Fig. 5: T-duality in binary dynamics evolving on small Erdős-Rényi random graphs.
From: Duality between predictability and reconstructability in complex systems
a, d Glauber dynamics, b, e SIS dynamics, and c, f Cowan dynamics. Each panel shows the reconstructability U(G ∣ X) ∈ [0, 1] (blue) and the predictability coefficient U(X ∣ G) ∈ [0, 1] (orange) as a function of the number of time steps T. We used graphs of N = 5 vertices and E = 5 edges, meaning an average degree of 〈k〉 = 2; we fixed τ = 1 in the top row, and τ = T/2 in the bottom row. Each symbol corresponds to the average value measured over 1000 samples. We also show different values of the coupling parameters using different symbols: a, d \(J \in \left\{\frac{1}{2},1,\,2\right\}\) for Glauber, b, e \(\lambda \in \left\{\frac12,1,\, 2\right\}\) for SIS, and c, f \(\nu \in \left\{\frac12,1,\,2\right\}\) for Cowan.
