#29 · Systems biology

Topological and geometric tests of higher-order structure in fMRI and functional data

The items share a focus on evaluating structure in high-dimensional biological and neural data through topology and geometry rather than through pointwise statistics. A topologically invariant permutation test compares functional data using 2-Wasserstein distances on persistent diagrams with heat kernel smoothing. A separate preprint applies Mahalanobis whitening before dimensionality reduction, motivated by Bures distance, to de-individualize fMRI signals. A published comparison sets topological data analysis against multivariate information theory for higher-order interactions, using toy shapes and human fMRI data. The dominant thread is the use of geometric or topological invariants to characterize relational structure. What is new relative to the earlier inference theme is that the emphasis falls on the representation and comparison of higher-order structure itself, with validation on toy shapes and human fMRI data.