Brain complexity born out of criticality

In this essay we elaborate on recent evidence demonstrating the presence of a second order phase transition in human brain dynamics and discuss its consequences for theoretical approaches to brain function. We review early evidence of criticality in brain dynamics at different spatial and temporal scales, and we stress how it was necessary to unify concepts and analysis techniques across scales to introduce the adequate order and control parameters which define the transition. A discussion on the relation between structural vs. dynamical complexity exposes future steps to understand the dynamics of the connectome (structure) from which emerges the cognitome (function).Comment: In Proceedings of the 12th Granada Seminar "Physics, Computation, and the Mind - Advances and Challenges at Interfaces-". (J. Marro, P. L. Garrido & J. J. Torres, Eds.) American Institute of Physics (2012, in press

Noise-induced memory in extended excitable systems

We describe a form of memory exhibited by extended excitable systems driven by stochastic fluctuations. Under such conditions, the system self-organizes into a state characterized by power-law correlations thus retaining long-term memory of previous states. The exponents are robust and model-independent. We discuss novel implications of these results for the functioning of cortical neurons as well as for networks of neurons.Comment: 4 pages, latex + 5 eps figure