Results 11 to 20 of about 71,917 (238)

Ricci Curvature on Polyhedral Surfaces via Optimal Transportation [PDF]

open access: yesAxioms, 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   +8 more sources

Detecting network anomalies using Forman–Ricci curvature and a case study for human brain networks [PDF]

open access: yesScientific 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   +2 more sources

FORMAN–RICCI CURVATURE FOR HYPERGRAPHS [PDF]

open access: hybridAdvances 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
openalex   +5 more sources

Ollivier Ricci curvature of directed hypergraphs [PDF]

open access: yesScientific Reports, 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 ...
Marzieh Eidi, Jürgen Jost
openaire   +5 more sources

Curvature Inheritance Symmetry in Ricci Flat Spacetimes [PDF]

open access: goldUniverse, 2022
In this article, we study curvature inheritance symmetry in Ricci flat spacetimes. We show that, if Ricci flat spacetimes are not of Petrov type N, and admit curvature inheritance symmetries, then the only existing symmetries are conformal motions.
Mohammad Salman   +2 more
doaj   +2 more sources

Non-local interaction in discrete Ricci curvature-induced biological aggregation [PDF]

open access: yesRoyal Society Open Science
We 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
doaj   +2 more sources

A Review of and Some Results for Ollivier–Ricci Network Curvature [PDF]

open access: yesMathematics, 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
doaj   +5 more sources

On $m$-th root metrics of isotropic projective Ricci curvature [PDF]

open access: yesAUT 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
doaj   +1 more source

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