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Results: 4

1.
Fig. 1.

Fig. 1. From: Genetic networks with canalyzing Boolean rules are always stable.

Examples of N = 20 networks with γ = 1(A), γ = 2(B), and γ = 3(C).

Stuart Kauffman, et al. Proc Natl Acad Sci U S A. 2004 December 7;101(49):17102-17107.
2.
Fig. 2.

Fig. 2. From: Genetic networks with canalyzing Boolean rules are always stable.

Robustness, r, and the probability of a node being true, w, at the equilibrium distribution of Boolean values, as functions of the exponent γ in the in-degree distribution pK (Eq. 1) for N = 20 (dotted), 100 (dashed), and ∞ (solid).

Stuart Kauffman, et al. Proc Natl Acad Sci U S A. 2004 December 7;101(49):17102-17107.
3.
Fig. 3.

Fig. 3. From: Genetic networks with canalyzing Boolean rules are always stable.

The number of attractors as a function of the exponent γ in the in-degree distribution pK (Eq. 1) for N = 20 (thick lines) and N → ∞ (thin lines). The curves show the cumulative number of attractors of length L for L = 1 (solid), L ≤ 2 (dashed), and L ≤ ∞ (dotted). The values for N → ∞ were calculated analytically, whereas the values for N = 20 are taken from full enumerations of the state space for at least 5,000 networks, with more networks at higher γ.

Stuart Kauffman, et al. Proc Natl Acad Sci U S A. 2004 December 7;101(49):17102-17107.
4.
Fig. 4.

Fig. 4. From: Genetic networks with canalyzing Boolean rules are always stable.

The average time evolution of perturbed fixed points in 5 × 5 cell tissues with periodic boundary conditions and N = 50 nodes (over many network realizations). Simulations from random initial states in generated networks were used to locate fixed points, which were perturbed by toggling the value of a single node. The mean distances to the unperturbed fixed point, 〈H(t)〉, as given by 20 subsequent simulation steps, are shown for γ = 2(A) and γ = 3 (B), for three different degrees of cell connectivity: κ = 0 (solid), 0.05 (dashed), and 0.1 (dotted).

Stuart Kauffman, et al. Proc Natl Acad Sci U S A. 2004 December 7;101(49):17102-17107.

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