Power laws and self-organized criticality in theory and nature

See on Scoop.itBiobit: Computational Neuroscience & Biocomputation

a comparative overview of distinct modeling
approaches together with a discussion of their potential relevance as
generative models for real-world phenomena…A
special section is devoted to an assessment of power-law scaling in the
neural activity.

Nima Dehghani‘s insight:

 Dimitrije Marković and Claudius Gros argue that:

"Finally, in spite of the evidence that quite different physical systems exhibit dynamical properties akin to the one observed in various sandpile models, there is no convincing proof that the generative mechanism for power-law scaling, as proposed by SOC, constitutes the true causal explanation. A substantial controversy regarding the interpretation of empirical data still persists, and the resolve of this controversy will, together with novel approaches for experimental setups and data analysis, require measurements with higher resolution.

On a final note, what one actually considers a self-organized process is to a certain extent a question of semantics. It is possible, in many circumstances, to tune a system toward a critical point. There is general agreement that the underlying process can be considered self-organized whenever this tuning process occurs through internal drives on time scales shorter than (or comparable to) the experimental time scale. The tuning of internal parameters may however also result from processes acting on much longer time scales, like, for example, Kauffman’s notion of “life at the edge of criticality”, as a consequence of Darwinian selection. In both cases the dynamical state will never be, for real-world systems, exactly at the critical point, but fluctuating around it, albeit on very long time scales."

See on www.sciencedirect.com


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