Related papers: Continuous-Flow Graph Transportation Distances
The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.
We introduce a novel definition of curvature for hypergraphs, a natural generalization of graphs, by introducing a multi-marginal optimal transport problem for a naturally defined random walk on the hypergraph. This curvature, termed…
There has been much work in the recent past in developing the idea of quantum geometry to characterize and understand the structure of many-particle states. For mean-field states, the quantum geometry has been defined and analysed in terms…
In this short note, we consider the problem of prescribing the Gauss curvature and image of the Gauss map for the graph of a function over a domain in Euclidean space. The prescription of the image of the Gauss map turns this into a second…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
Optimal transport (OT) is a powerful tool for measuring the distance between two defined probability distributions. In this paper, we develop a new manifold named the coupling matrix manifold (CMM), where each point on CMM can be regarded…
In this paper, we study dynamical optimal transport on a connected graph from the perspective of the Benamou-Brenier formulation, where densities are assigned to vertices and velocities to edges. However, directly using Newton's method on…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\"os-Renyi random graphs,…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
The recently developed bag-of-paths (BoP) framework consists in setting a Gibbs-Boltzmann distribution on all feasible paths of a graph. This probability distribution favors short paths over long ones, with a free parameter (the temperature…
The basic optimal transportation problem consists in finding the most effective way of moving masses from one location to another, while minimizing the transportation cost. Such concept has been found to be useful to understand various…
To study gap acceptance behaviour one needs the distribution (or probability density function) of gaps in the opposing stream. Further, in these times of widespread availability of large computing powers, traffic simulation has emerged as a…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
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 notion of transportation which is…
Continuous-time quantum walks (CTQWs) provide a valuable model for quantum transport, universal quantum computation and quantum spatial search, among others. Recently, the empowering role of new degrees of freedom in the Hamiltonian…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…
Optimal transport distances (OT) have been widely used in recent work in Machine Learning as ways to compare probability distributions. These are costly to compute when the data lives in high dimension. Recent work by Paty et al., 2019,…
Recently, Optimal Transport has been proposed as a probabilistic framework in Machine Learning for comparing and manipulating probability distributions. This is rooted in its rich history and theory, and has offered new solutions to…