Mappings between probabilistic Boolean networks

Probabilistic Boolean Networks (PBNs) comprise a graphical model based on uncertain rule-based dependencies between nodes and have been proposed as a model for genetic regulatory networks. As with any algebraic structure, the characterization of important mappings between PBNs is critical for both theory and application. This paper treats the construction of mappings to alter PBN structure while at the same time maintaining consistency with the original probability structure. It considers projections onto sub-networks, adjunctions of new nodes, resolution reduction mappings formed by merging nodes, and morphological mappings on the graph structure of the PBN. It places PBNs in the framework of many-sorted algebras and in that context de5nes homomorphisms between PBNs. ? 2002 Elsevier Science B.V. All rights reserved.