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Detecting network anomalies using Forman–Ricci curvature and a case study for human brain networks [PDF]
Scientific Reports, 2021 We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd).
Tanima Chatterjee +4 more
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Ollivier Ricci curvature of directed hypergraphs. [PDF]
Sci Rep, 2020 AbstractMany empirical networks incorporate higher order relations between elements and therefore are naturally modelled as, possibly directed and/or weighted, hypergraphs, rather than merely as graphs. In order to develop a systematic tool for the statistical analysis of such hypergraph, we propose a general definition of Ricci curvature on directed ...
Eidi M, Jost J.
europepmc +6 more sources
A Review of and Some Results for Ollivier–Ricci Network Curvature [PDF]
Mathematics, 2020 Characterizing topological properties and anomalous behaviors of higher-dimensional topological spaces via notions of curvatures is by now quite common in mainstream physics and mathematics, and it is therefore natural to try to extend these notions from
Nazanin Azarhooshang +2 more
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Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]
Royal Society Open ScienceWe investigate the collective dynamics of multi-agent systems in two- and three-dimensional environments generated by minimizing discrete Ricci curvature with local and non-local interaction neighbourhoods.
Jyotiranjan Beuria, Laxmidhar Behera
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On $m$-th root metrics of isotropic projective Ricci curvature [PDF]
AUT Journal of Mathematics and Computing, 2023 The Ricci curvature is introduced by spray on $M^n$. Sprays are deformed to projective sprays with a volume form $dV$ on $M^n$. The projective Ricci curvature is defined as the expression of Ricci curvature with sprays.
Mehran Gabrani +2 more
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FORMAN–RICCI CURVATURE FOR HYPERGRAPHS [PDF]
Advances in Complex Systems, 2021 Hypergraphs serve as models of complex networks that capture more general structures than binary relations. For graphs, a wide array of statistics has been devised to gauge different aspects of their structures. Hypergraphs lack behind in this respect.
Wilmer Leal +3 more
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Weighted Ricci curvature in Riemann-Finsler geometry [PDF]
AUT Journal of Mathematics and Computing, 2021 Ricci curvature is one of the important geometric quantities in Riemann-Finsler geometry. Together with the $S$-curvature, one can define a weighted Ricci curvature for a pair of Finsler metric and a volume form on a manifold.
Zhongmin Shen
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Frontiers in Aging Neuroscience, 2023 IntroductionGeometry-inspired notions of discrete Ricci curvature have been successfully used as markers of disrupted brain connectivity in neuropsychiatric disorders, but their ability to characterize age-related changes in functional connectivity is ...
Yasharth Yadav +8 more
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On Ricci Curvature of a Homogeneous Generalized Matsumoto Finsler Space
Mathematics, 2023 The characterization of Finsler spaces with Ricci curvature is an ancient and cumbersome one. In this paper, we have derived an expression of Ricci curvature for the homogeneous generalized Matsumoto change.
Yanlin Li +3 more
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On Scalar and Ricci Curvatures [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2021 The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature?
Besson, Gérard, Gallot, Sylvestre
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