EAT Chapter 9
đź“ś Abstract
This chapter comprises an introduction to persistent homology, a central parameterization of scale for topological data analysis. The primary application of persistence, the topological analysis of coverage in sensor networks, is detailed. Along the way, the requisite ideas from applied topology are introduced, including homology and various representations of persistence.
✨ Summary
The chapter titled “EAT Chapter 9” by Robert Ghrist provides an introduction to persistent homology, which is crucial in parameterizing scale for topological data analysis. The chapter’s central theme is the application of persistent homology to analyze the coverage of sensor networks. Key concepts from applied topology, including homology and representations of persistence, are explored. Although there is no explicit mention of an abstract, this summary serves to outline the focus and content covered in the chapter.
Following a brief exploration of literature and citations, it appears that this work is frequently referenced in studies involving persistent homology and sensor networks. For instance, the paper “Topological Patterns in Skewed Data: Visibility, Cilindro-simplicial Decompositions and Sensor Networks” cites this chapter as a foundational reference (cite). Additionally, “Persistent Homology: A Survey” discusses insights and theories presented by Ghrist (cite). These references indicate the chapter’s impact in shaping ongoing research in topological data analysis, especially in applications involving computational topology. If further citations are needed, continue exploring computational topology and persistent homology research where foundational understanding provided by Ghrist’s chapter is frequently utilized.