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2020 Optimal transport and barycenters for dendritic measures
Young-Heon Kim, Brendan Pass, David J. Schneider
Pure Appl. Anal. 2(3): 581-601 (2020). DOI: 10.2140/paa.2020.2.581

Abstract

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 tree-like 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.

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Young-Heon Kim. Brendan Pass. David J. Schneider. "Optimal transport and barycenters for dendritic measures." Pure Appl. Anal. 2 (3) 581 - 601, 2020. https://doi.org/10.2140/paa.2020.2.581

Information

Received: 10 October 2019; Revised: 21 February 2020; Accepted: 28 March 2020; Published: 2020
First available in Project Euclid: 22 January 2021

Digital Object Identifier: 10.2140/paa.2020.2.581

Subjects:
Primary: 49K99
Secondary: 92C80

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.2 • No. 3 • 2020
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