title: Characterizing short-term stability for Boolean networks over any distribution of transfer functions.
abstract: We present a characterization of short-term stability of Kauffman's NK (random) Boolean networks under arbitrary distributions of transfer functions. Given such a Boolean network where each transfer function is drawn from the same distribution, we present a formula that determines whether short-term chaos (damage spreading) will happen. Our main technical tool which enables the formal proof of this formula is the Fourier analysis of Boolean functions, which describes such functions as multilinear polynomials over the inputs. Numerical simulations on mixtures of threshold functions and nested canalyzing functions demonstrate the formula's correctness.
authors: University of California, Santa Cruz, California 95064, USA.
authors: C
authors: C
authors: Seshadhri
authors: Sandia National Laboratories, P.O. Box 969, Livermore, California 94551, USA.
authors: Andrew M
authors: AM
authors: Smith
authors: Vanderbilt University, Nashville, Tennessee 37235, USA.
authors: Yevgeniy
authors: Y
authors: Vorobeychik
authors: Sandia National Laboratories, P.O. Box 969, Livermore, California 94551, USA.
authors: Jackson R
authors: JR
authors: Mayo
authors: Sandia National Laboratories, P.O. Box 969, Livermore, California 94551, USA.
authors: Robert C
authors: RC
authors: Armstrong