Information Transfer and Criticality in the Ising Model on the Human Connectome

Abstract

We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows.

Rényi information flow in the Ising model with single-spin dynamics

“…Similar results on a measure related to T pw have been obtained by directly simulating the Ising model with the Metropolis dynamics and Glauber dynamics [18].…”

“…Instead, the Wolff MC method is used to calculate the information flows, according to Eqs. (17), (18), (23), and (24), in the kinetic Ising model with the Metropolis and the Glauber dynamics, respectively.…”

“…This is because the entropy flows have been expressed as ensemble averages of observables in the equilibrated system [see Eqs. (17), (18), (23), and (24)]. There is no need to extract the time series of the entropies appearing in the definitions of the flows.…”

“…The deviation from this relation is thus quantified as the transfer entropy [16]. The transfer entropy detects the directed exchange of information between two systems and thus might have more potential applications in the study of dynamic systems with time-series data available [17,18].…”

DynamicBC: A MATLAB Toolbox for Dynamic Brain Connectome Analysis

“…The structural connectomics essentially comprises a comprehensive map of the anatomical connections reflecting axonal pathways (Sporns et al, 2005), and the structural covariance connectivity interpreted as the phenotype of brain development and/or plasticity (Alexander-Bloch et al, 2013;He et al, 2007). Additionally, the functional connectomics can be captured as patterns of functional covariance network Zhang et al, 2011), functional connectivity (FC) and effective connectivity (EC) networks (Friston, 2009(Friston, , 2011Marinazzo et al, 2011Marinazzo et al, , 2014Wu et al, 2013b).…”