At 4pm on Monday, March 22, Professor Anca Radulescu from SUNY-New Paltz will describe an original study of neuroimaging data in humans that helped to discover connectivity patterns between prefrontal and limbic regions of the brain that led to creating and revising a mathematical model of neuron architecture in the human brain. Zoom link: ithaca.zoom.us/j/91482691861
Everyone is invited! Please join us for our Math Colloquium series this semester on Mondays at 4pm: ithaca.zoom.us/j/91482691861. Contact person: Prof. Ted Galanthay at tgalanthay@ithaca.edu.
This week we are hosting Professor Anca Radulescu from SUNY-New Paltz who will delivering a presentation entitled "Architecture-dependent bifurcations and clustering in brain networks."
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. However, the effect of connectivity patterns on network dynamics is only in the first stages of being understood. When the system is the brain, this becomes one of the most daunting current research questions: 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, analyzing differences within a group of subjects with wide differences in vulnerability to stress (from extremely stress resilient to extremely anxious). Our statistical analysis found that connectivity patterns between prefrontal and limbic regions could explain differences in emotion regulation efficiency between the two groups. We interpret this result within the theoretical framework of oriented networks with nonlinear nodes, by studying the relationship between edge configuration and ensemble dynamics.
We first illustrate this framework on networks of Wilson-Cowan oscillators (a historic ODE model describing mean-field firing dynamics in coupled neural populations). We use configuration dependent phase spaces and probabilistic bifurcation diagrams to investigate the relationship between classes of system architectures and classes of their possible dynamics. We differentiate between the effects on dynamics of altering edge weights, density, and configuration.
Since Wilson-Cowan is a mean-field model, it can only predict population-wide behavior, and does not offer any insight into spiking dynamics and individual synaptic restructuring. To illustrate the effects of network architecture on dynamical patterns at this level, we test the same framework on networks of reduced Hodgkin-Huxley type single neurons. Building upon a model of cluster synchronization in all-to-all inhibitory networks (by Golomb and Rinzel), we study the contributions of more complex network architectures to the clustering phenomenon.