Recent advances in computational transport have led to powerful applications in various domains. We will present here two recent methods and algorithms that leverage the evaluation of Wasserstein distances and barycentric projections from transport maps to:
(1) find a rigid body transformation that can fully or partially align density maps from Cryo-EM, with applications to atomic building
(2) perform transfer learning between populations for learning tasks, motivated by the detection of disparities (e.g. in treatment duration) from electronic health records.
These methods also led to some theoretical results on the optimality of point clouds and transfer error upper bound.