614: Selected Topics in Systems Biology, Spring 2020

Instructor: Konstantin Mischaikow

The focus of the course was on a novel approach, based on combinatorics, order theory, and algebraic topology, to the analysis of nonlinear data driven dynamical systems. Because of the range of background of the participants the course material provided introductory answers to the following questions: What is homology and how can it be computed efficiently? How do results from homological computations provide useful information about existence and structure of nonlinear dynamics? How can combinatorics and order theory be used to efficiently decompose dynamics and/or build a decomposition from finite sets of data? What is the Conley index? How is it computed? What does it tell us about nonlinear dynamics? How can we go from heuristic models to statements about global dynamics over large ranges of parameters? How can these statements be compared against experimental data? The course included two series of guest lectures. Prof. J. Gao, Computer Science, discussed problems associated with social network dynamics. This was followed by discussions on how techniques from the course could be applied to such problems. Prof. Y. Hung, Statistics, discussed how statistical uncertainty theory can be used to optimize the information available from time series data. This was followed by discussions on how these techniques could be employed in combination with the combinatorial methods to extract more information from limited data sets.