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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 ...
Minimum-Time Quantum Transport with Bounded Trap Velocity
Minimum-Time Quantum Transport Bounded Trap Velocity Optimization and Control
2011/8/30
Abstract: We formulate the problem of efficient transport of a quantum particle trapped in a harmonic potential which can move with a bounded velocity, as a minimum-time problem on a linear system wit...
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...
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...