33,993 research outputs found
The photo-neutrino process in astrophysical systems
Explicit expressions for the differential and total rates and emissivities of
neutrino pairs from the photo-neutrino process in hot and dense matter are derived. Full information about the
emitted neutrinos is retained by evaluating the squared matrix elements for
this process which was hitherto bypassed through the use of Lenard's identity
in obtaining the total neutrino emissivities. Accurate numerical results are
presented for widely varying conditions of temperature and density. Analytical
results helpful in understanding the qualitative behaviors of the rates and
emissivities in limiting situations are derived. The corresponding production
and absorption kernels in the source term of the Boltzmann equation for
neutrino transport are developed. The appropriate Legendre coefficients of
these kernels, in forms suitable for multigroup flux-limited diffusion schemes
are also provided.Comment: 26 pages and 7 figures. Version as accepted in Phys. Rev. D; three
figures and related discussion revise
Anisotropic diffusion processes in early vision
Summary form only given. Images often contain information at a number of different scales of resolution, so that the definition and generation of a good scale space is a key step in early vision. A scale space in which object boundaries are respected and smoothing only takes place within these boundaries has been defined that avoids the inaccuracies introduced by the usual method of low-pass-filtering the image with Gaussian kernels. The new scale space is generated by solving a nonlinear diffusion differential equation forward in time (the scale parameter). The original image is used as the initial condition, and the conduction coefficient c(x, y, t) varies in space and scale as a function of the gradient of the variable of interest (e.g. the image brightness). The algorithms are based on comparing the local values of different diffusion processes running in parallel on the same image
Local Kernels and the Geometric Structure of Data
We introduce a theory of local kernels, which generalize the kernels used in
the standard diffusion maps construction of nonparametric modeling. We prove
that evaluating a local kernel on a data set gives a discrete representation of
the generator of a continuous Markov process, which converges in the limit of
large data. We explicitly connect the drift and diffusion coefficients of the
process to the moments of the kernel. Moreover, when the kernel is symmetric,
the generator is the Laplace-Beltrami operator with respect to a geometry which
is influenced by the embedding geometry and the properties of the kernel. In
particular, this allows us to generate any Riemannian geometry by an
appropriate choice of local kernel. In this way, we continue a program of
Belkin, Niyogi, Coifman and others to reinterpret the current diverse
collection of kernel-based data analysis methods and place them in a geometric
framework. We show how to use this framework to design local kernels invariant
to various features of data. These data-driven local kernels can be used to
construct conformally invariant embeddings and reconstruct global
diffeomorphisms
Exact heat kernel on a hypersphere and its applications in kernel SVM
Many contemporary statistical learning methods assume a Euclidean feature
space. This paper presents a method for defining similarity based on
hyperspherical geometry and shows that it often improves the performance of
support vector machine compared to other competing similarity measures.
Specifically, the idea of using heat diffusion on a hypersphere to measure
similarity has been previously proposed, demonstrating promising results based
on a heuristic heat kernel obtained from the zeroth order parametrix expansion;
however, how well this heuristic kernel agrees with the exact hyperspherical
heat kernel remains unknown. This paper presents a higher order parametrix
expansion of the heat kernel on a unit hypersphere and discusses several
problems associated with this expansion method. We then compare the heuristic
kernel with an exact form of the heat kernel expressed in terms of a uniformly
and absolutely convergent series in high-dimensional angular momentum
eigenmodes. Being a natural measure of similarity between sample points
dwelling on a hypersphere, the exact kernel often shows superior performance in
kernel SVM classifications applied to text mining, tumor somatic mutation
imputation, and stock market analysis
Cortical spatio-temporal dimensionality reduction for visual grouping
The visual systems of many mammals, including humans, is able to integrate
the geometric information of visual stimuli and to perform cognitive tasks
already at the first stages of the cortical processing. This is thought to be
the result of a combination of mechanisms, which include feature extraction at
single cell level and geometric processing by means of cells connectivity. We
present a geometric model of such connectivities in the space of detected
features associated to spatio-temporal visual stimuli, and show how they can be
used to obtain low-level object segmentation. The main idea is that of defining
a spectral clustering procedure with anisotropic affinities over datasets
consisting of embeddings of the visual stimuli into higher dimensional spaces.
Neural plausibility of the proposed arguments will be discussed
Using seismic inversions to obtain an internal mixing processes indicator for main-sequence solar-like stars
Determining accurate and precise stellar ages is a major problem in
astrophysics. These determinations are either obtained through empirical
relations or model-dependent approaches. Currently, seismic modelling is one of
the best ways of providing accurate ages. However, current methods are affected
by simplifying assumptions concerning mixing processes. In this context,
providing new structural indicators which are less model-dependent and more
sensitive to such processes is crucial. We build a new indicator for core
conditions on the main sequence, which should be more sensitive to structural
differences and applicable to older stars than the indicator t presented in a
previous paper. We also wish to analyse the importance of the number and type
of modes for the inversion, as well as the impact of various constraints and
levels of accuracy in the forward modelling process that is used to obtain
reference models for the inversion. First, we present a method to obtain new
structural kernels and use them to build an indicator of central conditions in
stars and test it for various effects including atomic diffusion, various
initial helium abundances and metallicities, following the seismic inversion
method presented in our previous paper. We then study its accuracy for 7
different pulsation spectra including those of 16CygA and 16CygB and analyse
its dependence on the reference model by using different constraints and levels
of accuracy for its selection We observe that the inversion of the new
indicator using the SOLA method provides a good diagnostic for additional
mixing processes in central regions of stars. Its sensitivity allows us to test
for diffusive processes and chemical composition mismatch. We also observe that
octupole modes can improve the accuracy of the results, as well as modes of low
radial order.Comment: Accepted for publication in Astronomy and Astrophysic
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