Topic: topological data analysis

Michael Hill explains how topological data analysis extracts structural information from large datasets. Ideas about connectedness, holes and shape, traditionally associated with pure mathematics, provide tools for recognising patterns as the scale of analysis changes. The discussion explores applications including breast-cancer research and questions about fair voting.

Heather Harrington explains topological data analysis and the construction of barcodes that summarize the shape of a dataset across scales. She describes how these tools reveal structure in complex information and how they can support studies of proteins and diseases such as cancer. The interview was recorded at the European Congress of Mathematics.

Entorhinal grid cells, so-called because of their hexagonally tiled spatial receptive fields, are organized in modules which, collectively, are believed to form a population code for the animal’s position. Here, we apply topological data analysis to simultaneous recordings of hundreds of grid cells and show that joint activity of grid cells within a module lies on a toroidal manifold. Each position of the animal in its physical environment corresponds to a single location on the torus, and each grid cell is preferentially active within a single “field” on the torus. Toroidal firing positions p