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Optimal transport mapping via input convex neural

2022 4 5 2 Background on optimal transport Let Pand Qbe two probability distributions on Rdwith finite second order moments The Monge's optimal trans portation problem is to transport the probability mass under Qto Pwith the least amount of cost1 i.e minimize T T #Q=P 1 2 E X˘QkX T X k2 1 Any transport map Tachieving the minimum in 1 is called

A Deterministic Annealing Neural Network Algorithm for

In this article a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem Specifically the algorithm is derived from two neural network models and Lagrange barrier functions The Lagrange function is used to handle linear equality constraints and the barrier function is used to

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A Deterministic Annealing Neural Network Algorithm for

2019 12 19 Abstract In this article a deterministic annealing neural network algorithm is proposed to solve the minimum concave cost transportation problem Specifically the algorithm is derived from two neural network models and Lagrange barrier functions The Lagrange function is used to handle linear equality constraints and the barrier function is used to force the solution

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2021 4 3 Optimal Mass Transport OMT is a well studied problem with a variety of applications in a diverse set of fields ranging from Physics to Computer Vision and in particular Statistics and Data Science Since the original formulation of Monge in 1781 significant theoretical progress been made on the existence uniqueness and properties of the optimal transport maps The

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Convex Potential Flows Universal Probability Distributions

2020 9 28 Flow based models are powerful tools for designing probabilistic models with tractable density This paper introduces Convex Potential Flows CP Flow a natural and efficient parameterization of invertible models inspired by the optimal transport OT theory CP Flows are the gradient map of a strongly convex neural potential function The convexity implies

LOCAL MATCHING INDICATORS FOR TRANSPORT

2019 7 17 SIAM J DISCRETE MATH c 2012 Society for Industrial and Applied Mathematics Vol 26 No 2 pp 801–827 LOCAL MATCHING INDICATORS FOR TRANSPORT PROBLEMS WITH CONCAVE COSTS∗ JULIE DELON† JULIEN SALOMON‡ AND ANDREI SOBOLEVSKI§ Abstract In this paper we introduce a class of local indicators that enable us to compute

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Analytical solution for solute transport from a pulse

2019 9 10 dependent concave and convex dispersivity are obtained within the fractal and the Euclidean frameworks by using the extended Fourier series method The dispersion coefficient is considered to be proportional to the nth power of a non homogeneous quadratic spatial function where the index n is considered to vary

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The equivalence of convex and concave transport cost in

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The decomposition of optimal transportation problems

2014 12 4 in the norm case in 8 In the case of convex cost an attempt to use a similar approach of decomposing the transport problems can be found in 14 In order to state the main result in addition to the standard family of transference plans we introduce the notion of transference plan subjected to a partition given

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2012 5 28 1 Introduction Suppose that there exist p suppliers and q demanders and the transportation cost from the ith supplier to the jth demander is concave in the transportation amount xij.The concave cost transportation problem CCTP is a problem of finding the optimal transportation amount from suppliers to demanders such that the total cost is minimized

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