2023/03/03 by F. C. Sheldon, Sheldon, F. C., T. M. A. Fink +1 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Evolution and Genetic Dynamics #Evolutionary Algorithms and Applications #FOS: Biological sciences #FOS: Mathematics #FOS: Physical sciences #Gene Regulatory Network Analysis #Molecular Networks (q-bio.MN) #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2303.02079
openalex publication_date 2023/03/03 · openalex created_date 2023/03/07 · openalex updated_date 2026/07/28
The Kauffman model of genetic computation highlights the importance of criticality at the border of order and chaos. The model with connectivity one is of special interest because it is exactly solvable. But our understanding of its behavior is incomplete, and much of what we do know relies on heuristic arguments. Here, we show that the key quantities in the model are intimately related to aspects of number theory. Using these links, we derive improved bounds for the number of attractors as well as the mean attractor length, which is harder to compute. Our work suggests that number theory is the natural language for deducing many properties of the critical Kauffman model with connectivity one, and opens the door to further insight into this deceptively simple model.