On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions
Por:
Zertuche, F
Publicada:
1 abr 2009
Resumen:
NK-Kauffman networks L(K)(N) are a subset of the Boolean functions on N Boolean variables to themselves, Lambda(N)={xi:Z(2)(N)-> Z(2)(N)}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function Psi:L(K)(N)->Lambda(N). The probability P(K) that Psi(f)=Psi(f(')), when f(') is obtained through f by a change in one of its K-Boolean functions (b(K):Z(2)(K)-> Z(2)), and/or connections, is calculated. The leading term of the asymptotic expansion of P(K), for N > 1, turns out to depend on the probability to extract the tautology and contradiction Boolean functions, and in the average value of the distribution of probability of the Boolean functions, the other terms decay as O(1/N). In order to accomplish this, a classification of the Boolean functions in terms of what I have called their irreducible degree of connectivity is established. The mathematical findings are discussed in the biological context, where Psi is used to model the
Filiaciones:
Zertuche, F:
Univ Nacl Autonoma Mexico, Inst Matemat, Unidad Cuernavaca, Cuernavaca 62251, Morelos, Mexico
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