The Effects of State Dependent and State Independent Probabilistic Updating on Boolean Network Dynamics

摘要: We study semi-synchronous Boolean networks with robabilistic updating schemes and various topologies (tree, loop, random). As well as state independent probabilistic we investigate a dependent scheme which allows us to control the `accuracy' of nodes. A node is accurate at $n$ if it has been updated $n$, or its would be had updated. The re-evaluation probabilities are determined by `accuracy heuristic': stochastic equation depends on estimation of distribution; look ways estimating this distribution derive variance expressions for estimators. Through our work random trees observe that (in general) output function correlated inputs, becomes less number inputs increased. also discover correlation function's directly affects ability heuristic achieve node's target accuracy. Deterministic network dynamics viewed in new way, via distributions (the probability $1$ $0$). This view shows `activity' nodes across network. find in-degree increased topology effect activity functions dominates. present theoretical result support theory. To understand probabilistically use numerical approximation Flyvbjerg's frozen component. The concept stability addressed investigated. For loop active loops fall into two categories: those an odd inversion even number. discuss fixed point both cases. annealed indicates phase transition similar previously found deterministic networks.