1,767 research outputs found

    Iterated Brownian motion in an open set

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    Suppose a solid has a crack filled with a gas. If the crack reaches the surrounding medium, how long does it take the gas to diffuse out of the crack? Iterated Brownian motion serves as a model for diffusion in a crack. If \tau is the first exit time of iterated Brownian motion from the solid, then P(\tau>t) can be viewed as a measurement of the amount of contaminant left in the crack at time t. We determine the large time asymptotics of P(\tau>t) for both bounded and unbounded sets. We also discuss a strange connection between iterated Brownian motion and the parabolic operator {1/8}\Delta^2-\frac{\partial}{\partial t}

    Brain complexity born out of criticality

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    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

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    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
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