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Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
Consider the set of probability measures with given marginal distributions on the product of two complete, separable metric spaces, seen as a correspondence when the marginal distributions vary. In problems of optimal transport, continuity…
A non-autonomous version of the standard map with a periodic variation of the parameter is introduced and studied. Symmetry properties in the variables and parameters of the map are found and used to find relations between rotation numbers…
Transport is an important function in many network systems and understanding its behavior on biological, social, and technological networks is crucial for a wide range of applications. However, it is a property that is not well-understood…
Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a…
The main contribution reported in the paper is a novel paradigm through which mobile cellular traffic forecasting is made substantially more accurate. Specifically, by incorporating freely available road metrics we characterise the data…
We present a probabilistic graphical model formulation for the graph clustering problem. This enables to locally represent uncertainty of image partitions by approximate marginal distributions in a mathematically substantiated way, and to…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
In this paper, we present an approach to enhance and improve the current normal map rendering technique. Our algorithm is based on semi-discrete Optimal Mass Transportation (OMT) theory and has a solid theoretical base. The key difference…
We study orthogonal and symplectic matrix models with polynomial potentials and multi interval supports of the equilibrium measure. For these models we find the bounds (similar to the case of hermitian matrix models) for the rate of…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
This study proposes the application of a backcasting approach to a mobility model with the aim of defining an optimal decarbonization roadmap. The selected decision variable is the introduction of a fleet of shared autonomous vehicles. The…
We present BusTr, a machine-learned model for translating road traffic forecasts into predictions of bus delays, used by Google Maps to serve the majority of the world's public transit systems where no official real-time bus tracking is…
Global infrastructure robustness and local transport efficiency are critical requirements for transportation networks. However, since passengers often travel greedily to maximize their own benefit and trigger traffic jams, overall…
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.
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…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map.…
Planning a public transit network is a challenging optimization problem, but essential in order to realize the benefits of autonomous buses. We propose a novel algorithm for planning networks of routes for autonomous buses. We first train a…
Multimodal transportation systems can be represented as time-resolved multilayer networks where different transportation modes connecting the same set of nodes are associated to distinct network layers. Their quantitative description became…
We study the problem of planning Pareto-optimal journeys in public transit networks. Most existing algorithms and speed-up techniques work by computing subjourneys to intermediary stops until the destination is reached. In contrast, the…