Canalizing Boolean Functions Maximize the Mutual Information
Information Theory
2012-11-06 v2 math.IT
Adaptation and Self-Organizing Systems
Molecular Networks
Abstract
The ability of information processing in biologically motivated Boolean networks is of interest in recent information theoretic research. One measure to quantify this ability is the well known mutual information. Using Fourier analysis we show that canalizing functions maximize the mutual information between an input variable and the outcome of the function. We proof our result for Boolean functions with uniform distributed as well as product distributed input variables.
Cite
@article{arxiv.1207.7193,
title = {Canalizing Boolean Functions Maximize the Mutual Information},
author = {Johannes Georg Klotz and David Kracht and Martin Bossert and Steffen Schober},
journal= {arXiv preprint arXiv:1207.7193},
year = {2012}
}
Comments
Accepted at SCC 2013, Munich, Germany, www.scc2013.net