Many scientists claim that the default brain activity is in phase transition (charachterized by fractals) and that, during perceptions and higher thoughts, there is a bifurcation event and an exit from phase transition.
However, we find temporal fractal structures both in low EEG waves and in higher waves (such as in gamma spikes, traditionally associated with perceptions and higher thoughts): if the brain is not anymore in phase transition, the fractals must disappear, but, instead, the slope of fractal exponents
is even higher in gamma than in alpha waves (Raichle and his group, and many
others).
Which is the explanation of the persistence of bran fractals in all the functional states of the CNS?
I recall the default state appears to be in a metastable state, at the edge of a phase transition to other states. Thus, both the default state and other states would be considered to be outside the phase transition - on different sides of it though.
Interesting answer, Ashish. But... if you are right, and the brain is always outside phase transition, how do you explain the presence of fractals in all the brain states?
I think the possibilities are the following:
1) the brain in never in phase transition, the fractals do exist but are not linked in this case to the dynamical system.
2) the brain is always in phase transition, and the fractals are a landmark of it.
3) the importance of fractals is overrated in brain, they do exist but they do not mean anything
4) the brain is in phase transition during the default mode network and outside during perception and high cognitive activities; the fractals are not linked to this process.
5) The presence of fractals in the brain is at least equivocal and could be linked to artifacts coming from the blood or to an entropy transfer from the vessels.
6) the brain is always in a state of some kind of border and edge, and it is impossible to elucidate its charachteristics.
Comments?
Dear Arturo and Ashish,
This is a fascinating topic! Would you mind giving some references where this is described in more detail and where I could read more?
Thanks!!
Dear Markus,
the most recent review about fractals and brain (to my knowledge) is: "Scale-free brain activity: past, present, and future", by Biyu He, Trends in Cognitive Sciences, September 2014, Vol. 18, No. 9.
About brain and criticality, there is one (among many others) very nice: "Being critical of criticality in the brain", by Beggs & Timme, Frontiers in Psychology, 2012.
Karl Friston kindly sent me this answer:
"I prefer option 2 (the brain is always in phase transition, and the fractals are a landmark of it.). The brain exhibits self organised criticality (edge of chaos) that necessarily entails a power law scaling of dynamics (however you measure it). This is synonymous with a fractal nature to the dynamical measurement. Therefore, a fractal aspect to neuronal dynamics is an inevitable aspect of the healthy (self-organised) brain.
Well, I verify the great similarity between brain and nanowires of SiO2 obtained by dewetting transition after heating at high temperatures thin films Au/Si
I believe that the dewetting transition theory can help in this case because I observed that his action mechanism is similar with the mechanism of the glutamate excitotoxity and fractals dynamic
Dear Arturo, I have to stress that I am learning from your comments probably much more than what you can learn from me. Which is the paper of Raichle and his group that makes it clear that the brain is fractal before and after completing a task? What do you mean by the brain being fractal? Does it have to do with the brain being a generator of 1/f noise? If it does, I have the impression that it is not yet very well understood that there are many different kinds of 1/f noise. There is 1/f noise that is incompatible with the ergodic assumption that some of the authors quote by you do.
I am convinced that this is the kind of 1/f noise generated at crticality. Is spectrum is 1/f^{eta}, where eta = 3 - mu, with mu < 1 indicating temporal complexity. There is a form of 1/f noise generated by processes with infinite memory (and no crucial events), yielding a spectrum P(f) = 1/f^{eta} with eta < 1. It has a physical nature totally different from the ergodicity breaking 1/f noise.
As far as the brain doing a task is concerned, I have to say that my very limited knowledge refers to the work done years ago by a young Chicago psychologist, Joshua Correll, please see Correll, 1/f noise and effort on implicit measures of bias, Journal of Personality and Social Psychology 94, 48-59 (2008). The experiment made by Correll is very exciting. In fact, he is convinced that if if the brain has to realize a difficult task, then 1/f noise is replaced by white noise. If a cop with racial unconscious prejudices has to decide where or not to shoot an african american suspect, this is a very difficult task for him, and if it DOES NOT SHOOT, his/her brain generates white noise. I tried to make a mathematical model to explain this phenomenon,, P. Grigolini, G. Aquino, M. Bologna, M. Lukovi ́c, B. J. West, A theory of 1/f noise in human cognition, Physica A, 388, 4192-4204 (2009). However, I am not very happy about that, because I am convinced, reading the papers that you quote, that we are in the presence of very complex processes, and the model that I proposed may work on this issue but it may fail explaining other, and more important, properties. However, I am convinced that the criticality-induced TEMPORAL COMPLEXITY, that we propose as genuine signature of criticality, is not yet known, and there are many vague statement about the brain and criticality with no convincing theoretical foundation. I wrote a draft on that issue that is not yet published. If you are interested, I may send it to you. Congratulation for the nice work you are doing.
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