Topological Characterization of Complex Systems: Using Persistent Entropy

• Published in: Entropy (Basel, Switzerland) Vol. 17; no. 10; pp. 6872 - 6892
• Main Authors: Emanuela Merelli, Matteo Rucco, Peter Sloot, Luca Tesei
• Format: Journal Article
• Language: English
• Published: MDPI AG 01-10-2015
• Subjects: computational agents; higher dimensional automata; idiotypic network; immune system; persistent entropy automaton; topological data analysis
• ISSN: 1099-4300
• DOI: 10.3390/e17106872

In this paper, we propose a methodology for deriving a model of a complex system by exploiting the information extracted from topological data analysis. Central to our approach is the S[B] paradigm in which a complex system is represented by a two-level model. One level, the structural S one, is derived using the newly-introduced quantitative concept of persistent entropy, and it is described by a persistent entropy automaton. The other level, the behavioral B one, is characterized by a network of interacting computational agents. The presented methodology is applied to a real case study, the idiotypic network of the mammalian immune system.