Proceedings of the American Mathematical Society
Biological networks, Commutative algebra, Stochastic approximation, Dynamical systems
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
DINWOODIE, I. H. (2014). VANISHING CONFIGURATIONS IN NETWORK DYNAMICS WITH ASYNCHRONOUS UPDATES. Proceedings Of The American Mathematical Society, 142(9), 2991-3002.