Nonextensive Statistical Mechanics

7.8 Scale-Free Networks 283Fig. 7.84 Magnetic Resonance and Computered Tomography images. The goal is to make afast and accurate image registration. It uses a q-generalized mutual information. The algorithmachieves up to seven times faster convergence and four times more precise registration for q ≡α α c and nonsummable for 0 < α ≤ α c with α c ≃ 1, weexpect important changes to occur while crossing α ≃ 1. This is indeed observedin the time behavior of the Hamming distance. Since this quantity plays a roletotally analogous to the sensitivity to the initial conditions, it is natural to expectH(t) ∝ e λ q tq sen∝ t 1/(1−qsen) . The results can be seen in Figs. 7.92, 7.93, and 7.94.7.7 Self-Organized CriticalitySeveral studies have been done in connection with self-organized criticality (SOC),in connection with biological evolution [847,849,851–853], imitation games [848],atmospheric cascades [850], earthquakes [855, 856], and others [854].7.8 Scale-Free NetworksNetworks exist of various types [858–862]. They are typically characterized bysets of nodes (sites) and sets of directed or nondirected links (bonds) joining thenodes. These are the most studied, although it is clear that it is easy to generalizethe concept by also including plaquettes and other many-node, many-link, and