{"paper":{"title":"Phase Transition in NK-Kauffman Networks and its Correction for Boolean Irreducibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CG","authors_text":"Federico Zertuche","submitted_at":"2012-08-01T16:49:28Z","abstract_excerpt":"In a series of articles published in 1986 Derrida, and his colleagues studied two mean field treatments (the quenched and the annealed) for \\textit{NK}-Kauffman Networks. Their main results lead to a phase transition curve $ K_c \\, 2 \\, p_c \\left( 1 - p_c \\right) = 1 $ ($ 0 < p_c < 1 $) for the critical average connectivity $ K_c $ in terms of the bias $ p_c $ of extracting a \"$1$\" for the output of the automata. Values of $ K $ bigger than $ K_c $ correspond to the so-called chaotic phase; while $ K < K_c $, to an ordered phase. In~[F. Zertuche, {\\it On the robustness of NK-Kauffman networks "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0272","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}