., incoherent to the sparse
bases at a particular frequency band but with more weights on the
low-frequencies, which has a physical relation to the multi-resolution
representation of images.
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A simple connection between mass M of a particle or a body and time t is
proposed. The flow of time t depends on the relativechange of mass, i.e
\frac{\Delta M}{M}=- \mu dt, where \mu is unknown parameter. Some of the
simplest consequences from proposed dependence are discussed below.
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Computing the agreement between two continuous sequences is of great interest
in statistics when comparing two instruments or one instrument with a gold
standard. The probability of agreement (PA) quantifies the similarity between
two variables of interest, and it is useful for accounting what constitutes a
practically important difference. In this article we introduce a generalization
of the PA for the treatment of spatial variables. Our proposal makes the PA
dependent on the spatial lag. As a consequence, for isotropic stationary and
nonstationary spatial processes, the conditions for which the PA decays as a
function of the distance lag are established. Estimation is addressed through a
first-order approximation that guarantees the asymptotic normality of the
sample version of the PA. The sensitivity of the PA is studied for finite
sample size, with respect to the covariance parameters. The new method is
described and illustrated with real data involving autumnal changes in the
green chromatic coordinate (Gcc), an index of "greenness" that captures the
phenological stage of tree leaves, is associated with carbon flux from
ecosystems, and is estimated from repeated images of forest canopies.
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We investigate a lateral semiconductor quantum dot with a large number of
electrons in the semi-open Fano regime. In transport measurements we observe
three stable series of Fano resonances with similar lineshapes. We present a
simple model explaining the temperature and V_{SD} dependence of the
resonances. The Fano regime allows to investigate phase and coherence of the
electronic wave function and astonishingly, we find no signs of decoherence in
our system.
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We investigate the critical current, $I_C$, of ballistic Josephson junctions
made of encapsulated graphene/boron-nitride heterostructures. We observe a
crossover from the short to the long junction regimes as the length of the
device increases. In long ballistic junctions, $I_S$ is found to scale as
$\propto \exp(-k_bT/\delta E)$. The extracted energies $\delta E$ are
independent of the carrier density and proportional to the level spacing of the
ballistic cavity, as determined from Fabry-Perot oscillations of the junction
normal resistance. As $T\rightarrow 0$ the critical current of a long (or
short) junction saturates at a level determined by the product of $\delta E$
(or $\Delta$) and the number of the junction's transversal modes.
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We prove that if $p>d$ there is a unique gaussian distribution (in the sense
of Evans) on the space $\mathbb{Q}_p[x_1, \ldots, x_n]_{(d)}$ which is
invariant under the action of $\mathrm{GL}(n, \mathbb{Z}_p)$ by change of
variables. This gives the nonarchimedean counterpart of Kostlan's Theorem
\cite{Kostlan93} on the classification of orthogonally (respectively unitarily)
invariant gaussian measures on the space $\mathbb{R}[x_1, \ldots, x_n]_{(d)}$
(respectively $\mathbb{C}[x_1, \ldots, x_n]_{(d)}$). More generally, if $V$ is
an $n$-dimensional vector space over a nonarchimedean local field $K$ with ring
of integers $R$, and if $\lambda$ is a partition of an integer $d$, we study
the problem of determining the invariant lattices in the Schur module
$S_\lambda(V)$ under the action of the group $\mathrm{GL}(n,R)$.
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We report analytic solutions of a recently discovered quasi-exactly solvable
model consisting of two electrons, interacting {\em via} a Coulomb potential,
but restricted to remain on the surface of a $\mathcal{D}$-dimensional sphere.
Polynomial solutions are found for the ground state, and for some higher
($L\le3$) states. Kato cusp conditions and interdimensional degeneracies are
discussed.
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Outflows in the Active Galactic Nucleus (AGN) are considered to play a key
role in the host galaxy evolution through transfer of a large amount of energy.
A Narrow Line Region (NLR) in the AGN is composed of ionized gas extending from
pc-scales to kpc-scales. It has been suggested that shocks are required for
ionization of the NLR gas. If AGN outflows generate such shocks, they will
sweep through the NLR and the outflow energy will be transferred into a
galaxy-scale region. In order to study contribution of the AGN outflow to the
NLR-scale shock, we measure the
[\ion{Fe}{2}]$\lambda12570$/[\ion{P}{2}]$\lambda11886$ line ratio, which is a
good tracer of shocks, using near-infrared spectroscopic observations with
WINERED (Warm INfrared Echelle spectrograph to Realize Extreme Dispersion and
sensitivity) mounted on the New Technology Telescope. Among 13 Seyfert galaxies
we observed, the [\ion{Fe}{2}] and [\ion{P}{2}] lines were detected in 12 and 6
targets, respectively. The [\ion{Fe}{2}]/[\ion{P}{2}] ratios in 4 targets were
found to be higher than 10, which implies the existence of shocks. We also
found that the shock is likely to exist where an ionized outflow, i.e., a blue
wing in [\ion{S}{3}]$\lambda9533$, is present. Our result implies that the
ionized outflow present over a NLR-scale region sweeps through the interstellar
medium and generates a shock.
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In this paper, we study the behavior of the weighted composition operators
acting on Bergman spaces defined on strictly pseudoconvex domains via the
sparse domination technique from harmonic analysis. As a byproduct, we also
prove a weighted type estimate for the weighted composition operators which is
adapted to Sawyer-testing conditions. Our results extend the work by the first
author, Li, Shi and Wick under a much more general setting.
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The purpose of this paper is to study the relations between different
concepts of dispersive solution for the Vlasov-Poisson system in the
gravitational case. Moreover we give necessary conditions for the existence of
partially and totally dispersive solutions and a sufficient condition for the
occurence of statistical dispersion. These conditions take the form of
inequalities involving the energy, the mass and the momentum of the solution.
Examples of dispersive and non-dispersive solutions--steady states, periodic
solutions and virialized solutions--are also considered.
|
The voluminous nature of geospatial temporal data from physical monitors and
simulation models poses challenges to efficient data access, often resulting in
cumbersome temporal selection experiences in web-based data portals. Thus,
selecting a subset of time steps for prioritized visualization and pre-loading
is highly desirable. Addressing this issue, this paper establishes a
multifaceted definition of salient time steps via extensive need-finding
studies with domain experts to understand their workflows. Building on this, we
propose a novel approach that leverages autoencoders and dynamic programming to
facilitate user-driven temporal selections. Structural features, statistical
variations, and distance penalties are incorporated to make more flexible
selections. User-specified priorities, spatial regions, and aggregations are
used to combine different perspectives. We design and implement a web-based
interface to enable efficient and context-aware selection of time steps and
evaluate its efficacy and usability through case studies, quantitative
evaluations, and expert interviews.
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We have studied correlations in the speckle patterns generated by the
scattering of perfect optical vortex (POV) beams and used them for producing a
new-class of coherence functions, namely Bessel coherence functions. Higher
(zeroth) order Bessel coherence functions have been realized in cross
(auto)-correlation between the speckle patterns generated by the scattering of
perfect vortex beams of different orders. We have also studied the propagation
of produced Bessel coherence functions and characterized their divergence with
respect to the radius of their first ring for different orders m=0--4. We
observed that the divergence varies linearly with the order of the coherence
function. We provide the exact analytical expression for the auto-correlation
as well as cross-correlation functions for speckle patterns. Our experimental
results are in good agreement with the analytical results.
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We consider the long-time behaviour of a branching random walk in random
environment on the lattice $\Z^d$. The migration of particles proceeds
according to simple random walk in continuous time, while the medium is given
as a random potential of spatially dependent killing/branching rates. The main
objects of our interest are the annealed moments $< m_n^p > $, i.e., the $p$-th
moments over the medium of the $n$-th moment over the migration and
killing/branching, of the local and global population sizes. For $n=1$, this is
well-understood \cite{GM98}, as $m_1$ is closely connected with the parabolic
Anderson model. For some special distributions, \cite{A00} extended this to
$n\geq2$, but only as to the first term of the asymptotics, using (a recursive
version of) a Feynman-Kac formula for $m_n$.
In this work we derive also the second term of the asymptotics, for a much
larger class of distributions. In particular, we show that $< m_n^p >$ and $<
m_1^{np} >$ are asymptotically equal, up to an error $\e^{o(t)}$. The
cornerstone of our method is a direct Feynman-Kac-type formula for $m_n$, which
we establish using the spine techniques developed in \cite{HR11}.
