Nested canalizing Boolean  functions play an important role in biological motivated regulative networks but also in signal processing, such as in describing stack filters. It has been conjectured that this class of functions has 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 prove a tight upper bound on the average sensitivity for nested canalizing functions in dependence of the number of relevant input variables. We further show, that it is smaller than 4/3 as conjectured in literature. This shows a large number of functions appearing in biological networks belong to a class that has a very low average sensitivity, which is even close to a tight lower bound.
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.
A
(NCF)
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but also
and
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such as in
in particular
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this class of functions has
NCFs have
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Random
random
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, we prove
we provide
R
nested canalizing functions in dependence
NCFs as a function
R
We further show, that it
As conjectured in literature this bound
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as conjectured in literature. This shows
This shows that
D
a