{"paper":{"title":"On the Robustness of NK-Kauffman Networks Against Changes in their Connections and Boolean Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.AO"],"primary_cat":"q-bio.QM","authors_text":"Federico Zertuche","submitted_at":"2009-03-24T18:56:40Z","abstract_excerpt":"NK-Kauffman networks {\\cal L}^N_K are a subset of the Boolean functions on N Boolean variables to themselves, \\Lambda_N = {\\xi: \\IZ_2^N \\to \\IZ_2^N}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function \\Psi: {\\cal L}^N_K \\to \\Lambda_N. The probability {\\cal P}_K that \\Psi (f) = \\Psi (f'), when f' is obtained through f by a change of one of its K-Boolean functions (b_K: \\IZ_2^K \\to \\IZ_2), and/or connections; is calculated. The leading term of the asymptotic expansion of {\\cal P}_K, for N \\gg 1, turns out to depend on: the probabili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.4161","kind":"arxiv","version":1},"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"}