Measuring robustness of brain networks in autism spectrum disorder with Ricci curvature. [PDF]
Sci Rep, 2020 Ollivier–Ricci curvature is a method for measuring the robustness of connections in a network. In this work, we use curvature to measure changes in robustness of brain networks in children with autism spectrum disorder (ASD).
Simhal AK +7 more
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Ricci curvature of submanifolds in Kenmotsu space forms [PDF]
International Journal of Mathematics and Mathematical Sciences, 2002 In 1999, Chen established a sharp relationship between the Ricci curvature and the squared mean curvature for a submanifold in a Riemannian space form with arbitrary codimension.
Kadri Arslan +4 more
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Ricci curvature for metric-measure spaces via optimal transport [PDF]
, 2004 We dene a notion of a measured length space X having nonnegative N-Ricci curvature, for N 2 [1;1), or having1-Ricci curvature bounded below byK, forK2 R.
John Lott, Cédric Villani
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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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Mitigating Over-Smoothing and Over-Squashing using Augmentations of Forman-Ricci Curvature [PDF]
LOG IN, 2023 While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently.
Lukas Fesser, Melanie Weber
semanticscholar +1 more source
Revisiting Over-smoothing and Over-squashing using Ollivier's Ricci Curvature [PDF]
International Conference on Machine Learning, 2022 Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking ...
K. Nguyen +5 more
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Semilinear elliptic equations on manifolds with nonnegative Ricci curvature [PDF]
Journal of the European Mathematical Society (Print), 2022 In this paper we prove classification results for solutions to subcritical and critical semilinear elliptic equations with a nonnegative potential on noncompact manifolds with nonnegative Ricci curvature.
G. Catino, D. Monticelli
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Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework [PDF]
International Conference on Learning Representations, 2022 Bridging geometry and topology, curvature is a powerful and expressive invariant. While the utility of curvature has been theoretically and empirically confirmed in the context of manifolds and graphs, its generalization to the emerging domain of ...
Corinna Coupette +2 more
semanticscholar +1 more source
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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