2023/01/26 by Dongyao Bi, Bi, Dongyao, Lijun Zhang +4
Biochemistry, Genetics and Molecular Biology · Computer Science · Medicine · #Gene Regulatory Network Analysis #Computational Drug Discovery Methods #Cholinesterase and Neurodegenerative Diseases
paper · pdf · doi:10.48550/arxiv.2301.10961
This paper presents the following research findings on Boolean networks (BNs) and their dual subspaces.First, we establish a bijection between the dual subspaces of a BN and the partitions of its state set. Furthermore, we demonstrate that a dual subspace is M-invariant if and only if the associated partition is equitable (i.e., for every two cells of the partition, every two states in the former have the same number of out-neighbors in the latter) for the BN's state-transition graph (STG). Here M represents the structure matrix of the BN.Based on the equitable graphic representation, we provide, for the first time, a complete structural characterization of the smallest M-invariant dual subspaces generated by a set of Boolean functions. Given a set of output functions, we prove that a BN is observable if and only if the partition corresponding to the smallest M-invariant dual subspace generated by this set of functions is trivial (i.e., all partition cells are singletons). Building upon our structural characterization, we also present a method for constructing output functions that render the BN observable.