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We study a model situation in which direct limit ($\text{colim}$) and inverse
limit ($\lim$) do not commute, and offer some computations of their
"commutator".
The homology of a separable metrizable space $X$ has two well-known
approximants: $qH_n(X)$ ("\v{C}ech homology") and $pH_n(X)$ ("\v{C}ech homology
with compact supports"), which are not homology theories but are nevertheless
interesting as they are $\lim\text{colim}$ and $\text{colim}\lim$ applied to
homology of finite simplicial complexes. The homomorphism $\tau_X: pH_n(X)\to
qH_n(X)$, which is a special case of the natural map
$\text{colim}\lim\to\lim\text{colim}$, need not be either injective (P. S.
Alexandrov, 1947) or surjective (E. F. Mishchenko, 1953), but its surjectivity
for locally compact $X$ remains an open problem. In the case $n=0$ we obtain an
affirmative solution of this problem.
For locally compact $X$, the dual map in cohomology $pH^n(X)\to qH^n(X)$ is
shown to be surjective and its kernel is computed, in terms of $\lim^1$ and a
new functor $\lim^1_{\text{fg}}$. The original map $\tau_X$ is surjective and
its kernel is computed when $X$ is a "coronated polyhedron", i.e. contains a
compactum whose complement is a polyhedron.
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Automated License Plate Recognition(ALPR) is a system that automatically
reads and extracts data from vehicle license plates using image processing and
computer vision techniques. The Goal of LPR is to identify and read the license
plate number accurately and quickly, even under challenging, conditions such as
poor lighting, angled or obscured plates, and different plate fonts and
layouts. The proposed method consists of processing the Bengali low-resolution
blurred license plates and identifying the plate's characters. The processes
include image restoration using GFPGAN, Maximizing contrast, Morphological
image processing like dilation, feature extraction and Using Convolutional
Neural Networks (CNN), character segmentation and recognition are accomplished.
A dataset of 1292 images of Bengali digits and characters was prepared for this
project.
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In the rapidly evolving realm of artificial intelligence, deploying large
language models (LLMs) poses increasingly pressing computational and
environmental challenges. This paper introduces MELODI - Monitoring Energy
Levels and Optimization for Data-driven Inference - a multifaceted framework
crafted to monitor and analyze the energy consumed during LLM inference
processes. MELODI enables detailed observations of power consumption dynamics
and facilitates the creation of a comprehensive dataset reflective of energy
efficiency across varied deployment scenarios. The dataset, generated using
MELODI, encompasses a broad spectrum of LLM deployment frameworks, multiple
language models, and extensive prompt datasets, enabling a comparative analysis
of energy use. Using the dataset, we investigate how prompt attributes,
including length and complexity, correlate with energy expenditure. Our
findings indicate substantial disparities in energy efficiency, suggesting
ample scope for optimization and adoption of sustainable measures in LLM
deployment. Our contribution lies not only in the MELODI framework but also in
the novel dataset, a resource that can be expanded by other researchers. Thus,
MELODI is a foundational tool and dataset for advancing research into
energy-conscious LLM deployment, steering the field toward a more sustainable
future.
|
The brightest class of low mass X-ray binary source: the Z-track sources are
reviewed specifically with regard to the nature of the three distinct states of
the sources. A physical model is presented for the Cygnus X-2 sub-group in
which increasing mass accretion rate takes place on the Normal Branch resulting
in high neutron star temperature and radiation pressure responsible for inner
disk disruption and launching of jets. The Flaring Branch consists of unstable
nuclear burning on the neutron star. It is shown that the Sco X-1 like
sub-group is dominated by almost non-stop flaring consisting of both unstable
burning and increase of Mdot, causing higher neutron star temperatures.
Finally, results of Atoll source surveys are presented and a model for the
nature of the Banana and Island states in these sources is proposed. Motion
along the Banana state is caused by variation of Mdot. Measurements of the high
energy cut-off of the Comptonized emission E_CO provide the electron
temperature T_e of the Comptonizing ADC; above a luminosity of 2x10^37 erg/s
E_CO is a few keV and T_e equals the neutron star temperature. At lower
luminosities, the cut-off energy rises towards 100 keV showing heating of the
corona by an unknown process. This spectral hardening is the cause of the
Island state of Atoll sources. The models for Z-track and Atoll sources thus
constitute a unified model for low mass X-ray binary sources.
|
We introduce CoEdIT, a state-of-the-art text editing system for writing
assistance. CoEdIT takes instructions from the user specifying the attributes
of the desired text, such as "Make the sentence simpler" or "Write it in a more
neutral style," and outputs the edited text. We present a large language model
fine-tuned on a diverse collection of task-specific instructions for text
editing (a total of 82K instructions). Our model (1) achieves state-of-the-art
performance on various text editing benchmarks, (2) is competitive with
publicly available largest-sized LLMs trained on instructions while being
nearly 60x smaller, (3) is capable of generalizing to unseen edit instructions,
and (4) exhibits abilities to generalize to composite instructions containing
different combinations of edit actions. Through extensive qualitative and
quantitative analysis, we show that writers prefer the edits suggested by
CoEdIT relative to other state-of-the-art text editing models. Our code, data,
and models are publicly available at https://github.com/vipulraheja/coedit.
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Many complex multi-target prediction problems that concern large target
spaces are characterised by a need for efficient prediction strategies that
avoid the computation of predictions for all targets explicitly. Examples of
such problems emerge in several subfields of machine learning, such as
collaborative filtering, multi-label classification, dyadic prediction and
biological network inference. In this article we analyse efficient and exact
algorithms for computing the top-$K$ predictions in the above problem settings,
using a general class of models that we refer to as separable linear relational
models. We show how to use those inference algorithms, which are modifications
of well-known information retrieval methods, in a variety of machine learning
settings. Furthermore, we study the possibility of scoring items incompletely,
while still retaining an exact top-K retrieval. Experimental results in several
application domains reveal that the so-called threshold algorithm is very
scalable, performing often many orders of magnitude more efficiently than the
naive approach.
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Mathematical diffraction theory is concerned with the analysis of the
diffraction image of a given structure and the corresponding inverse problem of
structure determination. In recent years, the understanding of systems with
continuous and mixed spectra has improved considerably. Simultaneously, their
relevance has grown in practice as well. In this context, the phenomenon of
homometry shows various unexpected new facets. This is particularly so for
systems with stochastic components. After the introduction to the mathematical
tools, we briefly discuss pure point spectra, based on the Poisson summation
formula for lattice Dirac combs. This provides an elegant approach to the
diffraction formulas of infinite crystals and quasicrystals. We continue by
considering classic deterministic examples with singular or absolutely
continuous diffraction spectra. In particular, we recall an isospectral family
of structures with continuously varying entropy. We close with a summary of
more recent results on the diffraction of dynamical systems of algebraic or
stochastic origin.
|
Topological phylogenetic trees can be assigned edge weights in several
natural ways, highlighting different aspects of the tree. Here the rooted
triple and quartet metrizations are introduced, and applied to formulate novel
fast methods of inferring large trees from rooted triple and quartet data.
These methods can be applied in new statistically consistent procedures for
inference of a species tree from gene trees under the multispecies coalescent
model.
|
We seek a systematic tightening method to represent the monogamy relation for
some measure in multipartite quantum systems. By introducing a family of
parametrized bounds, we obtain tighter lowering bounds for the monogamy
relation compared with the most recently discovered relations. We provide
detailed examples to illustrate why our bounds are better.
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Tunable narrowband spectral filters with high light throughput and wide
dynamic range have remarkable applications such as in optical communications,
optical spectroscopy and spectral imaging. However, a cost is usually
associated with the filter narrowing either in the dynamic range, in the
throughput or the manufacturability. Here we report on a resonating planar
multilayered structure that exhibits transparency window in reflection with a
controllable full width at half maximum (sub-Angstroms till tens of nm) and
tunability over wide spectral range (>500nm in the visible and near infrared).
