title: Bounds on the average sensitivity of nested canalizing functions.
abstract: Nested canalizing Boolean functions (NCF) play an important role in biologically motivated regulatory 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 of 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 low average sensitivity, which is even close to a tight lower bound.
authors.affiliation: Institute of Communications Engineering, Ulm University, Ulm, Germany. johannes.klotz@uni-ulm.de
authors.forename: Johannes Georg
authors.initials: JG
authors.lastname: Klotz
authors.forename: Reinhard
authors.initials: R
authors.lastname: Heckel
authors.forename: Steffen
authors.initials: S
authors.lastname: Schober
mesh_terms: D003198:Computer Simulation; D005583:Fourier Analysis; D053263:Gene Regulatory Networks; D015233:Models, Statistical