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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Functional generative AI use correlates with better academic performance and enhanced prefrontal-hippocampal brain metrics, whereas socio-emotional use correlates with poorer mental health and reduced superior temporal and amygdalar volumes.
Kernel density estimation improves radio source count estimation over binned methods, as shown in simulations and LOFAR data analysis, with a new AstroKDE package.
DES Y3 weak lensing analysis with hybrid map-level statistics and simulation-based inference yields S8 = 0.808 ± 0.017, Ωm = 0.325 ± 0.024, and w < -0.766, improving the figure of merit by 60% over prior state-of-the-art.
Customized chromatic noise models for 67 pulsars detect non-dispersive delays in 21 cases, alter achromatic noise inferences in 19, and enable solar wind density estimates over 1.5 cycles.
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.
Customized chromatic noise models applied to NANOGrav 15 yr data raise the Bayes factor for Hellings-Downs GWB correlations by a factor of ~8, lower the amplitude to 2.1e-15, and increase the spectral index to 3.5.
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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.