The phenomenon is observed in TE and TM polarizations with much higher contrast
in TE. Fano type resonance originating from coupling between waveguide modes
and lossy surface electromagnetic waves supported by field distribution
calculations explains the phenomenon. The wide tuning range with high contrast
is mainly achieved using an absorptive layer with high imaginary to real part
ratio of the dielectric constant that enables excitation of lossy surface waves
known to exist over a wide spectral band in thin films. To avoid large losses,
it is found that the lossy layer should be ultrathin (6nm Cr layer for
example). The tuning is achieved by small angular scan of less than 2 degrees
or by modulating the refractive index or thickness of the submicron thick
waveguide layer from the visible till the near infrared range and in principle
it can be designed to operate in any spectral range. Such a thin variable index
or thickness layer can allow tuning at ultrahigh speed using conventional
electrooptic, magnetooptic, piezoelectric or thermooptic materials at
relatively low external fields.
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Electricity storage systems (ESS) are hailed by many scholars and
practitioners as a key element of the future electricity systems and a key step
toward the transition to renewables . Nonetheless, the global speed of ESS
implementation is relatively slow, and among possible reasons is the lack of
viable business models. We developed an agent-based model to simulate the
behavior of ESS within the Dutch electricity market. We adopted an exploratory
modeling analysis (EMA) approach to investigate the effects of two specific
business models on the value of ESS from the perspective of both investors and
the government under uncertainties in the ESS technical and economics
characteristics, and uncertainties in market conditions and regulations. Our
results show ESS is not profitable in most scenarios, and generally wholesale
arbitrage business model leads to more profit than reserve capacity. In
addition, ESS economic and technical characteristics play more important roles
in the value of ESS than market conditions, and carbon pricing.
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We use low-dispersion spectra obtained at the Magellan Observatory to study
the broad H-alpha emission from the reverse shock of the infant supernova
remnant SNR1987A. These spectra demonstrate that the spatio-kinematic structure
of the reverse shock can be distinguished from that of the circumstellar ring
and hotspots, even at ground-based spatial resolution. We measure a total
dereddened H-alpha flux of 1.99(pm0.22)e-13 ergs/s/cm2 at an epoch 18.00 years
after outburst. At 50 kpc, the total reverse shock luminosity in H-alpha is
roughly 15 Lsun, which implies a total flux of neutral hydrogen atoms across
the reverse shock of 8.9e46/s, or roughly 2.3e-3 Msun/yr. This represents an
increase by a factor ~4 since 1997. Lyman continuum radiation from gas shocked
by the forward blast wave can ionize neutral hydrogen atoms in the supernova
debris before they reach the reverse shock. If the inward flux of ionizing
photons exceeds the flux of hydrogen atoms approaching the reverse shock, this
pre-ionization will shut off the broad Ly-alpha and H-alpha emission. The
observed X-ray emission of SNR1987A implies that the ratio of ionizing flux to
hydrogen atom flux across the reverse shock is presently at least 0.04. The
X-ray emission is increasing much faster than the flux of atoms, and if these
trends continue, we estimate that the broad Ly-alpha and H-alpha emission will
vanish within about 7 years.
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The phonon propagation dynamics in a phononic crystal waveguide, realized via
a suspended one-dimensional membrane array with periodic air holes, is
investigated as function of its geometry. The bandstructure of the phononic
crystal can be engineered by modifying the characteristics of the phonon
standing waves in the waveguide by varying the waveguide width and the pitch of
the air holes. This enables the phonon transmission bands, the bandgaps, the
velocity and the nonlinear dispersion in the phononic crystal to be controlled.
Indeed the engineered bandstructure can also be tuned to sustain multiple
phonon modes in a given branch which whilst being spectrally degenerate can be
temporally resolved via their differing group velocities. This systematic study
reveals the key geometric parameters that enable the phonon transport in
phononic crystal waveguides to be fully controlled.
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Wireless networks can be self-sustaining by harvesting energy from
radio-frequency (RF) signals. Building on classic cognitive radio networks, we
propose a novel method for network coexisting where mobiles from a secondary
network, called secondary transmitters (STs), either harvest energy from
transmissions by nearby transmitters from a primary network, called primary
transmitters (PTs), or transmit information if PTs are sufficiently far away;
STs store harvested energy in rechargeable batteries with finite capacity and
use all available energy for subsequent transmission when batteries are fully
charged. In this model, each PT is centered at a guard zone and a harvesting
zone that are disks with given radiuses; a ST harvests energy if it lies in
some harvesting zone, transmits fixed-power signals if it is outside all guard
zones or else idles. Based on this model, the spatial throughput of the
secondary network is maximized using a stochastic-geometry model where PTs and
STs are modeled as independent homogeneous Poisson point processes (HPPPs),
under the outage constraints for coexisting networks and obtained in a simple
closed-form. It is observed from the result that the maximum secondary
throughput decreases linearly with the growing PT density, and the optimal ST
density is inversely proportional to the derived transmission probability for
STs.
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Quasi *-algebras possessing a sufficient family $\mathcal{M}$ of invariant
positive sesquilinear forms carry several topologies related to $\mathcal{M}$
which make every *-representation continuous. This leads to define the class of
locally convex quasi GA*-algebras whose main feature consists in the fact that
the family of their bounded elements, with respect to the family $\mathcal{M}$,
is a dense C*-algebra.
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Global fossil CO2 emissions in 2020 decreased 5.4%, from 36.7 Gt CO2 in 2019
to 34.8 Gt CO2 in 2020, an unprecedented decline of ~1.9 Gt CO2. We project
that global fossil CO2 emissions in 2021 will rebound 4.9% (4.1% to 5.7%)
compared to 2020 to 36.4 Gt CO2, returning nearly to 2019 emission levels of
36.7 Gt CO2. Emissions in China are expected to be 7% higher in 2021 than in
2019 (reaching 11.1 Gt CO2) and only slightly higher in India (a 3% increase in
2021 relative to 2019, and reaching 2.7 Gt CO2). In contrast, projected 2021
emissions in the United States (5.1 Gt CO2), European Union (2.8 Gt CO2), and
rest of the world (14.8 Gt CO2, in aggregate) remain below 2019 levels. For
fuels, CO2 emissions from coal in 2021 are expected to rebound above 2019
levels to 14.7 Gt CO2, primarily because of increased coal use in China, and
will remain only slightly (0.8%) below their previous peak in 2014. Emissions
from natural gas use should also rise above 2019 levels in 2021, continuing a
steady trend of rising gas use that dates back at least sixty years. Only CO2
emissions from oil remain well below 2019 levels in 2021.
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This paper explores various generalizations of the Mitchell order focusing
mostly on a generalization called the internal relation. The internal relation
lacks the implicit strength requirement in the definition of the Mitchell
order, and therefore can fail to be wellfounded. We establish some constraints
on the illfoundedness of the internal relation, which leads to a proof of a
conjecture of Steel regarding rank-to-rank cardinals.
|
Recent measurements for fusion cross section at energies around the Coulomb
barrier have systematically indicated a significant deviation of fusion cross
sections from a prediction of double-folding model. It has been argued that the
deviation can be accounted for if one uses a large value of surface diffuseness
parameter for a Woods-Saxon internuclear potential. We investigate this problem
using large-angle quasi-elastic scattering, that is a good counterpart of
fusion reaction. Towards a reconciliation of the apparent anomaly in the
diffuseness parameter for fusion reactions, we also discuss possible
ingredients which are missing in present nuclear reaction models. Those include
a deviation from the frozen density approximation, the effect of
antisymmetrization and the role of coordinate dependent moment of inertia for
the relative motion between the colliding nuclei.
|
We explore consequences of the existence of gluonic hot spots inside the
proton for coherent and incoherent exclusive vector meson production cross
sections in deep inelastic scattering. By working in the dilute limit of the
Color Glass Condensate framework to compute the cross sections for Gaussian hot
spots of fluctuating color charges and employing a non-relativistic vector
meson wave function, we are able to perform large parts of the calculation
analytically. We find that the coherent cross section is sensitive to both the
size of the target and the structure of the probe. The incoherent cross section
is dominated by color fluctuations at small transverse momentum transfer ($t$),
by proton and hot spot sizes as well as the structure of the probe at medium
$t$ and again by color fluctuations at large $t$. While the $t$-dependence of
the cross section is well reproduced in our model, the relative normalization
between the coherent and the incoherent cross sections points to the need for
additional fluctuations in the proton.
