Diversity of Cortical States at Non-Equilibrium Simulated by the   Ferromagnetic Ising Model Under Metropolis Dynamics
  This article investigates the relationship between the interconnectivity and simulated dynamics of the thalamocortical system from the specific perspective of attempting to maximize the diversity of cortical states. This is achieved by designing the dynamics such that they favor opposing activity between adjacent regions, thus promoting dynamic diversity while avoiding widespread activation or de-activation. The anti-ferromagnetic Ising model with Metropolis dynamics is adopted and applied to four variations of the large-scale connectivity of the cat thalamocortical system: (a) considering only cortical regions and connections; (b) considering the entire thalamocortical system; (c) the same as in (b) but with the thalamic connections rewired so as to maintain the statistics of node degree and node degree correlations; and (d) as in (b) but with attenuated weights of the connections between cortical and thalamic nodes. A series of interesting findings are obtained, including the identification of specific substructures revealed by correlations between the activity of adjacent regions in case (a) and a pronounced effect of the thalamic connections in splitting the thalamocortical regions into two large groups of nearly homogenous opposite activation (i.e. cortical regions and thalamic nuclei, respectively) in cases (b) and (c). The latter effect is due to the existence of dense connections between cortical and thalamic regions and the lack of interconnectivity between the latter. Another interesting result regarding case (d) is the fact that the pattern of thalamic correlations tended to mirror that of the cortical regions. The possibility to control the level of correlation between the cortical regions by varying the strength of thalamocortical connections is also identified and discussed. 
Luciano da Fontoura Costa and Olaf Sporns