Optimal Control of Boolean Control Networks with Discounted Cost: An Efficient Approach based on Deterministic Markov Decision Process

This paper deals with the infinite-horizon optimal control problem for Boolean control networks (BCNs) with a discounted-cost criterion. This problem has been investigated in existing studies with algorithms characterized by high computational complexity. We thus attempt to develop more efficient approaches for this problem from a deterministic Markov decision process (DMDP) perspective. First, we show the eligibility of a DMDP to model the control process of a BCN and the existence of an optimal solution. Next, two approaches are developed to handle the optimal control problem in a DMDP. One approach adopts the well-known value iteration algorithm, and the other resorts to the Madani's algorithm specifically designed for DMDPs. The latter approach can find an exact optimal solution and outperform existing methods in terms of time efficiency, while the former value iteration based approach usually obtains a near-optimal solution much faster than all others. The 9-state-4-input \textit{ara} operon network of the bacteria \textit{E. coli} is used to verify the effectiveness and performance of our approaches. Results show that both approaches can reduce the running time dramatically by several orders of magnitude compared with existing work

An improved transformation between Fibonacci FSRs and Galois FSRs

Feedback shift registers (FSRs), which have two configurations: Fibonacci and Galois, are a primitive building block in stream ciphers. In this paper, an improved transformation is proposed between Fibonacci FSRs and Galois FSRs. In the previous results, the number of stages is identical when constructing the equivalent FSRs. In this paper, there is no requirement to keep the number of stages equal for two equivalent FSRs here. More precisely, it is verified that an equivalent Galois FSR with fewer stages cannot be found for a Fibonacci FSR, but the converse is not true. Furthermore, the total number of equivalent Galois FSRs for a given Fibonacci FSR with n stages is calculated. In order to reduce the propagation time and memory, an effective algorithm is developed to find equivalent Galois FSR and is proved to own minimal operators and stages. Finally, the feasibility of our proposed strategies, to mutually transform Fibonacci FSRs and Galois FSRs, is demonstrated by numerical examples.Comment: 8 pages, 2 figure

Distributed Pinning Control Design for Probabilistic Boolean Networks

This paper investigates the stabilization of probabilistic Boolean networks (PBNs) via a novel pinning control strategy based on network structure. In a PBN, each node needs to choose a Boolean function from candidate Boolean function set at each time instance with certain probability. Owing to the stochasticity, the uniform state feedback controllers, which is independent of switching signal, might be out of work. Thereby, a criterion is derived to determine that under what condition uniform controllers can be applied, otherwise non-uniform controllers need to be utilized. Accordingly, an algorithm is designed to find a series of state feedback pinning controllers, under which such a PBN is stabilized to a prespecified steady state. It is worth pointing out that the pinning control used in this paper only requires local in-neighbors' information, rather than global information. Hence, it is also termed as distributed pinning control and reduces the computational complexity to a large extent. Profiting from this, it provides a potential to deal with some large-scale networks. Finally, the mammalian cell-cycle encountering a mutated phenotype is described as a PBN, and presented to demonstrate the obtained results