|
Intense electromagnetic fields are created in the quark-gluon plasma by the
external ultra-relativistic valence charges. The time-evolution and the
strength of this field are strongly affected by the electrical conductivity of
the plasma. Yet, it has recently been observed that the effect of the magnetic
field on the plasma flow is small. We compute the effect of plasma flow on
magnetic field and demonstrate that it is less than 10\%. These observations
indicate that the plasma hydrodynamics and the dynamics of electromagnetic
field decouple. Thus, it is a very good approximation, on the one hand, to
study QGP in the background electromagnetic field generated by external sources
and, on the other hand, to investigate the dynamics of magnetic field in the
background plasma. We also argue that the wake induced by the magnetic field in
plasma is negligible.
|
The present paper reports on the RXTE observations of the binary X-ray pulsar
4U0115+63, covering an outburst in 1999 March-April with 44 pointings. The 3-30
keV PCA spectra and the 15-50 keV HEXTE spectra were analyzed jointly for the
cyclotron resonance features. When the 3-50 keV luminosity at an assumed
distance of 7 kpc was in the range (5-13)x10^{37} erg s^{-1}, harmonic double
cyclotron features were observed in absorption at ~11 and ~22 keV, as was
measured previously during typical outbursts. As the luminosity decreased below
\~5x10^{37} erg s^{-1}, the second resonance disappeared, and the fundamental
resonance energy gradually increased, up to $\sim$16 keV at 0.16x10^{37} erg
s^{-1}. These results reconfirm the report by Mihara et al. (2004) using Ginga,
who observed a single absorption at ~16 keV in a minor (~10^{37} erg s^{-1})
outburst of this object. The luminosity-dependent cyclotron resonance energy
may be understood as a result of a decrease in the accretion column height, in
response to a decrease in the mass accretion rate.
|
We devise a method to certify nonclassical features via correlations of
phase-space distributions by unifying the notions of quasiprobabilities and
matrices of correlation functions. Our approach complements and extends recent
results that were based on Chebyshev's inequality [Phys. Rev. Lett. 124, 133601
(2020)]. The method developed here correlates arbitrary phase-space functions
at arbitrary points in phase space, including multimode scenarios and
higher-order correlations. Furthermore, our approach provides necessary and
sufficient nonclassicality criteria, applies to phase-space functions beyond
$s$-parametrized ones, and is accessible in experiments. To demonstrate the
power of our technique, the quantum characteristics of discrete- and
continuous-variable, single- and multimode, as well as pure and mixed states
are certified only employing second-order correlations and Husimi functions,
which always resemble a classical probability distribution. Moreover, nonlinear
generalizations of our approach are studied. Therefore, a versatile and broadly
applicable framework is devised to uncover quantum properties in terms of
matrices of phase-space distributions.
|
This paper gives a uniform, self-contained and direct approach to a variety
of obstruction-theoretic problems on manifolds of dimension 7 and 6. We give
necessary and sufficient cohomological criteria for the existence of various
G-structures on vector bundles over such manifolds especially using low
dimensional representations of the group U(2).
|
Capsule endoscopy is an evolutional technique for examining and diagnosing
intractable gastrointestinal diseases. Because of the huge amount of data,
analyzing capsule endoscope videos is very time-consuming and labor-intensive
for gastrointestinal medicalists. The development of intelligent long video
analysis algorithms for regional positioning and analysis of capsule endoscopic
video is therefore essential to reduce the workload of clinicians and assist in
improving the accuracy of disease diagnosis. In this paper, we propose a deep
model to ground shooting range of small intestine from a capsule endoscope
video which has duration of tens of hours. This is the first attempt to attack
the small intestine grounding task using deep neural network method. We model
the task as a 3-way classification problem, in which every video frame is
categorized into esophagus/stomach, small intestine or colorectum. To explore
long-range temporal dependency, a transformer module is built to fuse features
of multiple neighboring frames. Based on the classification model, we devise an
efficient search algorithm to efficiently locate the starting and ending
shooting boundaries of the small intestine. Without searching the small
intestine exhaustively in the full video, our method is implemented via
iteratively separating the video segment along the direction to the target
boundary in the middle. We collect 113 videos from a local hospital to validate
our method. In the 5-fold cross validation, the average IoU between the small
intestine segments located by our method and the ground-truths annotated by
broad-certificated gastroenterologists reaches 0.945.
|
We have measured the spatial distribution of motile Escherichia coli inside
spherical water droplets emulsified in oil. At low cell concentrations, the
cell density peaks at the water-oil interface; at increasing concentration, the
bulk of each droplet fills up uniformly while the surface peak remains.
Simulations and theory show that the bulk density results from a `traffic' of
cells leaving the surface layer, increasingly due to cell-cell scattering as
the surface coverage rises above $\sim 10\%$. Our findings show similarities
with the physics of a rarefied gas in a spherical cavity with attractive walls.
|
We give an expansion of the solution of the evolution equation for the
massless Dirac fields in the outer region of de Sitter-Reissner-Nordstr\"om
black hole in terms of resonances. By means of this method we describe the
decay of local energy for compactly supported data. The proof uses the cut-off
resolvent estimates for the semi-classical Schr\"odinger operators from Bony
and H\"afner, 2008. The method extends to the Dirac operators on spherically
symmetric asymptotically hyperbolic manifolds.
|
We present a theoretical analysis of the phonon-assisted relaxation in a
system composed of two self-assembled vertically stacked quantum dots. We
construct realistic model, which takes into account the geometry and strain
distribution in the system. We calculate phonon-assisted relaxation rates
between the two lowest states (in one- and two-electron cases). The relaxation
rates and energy levels are studied as a function of external (axial) electric
field and geometry of the structure (dot sizes). We show that the relaxation
times can be as low as 1~ps but efficent relaxation occurs only for very finely
tuned dots.
|
Our aim is to unify and extend the large deviation upper and lower bounds for
the occupation times of a Markov process with $L_2$ semigroups under minimal
conditions on the state space and the process trajectories; for example, no
strong Markov property is needed. The methods used here apply in both
continuous and discrete time. We present the proofs for continuous time only
because of the inherent technical difficulties in that situation; the proofs
can be adapted for discrete time in a straightforward manner.
|
The reduction of singularities of codimension one foliations is known in the
case of ambient dimension 2 (Seidenberg, A. (1968). Reduction of singularities
of the differential equation Ady= Bdx. American Journal of Mathematics, 90(1),
248-269) and 3 (Cano, F. (2004). Reduction of the singularities of codimension
one singular foliations in dimension three. Annals of mathematics, 160(3),
907-1011). However, in greater ambient dimension it is still an open problem.
In this work we prove the existence of local uniformization for codimension one
foliations in arbitrary ambient dimension, in the case of rational archimedean
valuations.
|
We report an optical one-way quantum computing experiment with stationary
quantum memory involved. First we create a hybrid four-qubit cluster state with
two qubits propagating as photons and the other two stationary and stored in a
laser-cooled atomic-ensemble quantum memory, and characterize it with
entanglement witness and quantum state tomography. Then, by making use of this
cluster state and fast operations of electro-optic modulators, we realize
memory-assisted feedforward operations and demonstrate deterministic
single-qubit rotation as an example.
|
We introduce a certain compactification of the space of projective
configurations i.e. orbits of the group $PGL(k)$ on the space of $n$ - tuples
of points in $P^{k-1}$ in general position. This compactification differs
considerably from Mumford's geometric invariant theory quotient. It is obtained
by considering limit position (in the Chow variety) of the closures of generic
orbits. The same result will be obtained if we study orbits of the maximal
torus on the Grassmannian $G(k,n)$. We study in detail the closures of the
torus orbits and their "visible contours" which are Veronese varieties in the
Grassmannian. For points on $P^1$ our construction gives the Grothemdieck -
Knudsen moduli space of stable $n$ -punctured curves of genus 0. The "Chow
quotient" interpretation of this space permits us to represent it as a blow up
of a projective space.
|
We study Superconductor-Ferromagnet-Superconductor (Nb-Cu0.47 Ni0.53-Nb)
Josephson junctions with spatial variations in the barrier thickness. Critical
current vs. magnetic flux diffraction patterns indicate that the critical
current density changes sign along the width of the junctions, creating
interfaces between 0 and pi junction regions around which spontaneous currents
can circulate. Shapiro steps observed at half-integer Josephson voltages can be
explained by the phase-locking of the spontaneous circulating currents to the
applied rf modulation.
|
We derive for deep-inelastic neutrino-proton scattering in the combination nu
P - nubar P the perturbative QCD corrections to three loops for the charged
current structure functions F_2, F_L and F_3. In leading twist approximation we
calculate the first five odd-integer Mellin moments in the case of F_2 and F_L
and the first five even-integer moments in the case of F_3. As a new result we
obtain the coefficient functions to O(alpha_s^3) while the corresponding
anomalous dimensions agree with known results in the literature.
