2012/08/31 by Federico Zertuche · 3 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Cellular Automata and Applications #Cellular automaton #Chaotic #Combinatorics #Computer science #Condensed matter physics #Discrete mathematics #Gene Regulatory Network Analysis #Irreducibility #Mathematics #Nonlinear Dynamics and Pattern Formation #Phase transition #Physics #Pure mathematics #Realization (probability) #Statistics #nlin.CG
paper · pdf · doi:10.1016/j.physd.2014.02.006
published in Physica D Nonlinear Phenomena 275, 35-42 (Elsevier BV) · 23 pages, 7 Figures on request. Published in Physica D: Nonlinear Phenomena: Vol.275 (2014) 35-42
openalex publication_date 2014/02/25 · arxiv created 2014/04/11 · arxiv updated 2014/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In a series of articles published in 1986 Derrida, and his colleagues studied two mean field treatments (the quenched and the annealed) for NK-Kauffman Networks. Their main results lead to a phase transition curve Kc 2 pc ( 1 - pc ) = 1 ( 0 < pc < 1 ) for the critical average connectivity Kc in terms of the bias pc of extracting a "1" for the output of the automata. Values of K bigger than Kc correspond to the so-called chaotic phase; while K < Kc , to an ordered phase. In~[F. Zertuche, \it On the robustness of NK-Kauffman networks against changes in their connections and Boolean functions. J.~Math.~Phys. \bf 50 (2009) 043513], a new classification for the Boolean functions, called \it Boolean irreducibility permitted the study of new phenomena of NK-Kauffman Networks. In the present work we study, once again the mean field treatment for NK-Kauffman Networks, correcting it for \it Boolean irreducibility. A shifted phase transition curve is found. In particular, for pc = 1 / 2 the predicted value Kc = 2 by Derrida \it et al. changes to Kc = 2.62140224613 … We support our results with numerical simulations.