Optimal transport and barycenters for dendritic measures

Jeudi 14 novembre 14:00-15:00 - Brendan Pass - University of Alberta

Résumé : We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a particular direction of orientation. Our motivation is the comparison of and interpolation between plants’ root systems. We characterize barycenters with respect to this metric, and establish that the
interpolations of root-like measures, using this new metric, are also root like, in a certain sense ; this property fails for conventional Wasserstein barycenters. We also establish geodesic convexity with
respect to this metric for a variety of functionals, some of which we expect to have biological importance.

Lieu : IMO, Salle 3L8

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