|
G\"odel's Incompleteness Theorems suggest that no single formal system can
capture the entirety of one's mathematical beliefs, while pointing at a
hierarchy of systems of increasing logical strength that make progressively
more explicit those \emph{implicit} assumptions. This notion of \emph{implicit
commitment} motivates directly or indirectly several research programmes in
logic and the foundations of mathematics; yet there hasn't been a direct
logical analysis of the notion of implicit commitment itself. In a recent
paper, \L elyk and Nicolai carried out an initial assessment of this project by
studying necessary conditions for implicit commitments; from seemingly weak
assumptions on implicit commitments of an arithmetical system $S$, it can be
derived that a uniform reflection principle for $S$ -- stating that all
numerical instances of theorems of $S$ are true -- must be contained in $S$'s
implicit commitments. This study gave rise to unexplored research avenues and
open questions. This paper addresses the main ones. We generalize this basic
framework for implicit commitments along two dimensions: in terms of iterations
of the basic implicit commitment operator, and via a study of implicit
commitments of theories in arbitrary first-order languages, not only couched in
an arithmetical language.
|
This paper is about the Fukaya category of a Fano hypersurface $X \subset
\mathbb{CP}^n$. Because these symplectic manifolds are monotone, both the
analysis and the algebra involved in the definition of the Fukaya category
simplify considerably. The first part of the paper is devoted to establishing
the main structures of the Fukaya category in the monotone case: the
closed-open string maps, weak proper Calabi-Yau structure, Abouzaid's
split-generation criterion, and their analogues when weak bounding cochains are
included. We then turn to computations of the Fukaya category of the
hypersurface $X$: we construct a configuration of monotone Lagrangian spheres
in $X$, and compute the associated disc potential. The result coincides with
the Hori-Vafa superpotential for the mirror of $X$ (up to a constant shift in
the Fano index $1$ case). As a consequence, we give a proof of Kontsevich's
homological mirror symmetry conjecture for $X$. We also explain how to extract
non-trivial information about Gromov-Witten invariants of $X$ from its Fukaya
category.
|
Software agents have emerged as promising tools for addressing complex
software engineering tasks. Existing works, on the other hand, frequently
oversimplify software development workflows, despite the fact that such
workflows are typically more complex in the real world. Thus, we propose
AgileCoder, a multi agent system that integrates Agile Methodology (AM) into
the framework. This system assigns specific AM roles - such as Product Manager,
Developer, and Tester to different agents, who then collaboratively develop
software based on user inputs. AgileCoder enhances development efficiency by
organizing work into sprints, focusing on incrementally developing software
through sprints. Additionally, we introduce Dynamic Code Graph Generator, a
module that creates a Code Dependency Graph dynamically as updates are made to
the codebase. This allows agents to better comprehend the codebase, leading to
more precise code generation and modifications throughout the software
development process. AgileCoder surpasses existing benchmarks, like ChatDev and
MetaGPT, establishing a new standard and showcasing the capabilities of multi
agent systems in advanced software engineering environments.
|
This note describes an integrated recognition system for identifying missing
and found objects as well as missing, dead, and found people during Hajj and
Umrah seasons in the two Holy cities of Makkah and Madina in the Kingdom of
Saudi Arabia. It is assumed that the total estimated number of pilgrims will
reach 20 millions during the next decade. The ultimate goal of this system is
to integrate facial recognition and object identification solutions into the
Hajj and Umrah rituals. The missing and found computerized system is part of
the CrowdSensing system for Hajj and Umrah crowd estimation, management and
safety.
|
The investigations of the crystal structure, magnetic and electronic
properties of the Co$_3$BO$_5$ at high temperatures were carried out using
powder x-ray diffraction, magnetic susceptibility, electrical resistivity, and
thermopower measurements. The orthorhombic symmetry (Sp.gr. Pbam) was
established at 300 K and no evidence of structural phase transitions was found
up to 1000 K. The thermal expansion of the crystal lattice is strongly
anisotropic. At $T<T_c=550$ K, a large thermal expansion along the c-axis is
observed with simultaneous contraction along a-axis. The activation energy of
the conductivity decreases significantly at high temperatures and follows the
thermal expansion variation, that exhibits two electronic transitions at ~500
and ~700 K, in coincidence with the anomalies of the heat capacity. Electronic
transport was found to be a dominant conduction mechanism in the entire
temperature range. The temperature dependence of the effective magnetic moment
reflects the evolution of the spin state of Co$^{3+}$ ions towards the spin
crossover to a high spin state. The interrelation between the crystal structure
and electronic properties is discussed.
|
In this paper, we identify two different sets of problems. The first covers
the problems that the iterative proportional fitting (IPF) algorithm was
developed to solve. These concern completing a population table by using a
sample. The other set concerns constructing a counterfactual population table
with the purpose of comparing two populations. The IPF is commonly applied by
social scientists to solve problems not only in the first set, but also in the
second one. We show that while it is legitimate to use the IPF for the first
set of problems, it is not the right tool to address the problems of the second
kind. We promote an alternative of the IPF, the NM-method, for solving problems
in the second set. We provide both theoretical and empirical comparisons of
these methods.
|
A light guide is an essential part of many scintillator counters and light
collection systems. There is large interest in an adiabatic light guide which
has high light transmission while converting the area of the light source to
the shape of the photo-detector. We propose a variation of the adiabatic light
guide which avoids a 90o twist of the strips, reduces the length of the light
pipe, and significantly cuts the cost of production.
|
The complex algebra of an inverse semigroup with finitely many idempotents in
each $\mathcal D$-class is stably finite by a result of Munn. This can be
proved fairly easily using $C^*$-algebras for inverse semigroups satisfying
this condition that have a Hausdorff universal groupoid, or more generally for
direct limits of inverse semigroups satisfying this condition and having
Hausdorff universal groupoids. It is not difficult to see that a finitely
presented inverse semigroup with a non-Hausdorff universal groupoid cannot be a
direct limit of inverse semigroups with Hausdorff universal groupoids. We
construct here countably many non-isomorphic finitely presented inverse
semigroups with finitely many idempotents in each $\mathcal D$-class and
non-Hausdorff universal groupoids. At this time there is not a clear
$C^*$-algebraic technique to prove these inverse semigroups have stably finite
complex algebras.
|
We make some simple observations on basic issues pertaining to
thermostatistical formalisms.
|
In this work we present a comparative investigation of the electronic
structures of NbO$_2$ and VO$_2$ obtained within the combination of density
functional theory and cluster-dynamical mean field theory calculations. We
investigate the role of dynamic electronic correlations on the electronic
structure of the metallic and insulating phases of NbO$_2$ and VO$_2$, with
focus on the mechanism responsible for the gap opening in the insulating
phases. For the rutile metallic phases of both oxides, we obtain that
electronic correlations lead to strong renormalization of the $t_{2g}$
subbands, as well as the emergence of incoherent Hubbard subbands, signaling
that electronic correlations are also important in the metallic phase of
NbO$_2$. Interestingly, we find that nonlocal dynamic correlations do play a
role in the gap formation of the (bct) insulating phase of NbO$_2$, by a
similar physical mechanism as that recently proposed by us in the case of the
(M$_1$) dimerized phase of VO$_2$ (\textit{Phys. Rev. Lett. 117, 056402
(2016)}). Although the effect of nonlocal dynamic correlations in the gap
opening of bct phase is less important than in the (M$_1$ and M$_2$) monoclinic
phases of VO$_2$, their presence indicates that the former is not a purely
Peierls-type insulator, as it was recently proposed.
|
The standard thin disk model predicts that when the accretion rate is over a
small fraction of the Eddington rate, which corresponds to $L \ga 0.06
L_{Edd}$, the inner region of the disk is radiation-pressure-dominated and
thermally unstable. However, observations of the high/soft state of black hole
X-ray binaries with luminosity well within this regime ($0.01L_{Edd} \la L \la
0.5L_{Edd}$) indicate that the disk has very little variability, i.e., quite
stable. Recent radiation magnetohydrodynamic simulations of a vertically
stratified shearing box have confirmed the absence of the thermal instability.
