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
doaj +3 more sources
Comparative analysis of two discretizations of Ricci curvature for complex networks. [PDF]
Sci Rep, 2018 We have performed an empirical comparison of two distinct notions of discrete Ricci curvature for graphs or networks, namely, the Forman-Ricci curvature and Ollivier-Ricci curvature.
Samal A +5 more
europepmc +4 more sources
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 +9 more sources
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
doaj +2 more sources
On the projective Ricci curvature [PDF]
arXiv, 2020 The notion of the Ricci curvature is defined for sprays on a manifold. With a volume form on a manifold, every spray can be deformed to a projective spray. The Ricci curvature of a projective spray is called the projective Ricci curvature. In this paper, we introduce the notion of projectively Ricci-flat sprays.
Zhongmin Shen, Liling Sun, Liling Sun
arxiv +5 more sources
Ricci curvature: An economic indicator for market fragility and systemic risk. [PDF]
Sci Adv, 2016 Researchers introduce the geometric concept of curvature toward the application of uncovering systemic risk and market fragility. Quantifying the systemic risk and fragility of financial systems is of vital importance in analyzing market efficiency ...
Sandhu RS, Georgiou TT, Tannenbaum AR.
europepmc +2 more sources
Ricci Curvature on Polyhedral Surfaces via Optimal Transportation [PDF]
Axioms, 2014 The problem of correctly defining geometric objects, such as the curvature, is a hard one in discrete geometry. In 2009, Ollivier defined a notion of curvature applicable to a wide category of measured metric spaces, in particular to graphs.
Benoît Loisel, Pascal Romon
doaj +6 more sources
Discrete Ricci curvatures capture age-related changes in human brain functional connectivity networks [PDF]
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
doaj +2 more sources
Introducing quantum Ricci curvature [PDF]
Physical Review D, 2017 Motivated by the search for geometric observables in nonperturbative quantum gravity, we define a notion of coarse-grained Ricci curvature. It is based on a particular way of extracting the local Ricci curvature of a smooth Riemannian manifold by ...
N. Klitgaard, R. Loll
semanticscholar +6 more sources
On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth. [PDF]
Calc Var Partial Differ Equ, 2022 Antonelli G +3 more
europepmc +3 more sources