2009/03/24 by Federico Zertuche · 9 citations
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Bioinformatics and Genomic Networks #Boolean expression #Boolean function #Boolean model #Boolean network #Combinatorics #Complete Boolean algebra #Discrete mathematics #Evolutionary Algorithms and Applications #Gene Regulatory Network Analysis #Mathematics #Maximum satisfiability problem #Parity function #Product term #Pure mathematics #Two-element Boolean algebra #math-ph #math.MP #nlin.AO #q-bio.QM
paper · pdf · doi:10.1063/1.3116166
published in Journal of Mathematical Physics 50(4) (American Institute of Physics) · 17 pages, 1 figure, Accepted in Journal of Mathematical Physics
arxiv created 2009/03/24 · openalex publication_date 2009/04/01 · arxiv updated 2015/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
N K -Kauffman networks LKN are a subset of the Boolean functions on N Boolean variables to themselves, ΛN=ξ:Z2N→Z2N. To each NK-Kauffman network it is possible to assign a unique Boolean function on N variables through the function Ψ:LKN→ΛN. The probability PK that Ψ(f)=Ψ(f′), when f′ is obtained through f by a change in one of its K-Boolean functions (bK:Z2K→Z2), and/or connections, is calculated. The leading term of the asymptotic expansion of PK, 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 Ψ is used to model the genotype-phenotype map.