In this paper, we revisit the thermal stability by linear analysis, taking into
account the role of magnetic field in the accretion flow. By assuming that the
field responses negatively to a positive temperature perturbation, we find that
the threshold of accretion rate above which the disk becomes thermally unstable
increases significantly compared with the case of not considering the role of
magnetic field. This accounts for the stability of the observed sources with
high luminosities. Our model also presents a possible explanation as to why
only GRS 1915+105 seems to show thermally unstable behavior. This peculiar
source holds the highest accretion rate (or luminosity) among the known high
state sources, which is well above the accretion rate threshold of the
instability.
|
We give a geometric description of variational principles in mechanics, with
special attention to constrained systems. For the general case of nonholonomic
constraints, a unified variational approach is given, and the equations of
motion of both vakonomic and nonholonomic frameworks are obtained. We study
specifically the existence of infinitesimal variations in both cases. When the
constraints are integrable, both formalisms are compared and it is proved that
they coincide. As examples, we give geometric formulations of the equations of
motion for the case of optimal control and for vakonomic and nonholonomic
mechanics with constraints linear in the velocities.
|
A new concept for generation of thrust for space propulsion is introduced.
Energetic thrust is generated in the form of plasmoids (confined plasma in
closed magnetic loops) when magnetic helicity (linked magnetic field lines) is
injected into an annular channel. Using a novel configuration of static
electric and magnetic fields, the concept utilizes a current-sheet instability
to spontaneously and continuously create plasmoids via magnetic reconnection.
The generated low-temperature plasma is simulated in a global annular geometry
using the extended magnetohydrodynamic model. Because the system-size plasmoid
is an Alfvenic outflow from the reconnection site, its thrust is proportional
to the square of the magnetic field strength and does not ideally depend on the
mass of the ion species of the plasma. Exhaust velocities in the range of 20 to
500 km/s, controllable by the coil currents, are observed in the simulations.
|
A wheel or sphere rolling without slipping on the inside of a sphere in a
uniform gravitational field can have stable circular orbits that lie wholly
above the "equator", while a particle sliding freely cannot.
|
The ability to control the generation of spins in arbitrary directions is a
long-sought goal in spintronics. Charge-to-spin interconversion (CSI) phenomena
depend strongly on symmetry. Systems with reduced crystal symmetry allow
anisotropic CSI with unconventional components, where charge and spin currents
and the spin polarization are not mutually perpendicular to each other. Here,
we demonstrate experimentally that the CSI in graphene-WTe2 induces spins with
components in all three spatial directions. By performing multi-terminal
nonlocal spin precession experiments, with specific magnetic field
orientations, we discuss how to disentangle the CSI from the spin Hall and
inverse spin galvanic effects.
|
The stochastic block model is a canonical random graph model for clustering
and community detection on network-structured data. Decades of extensive study
on the problem have established many profound results, among which the phase
transition at the Kesten-Stigum threshold is particularly interesting both from
a mathematical and an applied standpoint. It states that no estimator based on
the network topology can perform substantially better than chance on sparse
graphs if the model parameter is below a certain threshold. Nevertheless, if we
slightly extend the horizon to the ubiquitous semi-supervised setting, such a
fundamental limitation will disappear completely. We prove that with an
arbitrary fraction of the labels revealed, the detection problem is feasible
throughout the parameter domain. Moreover, we introduce two efficient
algorithms, one combinatorial and one based on optimization, to integrate label
information with graph structures. Our work brings a new perspective to the
stochastic model of networks and semidefinite program research.
|
We study the growing patterns formed by a deterministic cellular automaton,
the rotor-router model, in the presence of quenched noise. By the detailed
study of two cases, we show that: (a) the boundary of the pattern displays KPZ
fluctuations with a Tracy-Widom distribution, (b) as one increases the amount
of randomness, the rotor-router path undergoes a transition from a recurrent to
a transient walk. This transition is analysed here for the first time, and it
is shown that it falls in the 3D Anisotropic Directed Percolation universality
class.
|
The excitation of atomic levels due to interaction with electromagnetic waves
became of interest in accelerator physics in relation to high efficiency charge
exchange injection into rings for high beam power applications. Usually, the
beam density is so small that its influence on the wave is completely
neglected. Here we consider the case of dense beams - the beam dimensions are
large as compared to light reflection length. This paper shows that the waves
can be trapped in the medium under these conditions. Moreover, the atoms with
induced dipole moments start to interact strongly with each other, leading to
possibility to create some atomic patterns when the medium is relatively cold.
|
We formulate a quantum theory of the Universe based on Bayesian probability.
In this theory, the probability of the Universe is not a frequency probability,
which can be obtained by observing experimental results several times, but is a
Bayesian probability, which can define a probability of an event that occurs
just once. As an example, by applying the quantum theory of the Universe to an
action of a scalar field theory in the four dimensions as a toy model for the
theory of the Universe, we explicitly obtain the probability of the Universe
and the action of matters in the Universe.
|
In this article, we consider the phenomenon of complete coincidence of the
key properties of pairs of Calabi-Yau manifolds realized as hypersurfaces in
two different weighted projective spaces. More precisely, the first manifold in
such a pair is realized as a hypersurface in a weighted projective space, and
the second as a hypersurface in the orbifold of another weighted projective
space. The two manifolds in each pair have the same Hodge numbers and special
K\"ahler geometry on the complex structure moduli space and are associated with
the same $N=2$ gauge linear sigma model. We give the explanation of this
interesting coincidence using the Batyrev's correspondence between Calabi-Yau
manifolds and the reflexive polyhedra.
|
The van der Pauw method for two-dimensional samples of arbitrary shape with
an isolated hole is considered. Correlations between extreme values of the
resistances allow one to determine the specific resistivity of the sample and
the dimensionless parameter related to the geometry of the isolated hole, known
as the Riemann modulus. The parameter is invariant under conformal mappings.
Experimental verification of the method is presented.
|
Inspired by work of the first and second author, this paper studies the
Gromov width of the disk cotangent bundle of spheroids and Zoll spheres of
revolution. This is achieved with the use of techniques from integrable systems
and embedded contact homology capacities.
|
In this paper, we prove a global rigidity theorem for negatively curved
Finsler metrics on a compact manifold of dimension n>2. We show that for such a
Finsler manifold, if the flag curvature is a scalar function on the tangent
bundle, then the Finsler metric is of Randers type. We also study the case when
the Finsler metric is locally projectively flat.
|
Beam management is central in the operation of dense 5G cellular networks.
Focusing the energy radiated to mobile terminals (MTs) by increasing the number
of beams per cell increases signal power and decreases interference, and has
hence the potential to bring major improvements on area spectral efficiency
(ASE). This benefit, however, comes with unavoidable overheads that increase
with the number of beams and the MT speed. This paper proposes a first
system-level stochastic geometry model encompassing major aspects of the beam
management problem: frequencies, antennas, and propagation; physical layer,
wireless links, and coding; network geometry, interference, and resource
sharing; sensing, signaling, and mobility management. This model leads to a
simple analytical expression for the effective ASE that the typical user gets
in this context. This in turn allows one to find, for a wide variety of 5G
network scenarios including millimeter wave (mmWave) and sub-6 GHz, the number
of beams per cell that offers the best global trade-off between these benefits
and costs. We finally provide numerical results that discuss the effects of
different systemic trade-offs and performances of mmWave and sub-6 GHz 5G
deployments.
|
We review different definitions of the $\epsilon'$ parameter describing
direct CP violation in neutral kaon decays, which was precisely measured in
recent experiments, and point out the inconsistency of some of them due to a
CPT constraint. The proper comparison of the experimental results to the
theoretical computations is discussed.
|
For a convex body $K\subset\R^n$, the $k$th projection function of $K$
assigns to any $k$-dimensional linear subspace of $\R^n$ the $k$-volume of the
orthogonal projection of $K$ to that subspace. Let $K$ and $K_0$ be convex
bodies in $\R^n$, and let $K_0$ be centrally symmetric and satisfy a weak
regularity and curvature condition (which includes all $K_0$ with $\f K_0$ of
class $C^2$ with positive radii of curvature). Assume that $K$ and $K_0$ have
proportional 1st projection functions (i.e., width functions) and proportional
$k$th projection functions. For $2\le k<(n+1)/2$ and for $k=3, n=5$ we show
that $K$ and $K_0$ are homothetic. In the special case where $K_0$ is a
Euclidean ball, we thus obtain characterizations of Euclidean balls as convex
bodies of constant width and constant $k$-brightness.
