1,079 research outputs found
Proper Weyl Collineations in Kantowski-Sachs and Bianchi Type III Space-Times
A study of proper Weyl collineations in Kantowski-Sachs and Bianchi type III
space-times is given by using the rank of the 6X6 Weyl matrix and direct
integration techniques. Studying proper Weyl collineations in each of the above
space-times, it is shown that there exists no such possibility when the above
space-times admit proper Weyl collineations.Comment: 5 page
Proper projective collineation in non-static spherically symmetric space-times
We investigate the proper projective collineation in non-static spherically
symmetric space-times using direct integration and algebraic techniques.
Studying projective collineation in the above space-times, it is shown that the
space-times which admit proper projective collineations turn out to be very
special classes of static spherically symmetric space-times.Comment: 13 page
Symmetries of the Weyl tensor in Bianchi V spacetimes
Symmetries of geometrical and physical quantities in general relativity
provide important information about the curvature structure of the spacetimes.
Symmetries of the curvature and the Weyl tensors, known as curvature and Weyl
collineations respectively, are two of such important symmetries. Some results
on these symmetries for Bianchi type V spacetimes are discussed.Comment: 4 pages; Proc. 11th Marcel Grossmann Meeting on General Relativity,
World Scientific, 200
A classification scheme for edge-localized modes based on their probability distributions
We present here an automated classification scheme which is particularly well suited to scenarios
where the parameters have significant uncertainties or are stochastic quantities. To this end, the
parameters are modeled with probability distributions in a metric space and classification is conducted using the notion of nearest neighbors. The presented framework is then applied to the classification of type I and type III edge-localized modes (ELMs) from a set of carbon-wall plasmas at JET. This provides a fast, standardized classification of ELM types which is expected to significantly reduce the effort of ELM experts in identifying ELM types. Further, the classification scheme is general and can be applied to various other plasma phenomena as well.EURATOM 63305
Color texture discrimination using the principal geodesic distance on a multivariate generalized Gaussian manifold
We present a new texture discrimination method for textured color images in the wavelet domain. In each wavelet subband, the correlation between the color bands is modeled by a multivariate generalized Gaussian distribution with fixed shape parameter (Gaussian, Laplacian). On the corresponding Riemannian manifold, the shape of texture clusters is characterized by means of principal geodesic analysis, specifically by the principal geodesic along which the cluster exhibits its largest variance. Then, the similarity of a texture to a class is defined in terms of the Rao geodesic distance on the manifold from the texture's distribution to its projection on the principal geodesic of that class. This similarity measure is used in a classification scheme, referred to as principal geodesic classification (PGC). It is shown to perform significantly better than several other classifiers
Weyl collineations that are not curvature collineations
Though the Weyl tensor is a linear combination of the curvature tensor, Ricci
tensor and Ricci scalar, it does not have all and only the Lie symmetries of
these tensors since it is possible, in principle, that "asymmetries cancel".
Here we investigate if, when and how the symmetries can be different. It is
found that we can obtain a metric with a finite dimensional Lie algebra of Weyl
symmetries that properly contains the Lie algebra of curvature symmetries.
There is no example found for the converse requirement. It is speculated that
there may be a fundamental reason for this lack of "duality".Comment: 9 page
NeuroGraph: Benchmarks for Graph Machine Learning in Brain Connectomics
Machine learning provides a valuable tool for analyzing high-dimensional
functional neuroimaging data, and is proving effective in predicting various
neurological conditions, psychiatric disorders, and cognitive patterns. In
functional magnetic resonance imaging (MRI) research, interactions between
brain regions are commonly modeled using graph-based representations. The
potency of graph machine learning methods has been established across myriad
domains, marking a transformative step in data interpretation and predictive
modeling. Yet, despite their promise, the transposition of these techniques to
the neuroimaging domain has been challenging due to the expansive number of
potential preprocessing pipelines and the large parameter search space for
graph-based dataset construction. In this paper, we introduce NeuroGraph, a
collection of graph-based neuroimaging datasets, and demonstrated its utility
for predicting multiple categories of behavioral and cognitive traits. We delve
deeply into the dataset generation search space by crafting 35 datasets that
encompass static and dynamic brain connectivity, running in excess of 15
baseline methods for benchmarking. Additionally, we provide generic frameworks
for learning on both static and dynamic graphs. Our extensive experiments lead
to several key observations. Notably, using correlation vectors as node
features, incorporating larger number of regions of interest, and employing
sparser graphs lead to improved performance. To foster further advancements in
graph-based data driven neuroimaging analysis, we offer a comprehensive
open-source Python package that includes the benchmark datasets, baseline
implementations, model training, and standard evaluation.Comment: NeurIPS2
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