{"ID":2844733,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06153","arxiv_id":"2511.06153","title":"Topologically Invariant Permutation Test","abstract":"Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation test for detecting topological inequivalence. Under topological equivalence, topological features can be permuted separately between groups without distorting individual network structures. The test statistic uses $2$-Wasserstein distances on persistent diagrams, computed in closed form. To reduce variability in brain connectivities while preserving topology, heat kernel expansion on the Hodge Laplacian is applied with bandwidth $t$ controlling diffusion intensity. Theoretical results guarantee variance reduction through optimal Hilbert space projection. Simulations across diverse network topologies show superior performance compared to conventional two-sample tests and alternative metrics. Applied to resting-state fMRI data from the Multimodal Treatment of ADHD study, the method detects significant topological differences between cannabis users and non-users.","short_abstract":"Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation test for detecting topological inequivalence. Under topological equivalence, topolo...","url_abs":"https://arxiv.org/abs/2511.06153","url_pdf":"https://arxiv.org/pdf/2511.06153v2","authors":"[\"Sixtus Dakurah\"]","published":"2025-11-08T22:12:27Z","proceeding":"q-bio.NC","tasks":"[\"q-bio.NC\",\"math.AT\",\"stat.ME\"]","methods":"[\"Diffusion Model\",\"Generative Adversarial Network\"]","has_code":false}