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https://www.nist.gov/itl/math/acmd-seminar-architecture-dependent-bifurcations-and-clustering-brain-networks

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# ACMD Seminar: Architecture-dependent bifurcations and clustering in brain networks

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Anca Radulescu*Department of Mathematics, SUNY New Paltz*

Tuesday, April 13, 2021, 3:00 PM EDT (1:00 MDT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**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 con- nectivity (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 meanfield 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 meanfield 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 net- work architecture on dynamical patterns at this level, we test the same framework on networks of reduced Hogkin-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.

**Bio:** Anca Radulescu is Associate Professor in the Mathematics Department at State University of New York at New Paltz. She got her Ph.D. in Mathematics from Stony Book University (with a thesis in dynamical systems discussing the topological entropy of polynomials, under the supervision of John Milnor). She continued her training in computational and clinical neuroscience at the Cold Spring Harbor Labs and Stony Brook University Hospital, and in applied mathematics at University of Colorado at Boulder. Since her tenure-line appointment at SUNY New Paltz, her areas of research have centered around complex dynamics, and dynamical systems modeling in the natural sciences.

**Host:** Anthony Kearsley

**Note:**This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)

Mathematics and statistics

## Contacts

                -  Anthony J. Kearsley  anthony.kearsley@nist.gov      (301) 975-6103   
                -  Stephen Langer  stephen.langer@nist.gov      (301) 975-5423   

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