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We present a characterization of short-term stability of random Boolean networks under emph{arbitrary} distributions of transfer functions. Given any distribution of transfer functions for a random Boolean network, we present a formula that decides whether short-term chaos (damage spreading) will happen. We provide a formal proof for this formula, and empirically show that its predictions are accurate. Previous work only works for special cases of balanced families. It has been observed that these characterizations fail for unbalanced families, yet such families are widespread in real biological networks.
We consider the problem of studying the simulation capabilities of the dynamics of arbitrary networks of finite states machines. In these models, each node of the network takes two states 0 (passive) and 1 (active). The states of the nodes are update
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where only one affi
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expre
We derive a master stability function (MSF) for synchronization in networks of coupled dynamical systems with small but arbitrary parametric variations. Analogous to the MSF for identical systems, our generalized MSF simultaneously solves the linear
We show that a Boolean degree $d$ function on the slice $binom{[n]}{k} = { (x_1,ldots,x_n) in {0,1} : sum_{i=1}^n x_i = k }$ is a junta, assuming that $k,n-k$ are large enough. This generalizes a classical result of Nisan and Szegedy on the hypercube