"Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence"

One of my papers was just published in final form today. Here are some details.

Title: Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence

Authors: Michelle Feng and Mason A. Porter

Abstract: Spatial networks are ubiquitous in social, geographical, physical, and biological applications. To understand the large-scale structure of networks, it is important to develop methods that allow one to directly probe the effects of space on structure and dynamics. Historically, algebraic topology has provided one framework for rigorously and quantitatively describing the global structure of a space, and recent advances in topological data analysis have given scholars a new lens for analyzing network data. In this paper, we study a variety of spatial networks—including both synthetic and natural ones—using topological methods that we developed recently for analyzing spatial systems. We demonstrate that our methods are able to capture meaningful quantities, with specifics that depend on context, in spatial networks and thereby provide useful insights into the structure of those networks. We illustrate these ideas with examples of synthetic networks and dynamics on them, street networks in cities, snowflakes, and webs that were spun by spiders under the influence of various psychotropic substances.