A book chapter of ours was just published in final form. It is Chapter 16 in this book. Here are some other details about it.
Title: Topological Data Analysis of Spatial Systems
Authors: Michelle Feng, Abigail Hickok, and Mason A. Porter
Abstract: In this chapter, we discuss applications of topological data analysis (TDA) to spatial systems. We briefly review a recently proposed level-set construction of
filtered simplicial complexes, and we then examine persistent homology in two cases studies: street networks in Shanghai and anomalies in the spread of COVID-19 infections. We then summarize our results and provide an outlook on TDA in spatial systems.
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