概率布尔网络重构

Reconstruction of probabilistic Boolean networks

概率布尔网络是研究社会网络上的观念动力学以及基因调控网络的重要模型.对概率布尔网络的研究主要是利用Markov理论对系统的状态转移矩阵进行分析,矩阵的半张量积是将逻辑动态系统转化为代数形式的重要工具.本文主要利用矩阵的半张量积研究概率布尔网络到概率转移矩阵的逆问题,即将状态空间框架下的概率转移矩阵还原为原始的概率布尔网络.首先给出从状态概率转移矩阵构造概率布尔网络的算法,其次考虑到从概率状态转移矩阵到概率布尔网络构造的不唯一性,进一步改进了概率布尔网络逻辑表达的重构算法,最后通过实例检验了算法的有效性,并对未来的研究方向作出展望.

Probabilistic Boolean control networks（PBCNs） have received a great amount of attention in the field of opinion dynamics in social networks and gene（or genetic） regulatory networks. PBCNs have been transferred to state transition probability matrices. Using a Markov chain theory, the PBCN is investigated under a state space framework. In this paper, we address the problem of constructing a probabilistic Boolean control network from a prescribed transition probability matrix. First, an algorithm is given to obtain the realization of a PBCN.Second, because of the non-uniqueness of the logical realization of a PBCN, a modified algorithm is introduced to obtain other realizations of PBCNs. Finally, an illustrative example is given to demonstrate both the efficiency and effectiveness of the proposed algorithms. In addition, the future direction of the research is discussed.