Information transfer and criticality in the Ising model on the human connectome.
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.
Faculty of Psychology and Educational Sciences, Department of Data Analysis, Ghent University, Ghent, Belgium.
Daniele
D
Marinazzo
Dipartimento di Fisica, Università degli Studi di Bari and INFN Bari, Bari, Italy.
Mario
M
Pellicoro
Faculty of Psychology and Educational Sciences, Department of Data Analysis, Ghent University, Ghent, Belgium; Key Laboratory for NeuroInformation of Ministry of Education, School of Life Science and Technology, University of Electronic Science and Technology of China, Chengdu, China.
Guorong
G
Wu
Dipartimento di Fisica, Università degli Studi di Bari and INFN Bari, Bari, Italy.
Leonardo
L
Angelini
Ikerbasque, The Basque Foundation for Science, Bilbao, Spain; Biocruces Health Research Institute, Hospital Universitario de Cruces, Barakaldo, Spain.
Jesús M
JM
Cortés
Dipartimento di Fisica, Università degli Studi di Bari and INFN Bari, Bari, Italy; Ikerbasque, The Basque Foundation for Science, Bilbao, Spain; Biocruces Health Research Institute, Hospital Universitario de Cruces, Barakaldo, Spain.
Sebastiano
S
Stramaglia
D001921:Brain / Q000166:cytology; D003198:Computer Simulation; D063132:Connectome / Q000379:methods; D006801:Humans; D008606:Mental Processes; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009434:Neural Pathways / Q000502:physiology*