Canalization and the stability of NK-Kauffman networks

On the Number of NK-Kauffman Networks Mapped into a Functional Graph

“…As we may see from equation (23), for N → ∞, ϑ -1 N, K, 1  2 goes to zero exponentially for K  constant. However, if K grows with N in such a way that the product N φ (K) remains constant as N grows, we may obtain values for equation (23) throughout the range 0 < ϑ -1 N, K, 1  2 ≤ 1. From equation (10), Ψ is a many-to-one function in the case where ϑ -1 N, K, 1  2 ≈ 0, and an injective function if and only if ϑ -1 N, K, 1  2  1.…”

“…The probabilities Π p ( K (λ)) were calculated in [23] and we report the result in Appendix B for the interested reader. However, Π p  K 0 may be easily calculated by noting that  K 0  {τ, ¬ τ}.…”