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| Start Date: | 2/1/2013 | Start Time: | 4:00 PM |
| End Date: | 2/1/2013 | End Time: | 5:00 PM |
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Event Description
Dr. Juan Restrepo
Assistant Professor
Applied Mathematics Department
University of Colorado at Boulder
Criticality and dynamic range in network cascading processes
In this talk I will present recent results that describe the response of a network of coupled excitable systems to a stochastic stimulus. The motivation for our work is a series of recent experiments on cascades of excitation in rat cortical tissue cultures, where it is found that these neural networks maximize their dynamic range (the range of stimulus intensities resulting in distinguishable network responses). By studying a system of network-coupled excitable cellular automata, we find that the dynamic range is maximized when the largest eigenvalue of the transmission probability matrix is one. Analysis of this model allows us to determine the effect of the distribution of node degrees (the number of links per node), correlations between degrees of adjacent nodes, and other network structural properties on the network response. In the critical regime with maximum dynamic range, the response of the network is characterized by excitation avalanches with power-law distributions of size and duration, in agreement with experiments. Additional models that include inhibitory links and multiple network components will be discussed. |
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