Topological characterization of S[B] systems: From data to models of complexity

TL;DR

This paper introduces a novel methodology combining Topological Data Analysis and a two-level S[B] model to analyze complex systems, demonstrated through application to the mammal immune system's idiotypic network.

Contribution

It presents a new approach integrating Persistent Entropy and Higher Dimensional Automata for modeling complex systems at structural and behavioral levels.

Findings

Successful modeling of the mammal immune system's idiotypic network

Effective use of Persistent Entropy for structural analysis

Representation of system evolution as a Persistent Entropy Automaton

Abstract

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. The other level, the behavioral B one, is characterized by a network of interacting computational agents described by a Higher Dimensional Automaton. The methodology yields also a representation of the evolution of the derived two-level model as a Persistent Entropy Automaton. The presented methodology is applied to a real case study, the Idiotypic Network of the mammal immune system.