Generalized Entropies and Legendre Duality.

摘要

They have shown that a simple and computationally efficient algorithm can be derived to construct the alpha-Voronoi diagrams on the space of discrete probability distributions to make use of conformally flattened structure of alpha-geometry. They also studied 1) geometry for q-exponential families which are related with alpha-geometry, and its statistical applications, and 2) conformal flatness of level surfaces in Hessian domains. Especially they studied harmonic maps between level surfaces of Hessian domains and its relation to conformally flat structure.