A geometric approach to modeling and analyzing dynamics in biomedical time series

Event Description

Abstract:  Informed by physiology, the wave-shape oscillatory model for biomedical time series asserts that cycles lie on or near a low-dimensional manifold.

Recovering this manifold provides insight into the dynamics of the underlying system.  I present a manifold learning framework for biomedical time series analysis, and I provide a guarantee on the dynamical information which can be recovered using this framework.   We will discuss several applications in the analysis of electrocardiograms and blood pressure monitoring.  Time-permitting, we will examine further approaches to biomedical time series analysis which fuse traditional signal processing with modern mathematics. 


Bio:  John Malik is a Canadian PhD candidate in the Department of Mathematics at Duke University.  He completed his undergraduate and master’s degrees in mathematics at the University of Western Ontario.  He develops and uses tools from applied harmonic analysis, differential geometry, and nonlinear time-frequency analysis to extract clinically relevant information from biomedical time series. He is currently funded by the Myra and William Waldo Boone Fellowship.