|
We present the first Open Gravitational-wave Catalog (1-OGC), obtained by
using the public data from Advanced LIGO's first observing run to search for
compact-object binary mergers. Our analysis is based on new methods that
improve the separation between signals and noise in matched-filter searches for
gravitational waves from the merger of compact objects. The three most
significant signals in our catalog correspond to the binary black hole mergers
GW150914, GW151226, and LVT151012. We assume a common population of binary
black holes for these three signals by defining a region of parameter space
that is consistent with these events. Under this assumption, we find that
LVT151012 has a 97.6\% probability of being astrophysical in origin. No other
significant binary black hole candidates are found, nor did we observe any
significant binary neutron star or neutron star--black hole candidates. We make
available our complete catalog of events, including the sub-threshold
population of candidates.
|
We report a systematic study of anisotropy resistivity, magnetoresistance and
Hall effect of Li0.32(NH3)yFe2Te1.2Se0.8 single crystals. When compared to the
parent compound FeTe0.6Se0.4, the Li-NH3 intercalation not only increases the
superconducting transition temperature, but also enhances the electronic
anisotropy in both normal and superconducting states. Moreover, in contrast to
the parent compound, the Hall coefficient RH becomes negative at low
temperature, indicating electron-type carriers are dominant due to Li doping.
On the other hand, the sign reverse of RH at high temperature and the failure
of scaling behavior of magnetoresistance imply that hole pockets may be still
crossing or just below the Fermi energy level, leading to the multiband
behavior in Li0.32(NH3)yFe2Te1.2Se0.8.
|
Multilayer perceptrons (MLP) with one hidden layer have been used for a long
time to deal with non-linear regression. However, in some task, MLP's are too
powerful models and a small mean square error (MSE) may be more due to
overfitting than to actual modelling. If the noise of the regression model is
Gaussian, the overfitting of the model is totally determined by the behavior of
the likelihood ratio test statistic (LRTS), however in numerous cases the
assumption of normality of the noise is arbitrary if not false. In this paper,
we present an universal bound for the overfitting of such model under weak
assumptions, this bound is valid without Gaussian or identifiability
assumptions. The main application of this bound is to give a hint about
determining the true architecture of the MLP model when the number of data goes
to infinite. As an illustration, we use this theoretical result to propose and
compare effective criteria to find the true architecture of an MLP.
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We study point contact tunneling between two leads of a Tomonaga-Luttinger
liquid through two degenerate resonant levels in parallel. This is one of the
simplest cases of a quantum junction problem where the Fermi statistics of the
electrons plays a non-trivial role through the Klein factors appearing in
bosonization. Using a mapping to a `generalized Coulomb model' studied in the
context of the dissipative Hofstadter model, we find that any asymmetry in the
tunneling amplitudes from the two leads grows at low temperatures, so that
ultimately there is no conductance across the system. For the symmetric case,
we identify a non-trivial fixed point of this model; the conductance at that
point is generally different from the conductance through a single resonant
level.
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This paper has the goal of evaluating how changes in mobility has affected
the infection spread of Covid-19 throughout the 2020-2021 years. However,
identifying a "clean" causal relation is not an easy task due to a high number
of non-observable (behavioral) effects. We suggest the usage of Google Trends
and News-based indexes as controls for some of these behavioral effects and we
find that a 1\% increase in residential mobility (i.e. a reduction in overall
mobility) have significant impacts for reducing both Covid-19 cases (at least
3.02\% on a one-month horizon) and deaths (at least 2.43\% at the two-weeks
horizon) over the 2020-2021 sample. We also evaluate the effects of mobility on
Covid-19 spread on the restricted sample (only 2020) where vaccines were not
available. The results of diminishing mobility over cases and deaths on the
restricted sample are still observable (with similar magnitudes in terms of
residential mobility) and cumulative higher, as the effects of restricting
workplace mobility turns to be also significant: a 1\% decrease in workplace
mobility diminishes cases around 1\% and deaths around 2\%.
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Sampling-based motion planners are an effective means for generating
collision-free motion paths. However, the quality of these motion paths, with
respect to different quality measures such as path length, clearance,
smoothness or energy, is often notoriously low. This problem is accentuated in
the case of non-holonomic sampling-based motion planning, in which the space of
feasible motion trajectories is restricted. In this study, we combine the C-PRM
algorithm by Song and Amato with our recently introduced path-hybridization
approach, for creating high quality non-holonomic motion paths, with
combinations of several different quality measures such as path length,
smoothness or clearance, as well as the number of reverse car motions. Our
implementation includes a variety of code optimizations that result in nearly
real-time performance, and which we believe can be extended with further
optimizations to a real-time tool for the planning of high-quality car-like
motion.
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Ruling out the inverted neutrino hierarchy with neutrinoless double beta
decay experiments is possible if a limit on the effective mass below the
minimal theoretically possible value is reached. We stress that this lower
limit depends strongly on the value of the solar neutrino mixing angle: it
introduces an uncertainty of a factor of 2 within its current 3 sigma range. If
an experiment is not background-free, a factor of two in effective mass
corresponds to a combined factor of 16 improvement for the experimental
parameters running time, detector mass, background level and energy resolution.
Therefore, a more precise determination of theta(12) is crucial for the
interpretation of experimental results and the evaluation of the potential and
requirements for future experiments. We give the required half-lifes to exclude
(and touch) the inverted hierarchy regime for all double beta decay isotopes
with a Q-value above 2 MeV. The nuclear matrix elements from 6 different groups
and, if available, their errors are used and compared. We carefully put the
calculations on equal footing in what regards various convention issues. We
also use our compilation of matrix elements to give the reachable values of the
effective mass for a given half-life value.
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Patterns of microcircuitry suggest that the brain has an array of repeated
canonical computational units. Yet neural representations are distributed, so
the relevant computations may only be related indirectly to single-neuron
transformations. It thus remains an open challenge how to define canonical
distributed computations. We integrate normative and algorithmic theories of
neural computation into a mathematical framework for inferring canonical
distributed computations from large-scale neural activity patterns. At the
normative level, we hypothesize that the brain creates a structured internal
model of its environment, positing latent causes that explain its sensory
inputs, and uses those sensory inputs to infer the latent causes. At the
algorithmic level, we propose that this inference process is a nonlinear
message-passing algorithm on a graph-structured model of the world. Given a
time series of neural activity during a perceptual inference task, our
framework finds (i) the neural representation of relevant latent variables,
(ii) interactions between these variables that define the brain's internal
model of the world, and (iii) message-functions specifying the inference
algorithm. These targeted computational properties are then statistically
distinguishable due to the symmetries inherent in any canonical computation, up
to a global transformation. As a demonstration, we simulate recordings for a
model brain that implicitly implements an approximate inference algorithm on a
probabilistic graphical model. Given its external inputs and noisy neural
activity, we recover the latent variables, their neural representation and
dynamics, and canonical message-functions. We highlight features of
experimental design needed to successfully extract canonical computations from
neural data. Overall, this framework provides a new tool for discovering
interpretable structure in neural recordings.
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We construct oriented matroids of rank 3 on 13 points whose realization
spaces are disconnected. They are defined on smaller points than the known
examples with this property. Moreover, we construct the one on 13 points whose
realization space is a connected and non-irreducible semialgebraic variety.
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We apply our recently developed, selfconsistent renormalization group (RG)
method to STM spectra of a two-impurity Kondo system consisting of two cobalt
atoms connected by a one-dimensional Cu chain on a Cu surface. This RG method
was developed to describe local spin screening in multi-impurity Kondo systems
in presence of the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction. Using the
RKKY interaction of a one-dimensional chain, we explain the experimentally
observed suppression and oscillation of the Kondo temperature, $T_K(y)$, as a
function of the length of the chain and the corresponding RKKY interaction
parameter $y$, regardless of the RKKY coupling being ferromagnetic or
antiferromagnetic.
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This paper proposes a robust transient stability constrained optimal power
flow problem that addresses renewable uncertainties by the coordination of
generation re-dispatch and power flow router (PFR) tuning.PFR refers to a
general type of network-side controller that enlarges the feasible region of
the OPF problem. The coordination between network-side and generator-side
control in the proposed model is more general than the traditional methods
which focus on generation dispatch only. An offline-online solution framework
is developed to solve the problem efficiently. Under this framework the
original problem is significantly simplified, so that we only need to solve a
low-dimensional deterministic problem at the online stage to achieve real-time
implementation with a high robustness level. The proposed method is verified on
the modified New England 39-bus system. Numerical results demonstrate that the
proposed method is efficient and shows good performance on economy and
robustness.
