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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Simultaneous Optimal Transport
优化运输 矢量值度量 Wasserstein距离概念
2023/4/14
We propose a general framework of mass transport between vector-valued measures, which will be called simultaneous mass transport. The new framework is motivated by the need to transport resources of ...
Learning Probability Measures with respect to Optimal Transport Metrics
Learning Probability Measures Optimal Transport Metrics
2012/11/23
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection betw...
Optimal protocols and optimal transport in stochastic thermodynamics
Optimal protocols optimal transport stochastic thermodynamics
2011/3/2
Thermodynamics of small systems has become an important field of statistical physics. They
are driven out of equilibrium by a control, and the question is naturally posed how such a control can be op...
This paper is devoted to the study of couplings of the Lebesgue measure and the Poisson
point process. We prove existence and uniqueness of an optimal (i.e. 'asymptotically
optimal' and 'translation...
Optimal transport for multifractal random measures. Applications
Random measures multifractal processes optimal transport metric KPZ
2010/11/26
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new not...
An efficient numerical algorithm for the L2 optimal transport problem with applications to image processing
Monge-Amp`ere equation optimal transpor numerical solution
2010/12/14
We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method relies on a numerical res...
Ricci curvature, entropy and optimal transport
Ricci curvature entropy optimal transport curvature-dimension condition
2010/12/8
This is the lecture notes on the interplay between optimal transport and Riemannian geometry. On a Riemannian manifold, the convexity of entropy along optimal transport in the space of probability mea...
Introduction to Optimal Transport Theory
Monge problem linear programming Kantorovich potential existence
2010/12/9
These notes constitute a sort of Crash Course in Optimal Transport Theory. The different
features of the problem of Monge-Kantorovitch are treated, starting from convex duality issues.
The main prop...
Lecture Notes on Gradient Flows and Optimal Transport
Lecture Notes Gradient Flows Optimal Transport
2010/12/9
We present a short overview on the strongest variational formulation for gradient flows of geodesically -convex functionals in metric spaces, with applications to diffusion equations in Wasserstein s...
Models and applications of Optimal Transport in Economics, Traffic and Urban Planning
traffic congestion wardrop equilibrium optimal flows equilibrium problems
2010/12/9
Some optimization or equilibrium problems involving somehow the concept of optimal transport
are presented in these notes, mainly devoted to applications to economic and game theory
settings. A vari...
A structural model on a hypercube represented by optimal transport
determinant maximization Fourier series graphical model lasso optimal transport structural gradient model
2010/3/17
We propose a flexible statistical model for high-dimensional quantitative
data on a hypercube. Our model, called the structural gradient model (SGM),
is based on a one-to-one map on the hypercube th...