Math Colloquium - Stories from Data-Driven Analysis of Complex Systems
From Uncovering the Cause for the Demise of an Ancient Civilization to Classifying Cancer Tumor Types:Stories from Data-Driven Analysis of Complex SystemsDr. Nishant MalikAssistant ProfessorSchool of Mathematical Sciences, RITAbstract:This talk consists of two computational stories, and both revolve around the theme of combining ideas from machine learning with two core theoretical frameworks employed in complex systems analysis, namely, dynamical systems and networks. In the first story, we present a hybrid method that combines nonlinear time series analysis with manifold learning to identify dynamical transitions in a short time series. Nonlinear time series analysis is a collection of techniques rooted in nonlinear and stochastic dynamical systems, whereas manifold learning comes from dimensionality reduction techniques in machine learning. Through several numerical examples, we demonstrate that this hybrid method provides robust results in the presence of noise and missing values—two challenging and typical features of paleoclimate data. Furthermore, we apply the method to a time series of south Asian monsoon from Holocene and explore the role of climate change in the demise of Indus Valley Civilization. The second story presents a method to classify networks by combining ideas from network science with machine learning. We will illustrate the strengths of the method using several examples, including classifying cancer tumor types.Speaker Bio:Dr. Nishant Malik received his Ph.D. from the Potsdam Institute for Climate Impact Research in Germany, and the Physical Society of Berlin awarded the Carl Ramsauer Prize for 2012 to his Ph.D. work. Before joining RIT, he did his postdoctoral work at UNC-Chapel Hill and Dartmouth College. Dr. Malik has a wide range of research interests within the data-driven analysis and mathematical modeling of complex systems. In his research, he employs tools from network science, dynamical systems, and applied statstics and enjoys working on mathematical problems across disciplines in natural and social sciences.Intended Audience:Undergraduate and graduate SMS students.
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