Activity in Boolean networks

作者：Adiga Abhijin; Galyean Hilton; Kuhlman Chris J; Levet Michael; Mortveit Henning S^*; Wu Sichao

来源：Natural Computing, 2017, 16(3): 427-439.

DOI：10.1007/s11047-016-9584-z

• Boolean networks
• Finite dynamical system
• Activity
• Sensitivity
• Network
• Sensitive dependence on initial conditions

In this paper we extend the notion of activity for Boolean networks introduced by Shmulevich and Kauffman (Phys Rev Lett 93(4):48701:1-4, 2004). In contrast to existing theory, we take into account the actual graph structure of the Boolean network. The notion of activity measures the probability that a perturbation in an initial state produces a different successor state than that of the original unperturbed state. It captures the notion of sensitive dependence on initial conditions, and provides a way to rank vertices in terms of how they may impact predictions. We give basic results that aid in the computation of activity and apply this to Boolean networks with threshold functions and nor functions for elementary cellular automata, d-regular trees, square lattices, triangular lattices, and the ErdAs-Renyi random graph model. We conclude with some open questions and thoughts on directions for future research related to activity, including long-term activity.

• 出版日期2017-9
• 单位Virginia Tech; 美国弗吉尼亚理工大学(Virginia Tech)