Department of Mathematics

Gal Mishne, Gibbs Assistant Professor of Applied Mathematics at Yale University, will present this lecture as part of the Emerging Scholars in Arts & Science series.? This lecture series, co-sponsored by the College of Arts & Science and the Office of the Vice Provost for Inclusive Excellence, is intended to spark new conversations within the Vanderbilt community through guest presentations by early-career scholars from traditionally underrepresented backgrounds whose innovative research promises to make significant and lasting contributions to their fields of study. The series features three speakers each year: one each from the humanities, natural sciences, and social sciences.

Abstract: Experimental advances in neuroscience enable the acquisition of increasingly large-scale, high-dimensional and high-resolution neuronal and behavioral datasets, yet addressing the full spatiotemporal complexity of these datasets poses significant challenges for data analysis and modeling. I present a new geometric analysis framework, and demonstrate its application to the analysis of calcium imaging from the primary motor cortex in a learning mammal. To extract neuronal regions of interest, we develop Local Selective Spectral Clustering, a new method for identifying high-dimensional overlapping clusters while disregarding noisy clutter. We demonstrate the capability of this method to extract hundreds of detailed neurons with demixed and denoised time-traces. Next, we propose to represent and analyze the extracted time-traces as a rank-3 tensor of neurons, time-frames and trials. We introduce a data-driven method for tensor analysis and organization, which infers the coupled multi-scale structure of the data. In analyzing neuronal activity from the motor cortex we identify in an unsupervised manner: functional subsets of neurons, activity patterns associated with particular behaviors, and long-term temporal trends.

A reception will follow the lecture.