Next Article in Journal / Special Issue
Discrete Geometry—From Theory to Applications: A Case Study
Previous Article in Journal
Quantum Quasigroups and the Quantum Yang–Baxter Equation
Article Menu

Export Article

Open AccessArticle
Axioms 2016, 5(4), 26; doi:10.3390/axioms5040026

Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets

1,2,†
,
1,3
and
1,4,*
1
Max-Planck-Institute for Mathematics in the Sciences, Inselstrasse 22, 04103 Leipzig, Germany
2
Department of Mathematics, University of Leipzigt, Augustusplatz 10, 04109 Leipzig, Germany
3
Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
4
Departments of Mathematics and Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel
Current address: Program in Applied and Computational Mathematics, Princeton University, Fine Hall 221, Washington Road, Princeton, NJ 08544, USA.
*
Author to whom correspondence should be addressed.
Academic Editor: Humberto Bustince
Received: 10 September 2016 / Revised: 26 October 2016 / Accepted: 7 November 2016 / Published: 10 November 2016
(This article belongs to the Special Issue Discrete Geometry and its Applications)
View Full-Text   |   Download PDF [2282 KB, uploaded 10 November 2016]   |  

Abstract

We present a viable geometric solution for the detection of dynamic effects in complex networks. Building on Forman’s discretization of the classical notion of Ricci curvature, we introduce a novel geometric method to characterize different types of real-world networks with an emphasis on peer-to-peer networks. We study the classical Ricci-flow in a network-theoretic setting and introduce an analytic tool for characterizing dynamic effects. The formalism suggests a computational method for change detection and the identification of fast evolving network regions and yields insights into topological properties and the structure of the underlying data. View Full-Text
Keywords: Ricci flow; Forman curvature; complex systems; dynamic networks; change detection; peer-to-peer network Ricci flow; Forman curvature; complex systems; dynamic networks; change detection; peer-to-peer network
Figures

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Weber, M.; Jost, J.; Saucan, E. Forman-Ricci Flow for Change Detection in Large Dynamic Data Sets. Axioms 2016, 5, 26.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Axioms EISSN 2075-1680 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top