Related papers: Transport Inequalities. A Survey
Urban transportation is a complex phenomenon. Since many agents are constantly interacting in parallel, it is difficult to predict the future state of a transportation system. Because of this, optimization techniques tend to give obsolete…
We present a simple proof of the entropy-power inequality using an optimal transportation argument which takes the form of a simple change of variables. The same argument yields a reverse inequality involving a conditional differential…
Motivated by recent findings that human mobility is proxy for crime behavior in big cities and that there is a superlinear relationship between the people's movement and crime, this article aims to evaluate the impact of how these findings…
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…
Let $L=\DD+Z$ for a $C^1$ vector field $Z$ on a complete Riemannian manifold possibly with a boundary. By using the uniform distance, a number of transportation-cost inequalities on the path space for the (reflecting) $L$-diffusion process…
Existence and uniqueness for rough flows, transport and continuity equations driven by general geometric rough paths are established.
The problem for consistency between linear transports along paths and real bundle metrics in real vector bundles is stated. Necessary and/or sufficient conditions, as well as conditions for existence, for such consistency are derived. All…
Vehicle routing problems have been the focus of extensive research over the past sixty years, driven by their economic importance and their theoretical interest. The diversity of applications has motivated the study of a myriad of problem…
An inequality, which combines the concept of completely monotone functions with the theory of divided differences, is proposed. It is a straightforward generalization of a result, recently introduced by two of the present authors.
The increasing urbanization process we have been witnessing in the last decades is accompanied by a significant increase in traffic congestion in cities around the world. The effect of the congestion is represented in the enormous time…
As more and more people continue to live in highly urbanised areas across the globe, reliable accessibility to amenities and services plays a vital role in sustainable development. One of the challenges in addressing this issue is the…
In this paper, we consider Poincar\'e inequalities for non euclidean metrics on $\mathbb{R}^d$. These inequalities enable us to derive precise dimension free concentration inequalities for product measures. This technique is appropriate for…
The problem of branched transportation aims to describe the movement of masses when, due to concavity effects, they have the interest to travel together as much as possible, because the cost for a path of length
We develop a method to estimate from data travel latency cost functions in multi-class transportation networks, which accommodate different types of vehicles with very different characteristics (e.g., cars and trucks). Leveraging our…
This chapter provides new evidence on educational inequality and reviews the literature on the causes and consequences of unequal education. We document large achievement gaps between children from different socio-economic backgrounds, show…
Nowadays as the world population has become more interconnected and is relying on faster transportation methods, simplified connections and shorter commuting times, we witness a rapid increase in human mobility. In this situation unveiling…
By means of a novel variational approach and using dual maps techniques and general ideas of dynamical system theory we derive exact results about several models of transport flows, for which we also obtain a complete description of their…
We consider the problem of feasible coordination control for multiple homogeneous or heterogeneous mobile vehicles subject to various constraints (nonholonomic motion constraints, holonomic coordination constraints, equality/inequality…
Summary of results and overall conclusions on my works in the field of Bell inequalities and QM's alleged non-locality.
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…