Natural Computing

, Volume 16, Issue 3, pp 427–439 | Cite as

Activity in Boolean networks

  • Abhijin Adiga
  • Hilton Galyean
  • Chris J. Kuhlman
  • Michael Levet
  • Henning S. Mortveit
  • Sichao Wu
Article

Abstract

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 Erdős–Renyi random graph model. We conclude with some open questions and thoughts on directions for future research related to activity, including long-term activity.

Keywords

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

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Abhijin Adiga
    • 1
  • Hilton Galyean
    • 2
  • Chris J. Kuhlman
    • 1
  • Michael Levet
    • 4
  • Henning S. Mortveit
    • 1
    • 3
  • Sichao Wu
    • 1
  1. 1.Network Dynamics and Simulation Science Laboratory, VBIVirginia TechBlacksburgUSA
  2. 2.Department of PhysicsVirginia TechBlacksburgUSA
  3. 3.Department of MathematicsVirginia TechBlacksburgUSA
  4. 4.Department of Computer ScienceUniversity of South CarolinaColumbiaUSA

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