  We implement the Ising model on a structural connectivity matrix describing
the brain at a coarse scale. 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 number of incoming links.
