![]() In the second part of the talk, we will focus on class of zonotopes, that is, Show that that the question is polynomial time decidable. Relations to routed trajectories of particles and reflection groupoids and In the first part of the talk, I will discuss Ideal hyperbolic polyhedra and its study reveals a rich interplay of algebra, This question has strong ties to deformations of Delaunay subdivisions and Words, is there an inscribed polytope P’ that is normally equivalent (or strongly To an inscribed polytope that keeps corresponding faces parallel? In other Refined question: Given a polytope P, is there a continuous deformation of P In this talk, I will address the following In dimensions 4Īnd up, the Universality Theorem indicates that certifying inscribability isĭifficult if not hopeless. Rivin gave a complete answer to Steiner's question. Steinitz constructed the first counter examples and Steiner posed the question if any 3-dimensional polytope had a realization Matthieu Fradelizi, Alfredo Hubard, Mathieu Meyer and Edgardo I will also present a shorter solutionįor three dimensional case (this is a part of a joint work with Properties and ideas related to the volume product and a few differentĪpproaches to Mahler conjecture. Himself proved the conjectured inequality in R^2. Should be attained on the unit cube or its dual - cross-polytope. About the same time Mahler conjectured that the minimum Proved that the maximum of the volume product is attained on theĮuclidean ball. The minimum of the volume product vol(K)vol(K^* ). The Mahler conjecture is related to this problem and it asks for Understand the connection between the volumes of K and the polar body One of the major open problems in convex geometry is to Let K be convex, symmetric, with respect to the origin, body An Homogeneous Unbalanced Regularized Optimal Transport model with application to Optimal Transport with Boundary T.Séjourné, J Feydy, FX Vialard, A Trouvé, G Peyré : Sinkhorn divergences for unbalanced optimal transport. Nous ferons la lumière sur ce phénomène et proposerons une correction possible pour obtenir un modèle de transport régularisé déséquilibré homogène, introduit dans. Dans certains cas (non-standard), ce nouveau modèle fait apparaître des inhomogénéités qui peuvent mener à des incohérences numériques. Dans un travail récent, T.Séjourné et ses co-auteurs proposent un modèle unifiant ces deux formalismes. Si ce problème possède de nombreuses propriétés théoriques importantes, sa résolution numérique devient rapidement trop lourde et sa limitation aux mesures de probabilités est contraignante.Ĭet exposé proposera une introduction au problème de transport optimal, d'abord dans sa forme la plus classique, puis dans ses variantes modernes qui font son succès aujourd'hui notamment en apprentissage : la régularisation entropique et le transport déséquilibré. Le problème de transport optimal, dont les origines remontent à Monge, fournit une métrique pour comparer des mesures de probabilités via un problème d'optimisation.
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