  The canalizing properties of biological functions have been mainly studied in
the context of Boolean modelling of gene regulatory networks. An important
mathematical consequence of canalization is a low average sensitivity, which
ensures in particular the expected robustness to noise. In certain situations,
the Boolean description is too crude, and it may be necessary to consider
functions involving more than two levels of expression. We investigate here the
properties of nested canalization for these multivalued functions. We prove
that the average sensitivity of nested canalizing multivalued functions is
bounded above by a constant. In doing so, we introduce a generalization of
nested canalizing multivalued functions, which we call weakly nested
canalizing, for which this upper bound holds.
