scholarly journals An Approximation Lemma about the Cut Locus, with Applications in Optimal Transport Theory

2008 ◽  
Vol 15 (2) ◽  
pp. 149-154 ◽  
Author(s):  
Alessio Figalli ◽  
Cedric Villani
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Cut Locus ◽  
Approximation Lemma ◽  
Optimal Transport Theory

scholarly journals Wildlife Monitoring Using a Multi-UAV System with Optimal Transport Theory

2021 ◽  
Vol 11 (9) ◽  
pp. 4070
Author(s):  
Rabiul Hasan Kabir ◽  
Kooktae Lee
Keyword(s):  
Detection Rate ◽  
Transport Theory ◽  
Optimal Transport ◽  
Position Estimation ◽  
Wildlife Monitoring ◽  
High Detection Rate ◽  
Monitoring Strategies ◽  
Spatio Temporal ◽  
Optimal Transport Theory ◽  
Multi Uav

This paper addresses a wildlife monitoring problem using a team of unmanned aerial vehicles (UAVs) with the optimal transport theory. The state-of-the-art technology using UAVs has been an increasingly popular tool to monitor wildlife compared to the traditional methods such as satellite imagery-based sensing or GPS trackers. However, there still exist unsolved problems as to how the UAVs need to cover a spacious domain to detect animals as many as possible. In this paper, we propose the optimal transport-based wildlife monitoring strategy for a multi-UAV system, to prioritize monitoring areas while incorporating complementary information such as GPS trackers and satellite-based sensing. Through the proposed scheme, the UAVs can explore the large-size domain effectively and collaboratively with a given priority. The time-varying nature of wildlife due to their movements is modeled as a stochastic process, which is included in the proposed work to reflect the spatio-temporal evolution of their position estimation. In this way, the proposed monitoring plan can lead to wildlife monitoring with a high detection rate. Various simulation results including statistical data are provided to validate the proposed work. In all different simulations, it is shown that the proposed scheme significantly outperforms other UAV-based wildlife monitoring strategies in terms of the target detection rate up to 3.6 times.

Schrödinger dynamics and optimal transport of measures

2021 ◽  
pp. 2150016
Author(s):  
Lorenzo Zanelli
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Transport Theory ◽  
Optimal Transport ◽  
Time Dependent ◽  
Probability Measures ◽  
Flat Torus ◽  
Optimal Transport Theory

In this paper, we recover a class of displacement interpolations of probability measures, in the sense of the Optimal Transport theory, by means of semiclassical measures associated with solutions of Schrödinger equation defined on the flat torus. Moreover, we prove the completing viewpoint by proving that a family of displacement interpolations can always be viewed as a path of time-dependent semiclassical measures.

Multi-projection of unequal dimension optimal transport theory for Generative Adversary Networks

2020 ◽  
Vol 128 ◽  
pp. 107-125
Author(s):  
Judy Yangjun Lin ◽  
Shaoyan Guo ◽  
Longhan Xie ◽  
Gu Xu
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Optimal Transport Theory

scholarly journals From Nash to Cournot–Nash equilibria via the Monge–Kantorovich problem

2014 ◽  
Vol 372 (2028) ◽  
pp. 20130398 ◽  
Author(s):  
Adrien Blanchet ◽  
Guillaume Carlier
Keyword(s):  
Nash Equilibria ◽  
Transport Theory ◽  
Optimal Transport ◽  
Strategic Interactions ◽  
Complex Issue ◽  
Optimal Transport Theory ◽  
Kantorovich Problem

The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of N player games. Analysis of Nash equilibria is however a complex issue when the number of players is large. In this article, we emphasize the role of optimal transport theory in (i) the passage from Nash to Cournot–Nash equilibria as the number of players tends to infinity and (ii) the analysis of Cournot–Nash equilibria.

scholarly journals Building Markov State Models Using Optimal Transport Theory

2018 ◽  
Author(s):  
Purushottam Dixit ◽  
Ken Dill
Keyword(s):  
Transport Theory ◽  
Optimal Transport ◽  
Conformational Dynamics ◽  
Computational Estimation ◽  
Markov State ◽  
Markov State Models ◽  
Path Cost ◽  
Transient Events ◽  
State Models ◽  
Optimal Transport Theory

Markov State Models (MSMs) describe the rates and routes in conformational dynamics of biomolecules. Computational estimation of MSMs can be expensive because<br>molecular simulations are slow to nd and sample the rare transient events. We describe here an e cient approximate way to determine MSM rate matrices by combining Maximum Caliber (maximizing path entropies) with Optimal Transport Theory (minimizing some path cost function, as when routing trucks on transportation<br>networks) to patch together transient dynamical information from multiple nonequilibrium<br>simulations. We give toy examples.

Optimal Transport Methods in Economics

2016 ◽  
Author(s):  
Alfred Galichon
Keyword(s):  
Network Flow ◽  
Transport Theory ◽  
Optimal Transport ◽  
Discrete Choice Models ◽  
Economic Modeling ◽  
Estimation Methods ◽  
Job Seekers ◽  
Flow Problems ◽  
Optimal Transport Theory ◽  
Real Estate Prices

Optimal transport theory is used widely to solve problems in mathematics and some areas of the sciences, but it can also be used to understand a range of problems in applied economics, such as the matching between job seekers and jobs, the determinants of real estate prices, and the formation of matrimonial unions. This is the first text to develop clear applications of optimal transport to economic modeling, statistics, and econometrics. It covers the basic results of the theory as well as their relations to linear programming, network flow problems, convex analysis, and computational geometry. Emphasizing computational methods, it also includes programming examples that provide details on implementation. Applications include discrete choice models, models of differential demand, and quantile-based statistical estimation methods, as well as asset pricing models. The book also features numerous exercises throughout that help to develop mathematical agility, deepen computational skills, and strengthen economic intuition.

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