Considering that mean field theory approaches have been used for neuronal dynamics, and that renormalization group theory has been used in other networks to describe their properties, I wanted to know whether it is useful or interesting to describe the behavior of a neuronal system based on its critical exponents. Thank you in advance.
Critical exponents describe properties that don't depend on whether the network describes brain function or some other system.
If the network does show scale free behavior, then critical exponents can be defined and they characterize the behavior of certain quantities.
That's why it's wrong to ask whether it's useful or interesting to describe the behavior of a neuronal system based on its critical properties-but whether it does have such properties at all.
As long as you are near a 2nd order phase transition, there will be critical exponents. I would think criticality could be useful to detect a change of mental states but in order to entangle them we need to look deeper than just at large scale correlations. Maybe consciousness turns out to be a phase transition from some low level mutual perception patterns into a high level of intermodal perception. And Yes the last sentence was somewhat ill defined.
Thank you everyone who took the time to answer this question. It was a topic that was bugging me out in the beginning, but now I have a clearer perspective on how to proceed.
There exist many publications and reviews on neural networks and critical phenomena. For example, rather recently, the book "Criticality in neural systems"
has been edited by D. Plenz, E. Niebur, and H. G. Schuster, ISBN-978-3-527-41104- 7 (Wiley, 2014).
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