Topological data analysis (TDA) visualizes the “shape” of data from the spatial connectivity between discrete points. Prof. Crawford and his lab group use TDA to summarize complex patterns that underlie high-dimensional biological data. They are particularly interested in the “sub-image” selection problem where the goal is to identify the physical features of a collection of 3D shapes (e.g., tumors and single cell formations) that best explain the variation in a given trait or phenotype. Actively collaborating with faculty in the Center for Computational Molecular Biology, the School of Engineering, and the Robert J. & Nancy D. Carney Institute for Brain Science, the Crawford Lab works to develop unified statistical and machine learning frameworks that generalize the use of topological summary statistics in 3D shape analyses. Current application areas include: radiomics with clinical imaging of brain-based diseases, molecular biology with 3D microscopy of cells, biophysics with molecular dynamics simulations,  and anthropology with computed tomography (CT) scans of bones.