APPLIED TOPOLOGY GROUP

News

Schematic diagram for the method of analogous cycles, demonstrating how a persistent circular feature is identified as shared across two complexes.

Tracking Cycles in PNAS!

With Iris Yoon and collaborators, we demonstrate how the method of analogous cycles can be applied to track structure across neural manifolds, allowing us to study how topologically-structured information evolves as it is processed by the brain. Read the paper here!

Mapping Space Signatures in Adv. in Appl. Math!

With Darrick Lee, Vidit Nanda, and Harald Oberhauser, we describe how a cubical variant of Chen's iterated integrals construction extends the classical path signature to higher-dimensional domains, providing a mathematically-robust feature set for characterizing and classifying surfaces and beyond. Read the paper here!

A noisy spherical point cloud and an embedded representative of the simplicial two cycle in its Vietoris-Rips complex.

Open Applied Topology available!

The Open Applied Topology (OAT) software package, developed by Gregory Henselman-Pestrusek at PNNL in collaboration with us and Lori Ziegelmeier as part of the NSF-funded ExHACT project, expands the horizons of topological data analysis by allowing us to work directly with chain complexes. Explore cycle representatives, compute maps on homology, and more!

Who are we?

The Applied Topology Group at Oregon State University develops new mathematical tools for describing and comparing shapes and applies them in collaboration with domain experts to uncover organizational principles in neural, biological, and complex systems.