From multivalued to Boolean functions: Preservation of soft nested canalization

Nested canalization (NC) is a property of Boolean functions which has been recently extended to multivalued functions. We study the effect of the Van Ham mapping (from multivalued to Boolean functions) on this property. We introduce the class of softly nested canalizing (SNC) multivalued functions, and prove that the Van Ham mapping sends SNC multivalued functions to NC Boolean functions. Since NC multivalued functions are SNC, this preservation property holds for NC multivalued functions as well. We also study the relevance of SNC functions in the context of gene regulatory network modelling.

Automated summary

This paper studies the extension of the nested canalization property to multivalued functions and investigates the effect of the Van Ham mapping on this property. The study finds that the Van Ham mapping transforms softly nested canalizing multivalued functions into nested canalization Boolean functions, a property that is also relevant in the modeling of gene regulatory networks.