Constructs empirical Hodge operators on point clouds that converge in probability to the true Hodge Laplacian, recovering Betti numbers and harmonic k-forms consistently.
Finding the homology of submanifolds with high782 confidence from random samples.Discrete & Computational Geometry, 39(1-3):419–441, March 2008
3 Pith papers cite this work. Polarity classification is still indexing.
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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.
Introduces tangential Bayes denoiser for Riemannian Gaussian mixtures on manifolds via spectral Laplace-Beltrami approximation, with nearly Bayes risk in low noise and minimax optimality on the circle.
citing papers explorer
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Empirical Hodge Laplacians: Spectral Convergence and Harmonic Forms from Point Clouds
Constructs empirical Hodge operators on point clouds that converge in probability to the true Hodge Laplacian, recovering Betti numbers and harmonic k-forms consistently.