Graph theory, dynamics, and how to classify brains

Theoretical Biology Seminar

Meeting Details

For more information about this meeting, contact Kristin Berrigan, Carina Curto, Jessica Conway, Leonid Berlyand, Wenrui Hao, Timothy Reluga, Vladimir Itskov, Alexander Gavrikov.

Speaker: Anca Radulescu, SUNY New Paltz

Abstract: Modeling complex networks and understanding how their hardwired circuitry relates to their dynamic evolution in time can be of great importance to applications in the life sciences. When the system is the brain,this becomes one of the most daunting research questions of our century: can brain connectivity (the “connectome”) be used to predict brain function and ultimately behavior? We will start by describing an original study of neuroimaging data in humans, comparing a group of patients with schizophrenia with a group of healthy controls. We found that connectivity patterns between prefrontal and limbic regions can be help accountable for differences in emotion regulation efficiency between the two groups. This result can be explained within the theoretical framework of oriented nonlinear dynamic net-works. To illustrate this framework, we will consider two examples: one in continuous, and one in discrete time. In continuous time, we use configuration dependent phase spaces and probabilistic bifurcation diagrams. In discrete time, we use complex quadratic nodes and define extensions of the traditional Julia and Mandelbrot sets. Finally, we return to interpreting our results in the context of brain networks, synaptic restructuring and neural dynamics in learning networks. As our newest application to human brain function, we show how the topology of the Mandelbrot set can be used to classify human connectomes obtained with tractography measures, and how this can be further used to predict the subject’s “emotional profile.”

Room Reservation Information

Room Number: 106 McAllister

Date: 02/18/2020

Time: 1:30pm - 2:30pm