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The ratio of L1 and L2 norms (L1/L2), serving as a sparse promoting function,
receives considerable attentions recently due to its effectiveness for sparse
signal recovery. In this paper, we propose an L1/L2 based penalty model for
recovering sparse signals from noiseless or noisy observations. It is proven
that stationary points of the proposed problem tend to those of the
elliptically constrained L1/L2 minimization problem as the smoothing parameter
goes to zero. Moreover, inspired by the parametric approach for the fractional
programming, we design a parameterized proximal-gradient algorithm (PPGA) as
well as its line search counterpart (PPGA_L) for solving the proposed model.
The closed-form solution of the involved proximity operator is derived, which
enable the efficiency of the proposed algorithms. We establish the global
convergence of the entire sequences generated by PPGA and PPGA_L with monotone
objective values by taking advantage of the fact that the objective of the
proposed model is a KL function. Numerical experiments show the efficiency of
the proposed algorithms over the state-of-the-art methods in both noiseless and
noisy sparse signal recovery problems.
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Monolayer islands of molybdenum disulfide (MoS$_2$) on Au(111) form a
characteristic moir\'e structure, leading to locally different stacking
sequences at the S-Mo-S-Au interface. Using low-temperature scanning tunneling
microscopy (STM) and atomic force microscopy (AFM), we find that the moir\'e
islands exhibit a unique orientation with respect to the Au crystal structure.
This indicates a clear preference of MoS$_2$ growth in a regular stacking
fashion. We further probe the influence of the local atomic structure on the
electronic properties. Differential conductance spectra show pronounced
features of the valence band and conduction band, some of which undergo
significant shifts depending on the local atomic structure. We also determine
the tunneling decay constant as a function of the bias voltage by a
height-modulated spectroscopy method. This allows for an increased sensitivity
of states with non-negligible parallel momentum $k_\parallel$ and the
identification of the origin of the states from different areas in the
Brillouin zone.
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Node Importance Estimation (NIE) is crucial for integrating external
information into Large Language Models through Retriever-Augmented Generation.
Traditional methods, focusing on static, single-graph characteristics, lack
adaptability to new graphs and user-specific requirements. CADReN, our proposed
method, addresses these limitations by introducing a Contextual Anchor (CA)
mechanism. This approach enables the network to assess node importance relative
to the CA, considering both structural and semantic features within Knowledge
Graphs (KGs). Extensive experiments show that CADReN achieves better
performance in cross-graph NIE task, with zero-shot prediction ability. CADReN
is also proven to match the performance of previous models on single-graph NIE
task. Additionally, we introduce and opensource two new datasets, RIC200 and
WK1K, specifically designed for cross-graph NIE research, providing a valuable
resource for future developments in this domain.
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A spherically symmetric comoving fluid solution of Einstein's equations is
adapted for cosmological application by extending the geometry of standard FRW
cosmology using a generalised curvature term. The resulting model retains many
of the known cosmological properties including homogeneity of energy density,
its relationship with internal pressure including equations of state, although
in each case they have a generalised structure. It is shown that the adapted
model does not require the inclusion of the arbitrary cosmological constant and
the vacuum energy solution is discussed in its absence. The Hubble constant and
deceleration parameter are also shown to have a form which characterises the
modified geometry of the new model. These forms are calculated using current
observational data and show how the standard cosmological geometry can be
amended in a way which is consistent with an observed flat curvature and a
decelerating universe. Finally the solution is also considered in the context
of gravitational collapse where it is shown how fluids spheres obeying a
central equation of state can be matched to empty spacetime.
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A synoptic view on the long-established theory of light propagation in
crystalline dielectrics is presented, providing a new exact solution for the
microscopic local electromagnetic field thus disclosing the role of the
divergence-free (transversal) and curl-free (longitudinal) parts of the
electromagnetic field inside a material as a function of the density of
polarizable atoms. Our results enable fast and efficient calculation of the
photonic bandstructure and also the (non-local) dielectric tensor, solely with
the crystalline symmetry and atom-individual polarizabilities as input.
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We extend collisional quantum thermometry schemes to allow for stochasticity
in the waiting time between successive collisions. We establish that
introducing randomness through a suitable waiting time distribution, the
Weibull distribution, allows to significantly extend the parameter range for
which an advantage over the thermal Fisher information is attained. These
results are explicitly demonstrated for dephasing interactions and also hold
for partial swap interactions. Furthermore, we show that the optimal
measurements can be performed locally, thus implying that genuine quantum
correlations do not play a role in achieving this advantage. We explicitly
confirm this by examining the correlation properties for the deterministic
collisional model.
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We prove Lusztig's conjectures ${\bf P1}$-${\bf P15}$ for the affine Weyl
group of type $\tilde{C}_2$ for all choices of positive weight function. Our
approach to computing Lusztig's $\mathbf{a}$-function is based on the notion of
a `balanced system of cell representations'. Once this system is established
roughly half of the conjectures ${\bf P1}$-${\bf P15}$ follow. Next we
establish an `asymptotic Plancherel Theorem' for type $\tilde{C}_2$, from which
the remaining conjectures follow. Combined with existing results in the
literature this completes the proof of Lusztig's conjectures for all rank $1$
and $2$ affine Weyl groups for all choices of parameters.
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Overcoming the diffraction limit to achieve high optical resolution is one of
the main challenges in the fields of plasmonics, nanooptics and nanophotonics.
In this work, we introduce novel plasmonic structures consisting of
nanoantennas (nanoprisms, single bowtie nanoantennas and double bowtie
nanoantennas) integrated in the center of ring diffraction gratings.
Propagating surface plasmon polaritons (SPPs) are generated by the ring grating
and coupled with localized surface plasmons (LSPs) at the nanoantennas exciting
emitters placed in their gap. SPPs are widely used for optical waveguiding but
provide low resolution due to their weak spatial confinement. Oppositely, LSPs
provide excellent sub-wavelength confinement but induce large losses. The
phenomenon of SPP-LSP coupling witnessed in our structures allows achieving
more precise focusing at the nanoscale, causing an increase in the fluorescence
emission of the emitters. FDTD simulations as well as experimental fabrication
and optical characterization results are presented to study plasmon-emitter
coupling between an ensemble of dye molecules and our integrated plasmonic
structures. A comparison is given to highlight the importance of each structure
on the photoluminescence and radiative decay enhancement of the molecules.
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Self-supervised models trained with a contrastive loss such as CLIP have
shown to be very powerful in zero-shot classification settings. However, to be
used as a zero-shot classifier these models require the user to provide new
captions over a fixed set of labels at test time. In many settings, it is hard
or impossible to know if a new query caption is compatible with the source
captions used to train the model. We address these limitations by framing the
zero-shot classification task as an outlier detection problem and develop a
conformal prediction procedure to assess when a given test caption may be
reliably used. On a real-world medical example, we show that our proposed
conformal procedure improves the reliability of CLIP-style models in the
zero-shot classification setting, and we provide an empirical analysis of the
factors that may affect its performance.
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We prove the equivalence of the Jacobian Conjecture (JC(n)) and the
Conjecture on the cardinality of the set of fixed points of a polynomial
nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).
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We develop a new second-order unstaggered path-conservative central-upwind
(PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations.
The new scheme possesses several important properties: it locally preserves the
divergence-free constraint, it does not rely on any (approximate) Riemann
problem solver, and it robustly produces high-resolution and non-oscillatory
results. The derivation of the scheme is based on the Godunov-Powell
nonconservative modifications of the studied MHD systems. The local
divergence-free property is enforced by augmenting the modified systems with
the evolution equations for the corresponding derivatives of the magnetic field
components. These derivatives are then used to design a special piecewise
linear reconstruction of the magnetic field, which guarantees a non-oscillatory
nature of the resulting scheme. In addition, the proposed PCCU discretization
accounts for the jump of the nonconservative product terms across cell
interfaces, thereby ensuring stability. We test the proposed PCCU scheme on
several benchmarks for both ideal and shallow water MHD systems. The obtained
numerical results illustrate the performance of the new scheme, its robustness,
and its ability not only to achieve high resolution, but also preserve the
positivity of computed quantities such as density, pressure, and water depth.
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