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College of Liberal Arts and Sciences | Mathematics

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November 13, 2018 | 2:00 p.m. - 3:00 p.m.
Category: Seminar
Location: Faculty/Administration #1140 | Map
656 W. Kirby
Detroit, MI 48202
Cost: Free

Speaker: Vaibhav Diwadkar, Department of Psychiatry and Behavioral Neurosciences, Wayne State University

Title: Delay embedding theorems and the reconstruction of brain network dynamics: Applications of convergent cross mapping

Abstract:

Recovering “causality” and dynamics between elements of a dynamical system based on observational time series data, is an acutely challenging problem. The problem is amplified for a deterministic, maximally dynamic but highly “noisy” system like the brain which is characterized by moderate to weak coupling relationships between its constituents (regions).

Here within the framework of dynamical systems theory and delay embedding theorems (e.g., Takens’ theorem) we convergent cross mapping (CCM)(Sugihara et al., 2012) to recover functional brain structure from fMRI data. CCM tests for causation and dynamics (between two system variables X & Y) by measuring the extent to which the historical record of Y’s values in a time series L, can reliably estimate states of X.  This happens only if within the system, X is “causally” influencing Y.  In more detail, CCM looks for the signature of X in Y’s time series by seeing whether there is a correspondence between the “library” of points in the attractor manifold built from Y, MY, and points in the X manifold, MX where these two manifolds are constructed from lagged coordinates of the time-series variables Y and X, respectively. Using these methods, we provide novel demonstrations of how CCM recovers delayed dynamics between brain networks when such should be expected (e.g., during sustained memory maintenance), but not under conditions when such delayed dynamics are not expected (e.g., during transient motor responding).

As I will suggest, there are countless opportunities for the study of geometric and topological relationships within high-dimensional and complex fMRI data. Should these methods be applied, the acquisition and analyses of fMRI data need not be limited to an exercise in the production and publication of largely meaningless “results”, but can lead to meaningful understanding brain function.

For more information about this event, please contact Department of Mathematics at 3135772479 or math@wayne.edu.