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Vanishing configurations in network dynamics with asynchronous updates


Author: Ian H. Dinwoodie
Journal: Proc. Amer. Math. Soc. 142 (2014), 2991-3002
MSC (2010): Primary 13P25, 62M86
DOI: https://doi.org/10.1090/S0002-9939-2014-12044-2
Published electronically: May 22, 2014
MathSciNet review: 3223354
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Abstract: We consider Boolean dynamics for biological networks where stochasticity is introduced through asynchronous updates. An exact method is given for finding states which can reach a steady state with positive probability, and a method is given for finding states which cannot reach other steady states. These methods are based on computational commutative algebra. The algorithms are applied to dynamics of a cell survival network to determine node assignments that exclude termination in a cancerous state.


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Additional Information

Ian H. Dinwoodie
Affiliation: Department of Mathematical Sciences, Portland State University, Portland, Oregon 97201

DOI: https://doi.org/10.1090/S0002-9939-2014-12044-2
Keywords: Asynchronous network, basin of attraction, Boolean network, Groebner basis, Markov chain.
Received by editor(s): June 25, 2012
Received by editor(s) in revised form: September 25, 2012
Published electronically: May 22, 2014
Communicated by: David Levin
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.