Synchronization of Coupled Boolean Networks With Different Update Scheme

Abstract

In this paper, the synchronization of coupled Boolean networks with asynchronous update scheme is investigated. First, the asynchronous Boolean dynamics is transformed into a linear expression with the semi-tensor product technique. Then, the synchronization cycle is proposed to establish the synchronization conditions of asynchronous Boolean networks. Furthermore, an algorithm is given, which can be used to quickly check whether there exists the synchronization cycle in the coefficient matrix of the Boolean function. Finally, an example is provided to verify the efficiency of the theoretical analysis. INDEX TERMS Asynchronous update scheme, Boolean network, synchronization, semi-tensor product.

Double Deep-Q Learning-Based Output Tracking of Probabilistic Boolean Control Networks

“…subject to systems (17) and (18). (19) With this settings, the agent is guided to find deterministic policies µ(Z t ) that can steer the state of the system X t along the reference trajectory X r t , while minimizing the cost associated to the action performed, i.e., finding the expected optimal shortest path.…”

“…To solve the optimization problem (19) in a modelfree context, we use an episodic framework. The RL term ''episode'' represents the interactions between the agent and the system from an initial state X 0 towards a terminal condition, e.g., X T = X r T , by following some policy that achieves exploration, i.e., the random selection of various actions at various states.…”