  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.
