1,767 research outputs found
Iterated Brownian motion in an open set
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
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
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