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 . 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.
Highlights
Boolean networks play an important role in modeling and understanding signal transduction and regulatory networks
We give a tight upper bound on the average sensitivity of Nested canalizing Boolean functions (NCF)
In [21] an upper bound on the average sensitivity of NCF has been conjectured
Summary
Boolean networks play an important role in modeling and understanding signal transduction and regulatory networks. One line of research focuses on the dynamical stability of randomly created networks. Random Boolean networks tend to be unstable, if the functions are chosen from the set of all Boolean functions with average number of variables (average in-degree) larger than two [4]. This can be attributed to the fact that the expected average sensitivity of random Boolean functions with an in-degree w2 is larger than one. The expected average sensitivity is an appropriate measure for the stability of random Boolean networks [5,6]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
