Figure 1.
Ising model on the different brain connectomes.
a,b: 66-nodes connectome. c,d: 998-nodes connectome. a: The following quantities are depicted versus the inverse temperature : the susceptibility
; the heat capacity C; the total transfer entropy TE, i.e. the sum of all the information flows in all network pairs; R the ratio between the standard deviations of outgoing and incoming information flows). b: The distribution of the node-measure
in comparison with different topological measures such as the nodes strength (the sum of the connections weights to each node in the connectivity matrix
), the efficiency and the nodes betweenness. The values of r have been normalized to the interval [0,1]. Nodes have been ordered according to increasing strength. Note that r is not fully explained by the strength as there are nodes with intermediate strength but with high r. Here the value of the temperature corresponds to the one that maximized R but similar patterns are obtained varying
. c: same as in panel a but for the 998-nodes connectome. d: same as in panel c but for the 998-nodes connectome.
Figure 2.
Ratio r of outgoing and incoming information per node at criticality.
r is depicted as a function of the nodes strength for both 66 and 989 nodes connectome.
Figure 3.
Localization of areas which are bottlenecks of information.
The value of r for each region for the Ising model on brain networks, for the 66-nodes connectome (top) and the 998 nodes one (bottom). The size of the spheres is proportional to r, thus showing the most prone regions to became bottlenecks of information.
Figure 4.
Ising model with different dynamics.
a: Transfer Entropy versus the inverse temperature for the Ising model implemented on the 66-nodes human connectome with four different dynamics (Glauber, Metropolis, Wolff and Heat Bath). b: Transfer Entropy versus the inverse temperature
for the Ising model implemented on an deterministic scale free network (81 nodes) with Heat Bath and Metropolis dynamics.
Figure 5.
The average time between two consecutive spin flips across the different brain areas.
66-nodes and 998-nodes connectomes.
Figure 6.
Rich club coefficient for the network of the information transfer as a function of
and the degree
.