Pattern statistics and model comparison via topological data analysis

In this talk, I will give an overview of several data-driven questions that can be tackled using topological data analysis (TDA) and other quantitative approaches. First, I will discuss stochastic agent-based models of zebrafish-skin patterns and outline how TDA can be used to quantify patterns emerging from these models, compute their summary statistics, and compare different models and parameter sets. In the second part, I will focus on the design of appropriate feature functions to classify patterns and to continue bifurcation and transition curves in parameter space at which new patterns emerge or different patterned states prevail. This talk is based on joint work with Electa Cleveland, Samuel Maffa, Melissa McGuirl, Alexandria Volkening, Wenjun Zhao, and Angela Zhu.