Nested canalizing Boolean (NCF) functions play an important role in
biological motivated regulative networks and in signal processing, in
particular describing stack filters. It has been conjectured that NCFs have a
stabilizing effect on the network dynamics. It is well known that the average
sensitivity plays a central role for the stability of (random) Boolean
networks. Here we provide a tight upper bound on the average sensitivity for
NCFs as a function of the number of relevant input variables. As conjectured in
literature this bound is smaller than 4/3 This shows that a large number of
functions appearing in biological networks belong to a class that has very low
average sensitivity, which is even close to a tight lower bound.Comment: revised submission to PLOS ON
