For 1-manifolds in R^2, vineyard monodromy on small loops arises precisely when the loop intersects a singularity of the distance function on the symmetry set.
Extending persistence using poincar´ e and lefschetz duality.Foundations of Computa- tional Mathematics, 9(1):79–103, Feb 2009
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PLACE delivers a closed-form certified classification method for point clouds and graphs based on persistent homology with explicit excess-risk bounds, selection rules, and training-time certificates.
Hybrid models that add persistent-homology features from fixation time series to traditional statistical features outperform purely statistical baselines for dyslexia detection on the Copenhagen Corpus.
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