Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2007-08-16
Published in: Journal of Mathematical Physics Vol.48 (2007) 083506
Nonlinear Sciences
Adaptation and Self-Organizing Systems
4 figures 18 pages
Scientific paper
10.1063/1.2768747
We determine the average number $ \vartheta (N, K) $, of \textit{NK}-Kauffman networks that give rise to the same binary function. We show that, for $ N \gg 1 $, there exists a connectivity critical value $ K_c $ such that $ \vartheta(N,K) \approx e^{\phi N} $ ($ \phi > 0 $) for $ K < K_c $ and $\vartheta(N,K) \approx 1 $ for $ K > K_c $. We find that $ K_c $ is not a constant, but scales very slowly with $ N $, as $ K_c \approx \log_2 \log_2 (2N / \ln 2) $. The problem of genetic robustness emerges as a statistical property of the ensemble of \textit{NK}-Kauffman networks and impose tight constraints in the average number of epistatic interactions that the genotype-phenotype map can have.
Romero David
Zertuche Federico
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