|
Abstract:
|
Interdependence among multiple brain regions is of great interest, and a leading theory is that communication across areas may be facilitated by neural oscillations. One way to establish association of multiple oscillating signals is by showing their phases to be correlated (across repeated measurements). We describe an example in which 24 recordings have been made simultaneously from 4 regions of the brain, repeatedly. To analyze such multivariate angular data we have developed a natural analogue to Gaussian graphical models, which we call torus graphs, because angles lie on the circle and the product of circles is a torus. We show that torus graphs have nice properties and, in the data, find phase relationships that previous methods obscure. Interestingly, dependence in torus graphs can be quite different than in Gaussian graphs: in the bivariate Gaussian case, a single scalar, correlation, can describe both positive and negative association; in a 2-dimensional torus graph a complete description of association requires 2 complex numbers.
|
