Bounds on the Average Sensitivity of Nested Canalizing Functions

TL;DR

This paper establishes a tight upper bound on the average sensitivity of nested canalizing Boolean functions, demonstrating their low sensitivity and potential stabilizing effect in biological and signal processing networks.

Contribution

It provides the first tight upper bound on the average sensitivity of NCFs as a function of relevant variables, confirming their low sensitivity in biological networks.

Findings

Upper bound on average sensitivity is smaller than 4/3.

Many biological network functions have very low average sensitivity.

The bound is tight and close to the lower bound for NCFs.

Abstract

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.