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We introduce a new parameterization strategy that can be used to design algorithms simulating geometric flows on Wasserstein manifold, the probability density space equipped with optimal t...
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First, we review the semi-discrete optimal transport problem and its relation to a Laguerre tessellation. Then, we propose a new method for solving the semi-discrete optimal transpor...
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We develop a Voronoi cell-based model of epithelial cell dynamics and apply it to two different phenomena: (1) the regulation of the cornea, and (2) potential pathways for the evolution of...
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Machine Learning (ML) is a scientific study of numerical algorithms and statistical models that computer systems use to effectively predict a specific task without using specific human ins...
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The multiscale decomposition of images developed by Tadmor, Nezzar and Vese in 2004 has been extended to other imaging applications and to inverse problems, even in the nonlinear case, by ...
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We propose a general method to identify nonlinear Fokker-Planck-Kolmogorov equations (FPK equations) as gradient flows on the space of Borel probability measures on Rd with a natural ...
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We characterize the Bonnet surfaces with the single requirement that the mean curvature H of a surface in R^3 admit a reduction to an ordinary differential equation which possesses the Pai...