Rounding of phase transitions in cortical networks: the advantages of a low-dimensional brain
Paolo Moretti
Institute for Materials Simulation – WW8, FAU
Wednesday, 21. January 2015, 17:00
WW8, Raum 2.018, Dr.-Mack-Str. 77, Fürth
Propagation of activity in the brain occurs through dynamic processes that require a high degree of signal integration. In nature, such dynamic protocols are normally associated with pattern formation, metastability and discontinuous phase transitions. This observation contrasts with the experimental evidence of critical phenomena in brain activity, which on the other hand would imply that the brain sits constantly at criticality, in the vicinity of a continuous phase transition.
I will show that, being the brain connectivity network finite- (low-) dimensional, there exist a threshold value of the dimension below which disorder always turns discontinuous phase transitions in continuous ones, allowing the brain to access the functional benefits of criticality (enhanced susceptibility, system-wide correlations and so on) [1].
A well known result in equilibrium thermodynamics is that, in systems of dimension 2 or less, bond disorder effectively rounds discontinuous phase transitions into continuous ones. Our numerical results suggest that this phenomenon can be extended to brain dynamics and non-equilibrium phenomena in general. Such results may be relevant for problems of materials science, in which dynamics are sometimes confined to low-dimensional activity patterns (such as shear bands or cracks).
[1] P. Villa, P. Moretti, M. A. Munoz J. Stat. Mech. (2015) P01003