Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
The work introduces subsampling confidence bounds for persistence diagrams of time-delay embeddings and an asymptotically valid test for periodicity that performs comparably to Lomb-Scargle on periodic data and better on chirps.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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Fast Computation of Free-Support Wasserstein Medians
Direct fixed-weight solver for free-support Wasserstein medians relocates atoms using OT barycentric projections and inverse-distance weights, achieving monotone descent on smoothed objectives with fewer subproblems than nested Weiszfeld baselines.
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Heat-Kernel Entropy Profiles and Geometric Effective Sample Size for Weighted Measures on Manifolds
Heat-kernel smoothing over weighted points on a compact manifold yields a scale-dependent geometric effective sample size that discounts nearby and duplicate particles.
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Subsampling Confidence Bound for Persistent Diagram via Time-delay Embedding
The work introduces subsampling confidence bounds for persistence diagrams of time-delay embeddings and an asymptotically valid test for periodicity that performs comparably to Lomb-Scargle on periodic data and better on chirps.
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Density Evolution: A Multiscale View of Density Estimation
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
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