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Center for Nonlinear Studies |
Distinct brain areas communicate during performance of a task and there is great interest in using statistical associations between signals recorded from particular brain areas to understand cross-area cooperation. I will give a brief overview of my work addressing this problem before focusing in detail on a particular project in which I seek to identify consistent phase relationships of oscillations in distinct areas as a marker of cross-area communication. A thorough description of such cross-area interactions would then be based on a graph, where each node represents the phase of an oscillation in a particular brain area, and each edge corresponds to some measure of association. However, Gaussian graphical models cannot solve this problem because angles are topologically circular. We have developed the appropriate analogue of Gaussian graphical models, which we call Torus Graphs. Each torus graphical model is an exponential family on a multidimensional torus. We show how statistical inferences in this setting can be produced, and lead to interesting descriptions of brain region interactions in the context of an experiment on associative memory. This framework also unifies, and improves understanding of many methods that have appeared previously in circular statistics.
Host: Jim Gattiker