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Explore the application of directed graphs in time series and biological network analysis through this 43-minute lecture. Delve into the concept of extremal events as a method for characterizing experimental time series data. Examine the challenges posed by discrete sampling in experimental measurements and the resulting uncertainty in determining the true timing of extrema. Learn about the construction of a weighted directed acyclic graph (DAG) called an extremal event DAG, utilizing persistent homology techniques to achieve robustness against measurement noise. Investigate the theoretical properties of this DAG, its applications in data comparison, and its relevance to biological systems. Gain insights into how this approach can be applied to genomic time series and biological network analysis, providing a novel perspective on interpreting complex experimental data.
