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.
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Acknowledgments
We thank our external collaborators and members of the Network Dynamics and Simulation Science Laboratory (NDSSL) for their suggestions and comments. We also thank two anonymous reviewers for valuable comments. This work has been partially supported by DTRA Grant HDTRA1-11-1-0016.
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Adiga, A., Galyean, H., Kuhlman, C.J. et al. Activity in Boolean networks. Nat Comput 16, 427–439 (2017). https://doi.org/10.1007/s11047-016-9584-z
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DOI: https://doi.org/10.1007/s11047-016-9584-z