Cookies?
Library Header Image
LSE Research Online LSE Library Services

Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction

Dini, Paolo and Nehaniv, Chrystopher L. and Egri-Nagy, Attila and Schilstra, Maria J. (2013) Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction. Biosystems, 112 (2). pp. 145-162. ISSN 0303-2647

[img]
Preview
PDF - Accepted Version
Download (1MB) | Preview
Identification Number: 10.1016/j.biosystems.2013.03.003

Abstract

Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn.

Item Type: Article
Official URL: http://www.journals.elsevier.com/biosystems
Additional Information: © 2013 Elsevier Ireland Ltd.
Subjects: Q Science > QA Mathematics
Sets: Departments > Media and Communications
Date Deposited: 09 May 2013 15:56
Last Modified: 20 Jun 2014 09:58
Projects: INFSO-FP6-507953, INFSO-FP6-027748, INFSO-FP6-034824, INFSO-FP7-288021, CNECT-ICT-318202
Funders: Digital Business Ecosystem
URI: http://eprints.lse.ac.uk/id/eprint/49851

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics