The topology of data

A wealth of complex data is increasingly available in almost every aspect of the physical and social world. Such copious data offer the potential to help unlock new ways of understanding and manipulating our surroundings. The demographic characteristics of human populations convey information about heterogeneous regions of a city or a country, and our online activities encode data about who we are and what we do. Networked systems—in people, cities, animals, plants, computers, and more—are also rich in data, which are present both in their structure and in their dynamics. The flows of nutrients in vascular structures, the complicated dynamics of fluids, and the forces in granular materials all provide huge amounts of complex data. Parsing—and hopefully eventually understanding—such data requires a diverse set of tools.