相关论文: Comparing comparisons between vehicular traffic st…

We generalize the phase transition model studied in [R. Colombo. Hyperbolic phase transition in traffic flow.\ SIAM J.\ Appl.\ Math., 63(2):708-721, 2002], that describes the evolution of vehicular traffic along a one-lane road. Two…

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…

Recently, motivated by the pioneer works in revealing the small-world effect and scale-free property of various real-life networks, many scientists devote themselves to studying complex networks. In this paper, we give a brief review on the…

We study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This…

This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…

We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average…

Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…

We give a brief overview on the relation between Connes spectral distance in noncommutative geometry and the Wasserstein distance of order 1 in optimal transport. We first recall how these two distances coincide on the space of probability…

Transportation networks serve as windows into the complex world of urban systems. By properly characterizing a road network, we can therefore better understand its encompassing urban system. This study offers a geometrical approach towards…

This work provides a comprehensive analysis on naturalistic driving behavior for highways based on the highD data set. Two thematic fields are considered. First, some macroscopic and microscopic traffic statistics are provided. These…

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…

We investigate urban street networks as a whole within the frameworks of information physics and statistical physics. Urban street networks are envisaged as evolving social systems subject to a Boltzmann-mesoscopic entropy conservation. For…

Traffic microsimulation is a crucial tool that uses microscopic traffic models, such as car-following and lane-change models, to simulate the trajectories of individual agents. This digital platform allows for the assessment of the impact…

We introduce a general framework for analyzing data modeled as parameterized families of networks. Building on a Gromov-Wasserstein variant of optimal transport, we define a family of parameterized Gromov-Wasserstein distances for comparing…

Urbanization leads to an increase of traffic in cities. The Macroscopic Fundamental Diagram (MFD) suggests to describe urban traffic at a zonal level, in order to measure and control traffic. However, for a proper estimation, all data needs…

Traffic simulations are made more realistic by giving individual drivers intentions, i.e. an idea of where they want to go. One possible implementation of this idea is to give each driver an exact pre-computed path, that is, a sequence of…

Optimal transport provides a powerful mathematical framework with applications spanning numerous fields. A cornerstone within this domain is the $p$-Wasserstein distance, which serves to quantify the cost of transporting one probability…

Quadratic Wasserstein distances are obtained between dynamical systems (with states as special case), on $\mathbb{Z}_2$-graded von Neumann algebras. This is achieved through a systematic translation from non-graded to $\mathbb{Z}_2$-graded…

We introduce a cellular automaton model coupled with a transport equation for flows on graphs. The direction of the flow is described by a switching process where the switching probability dynamically changes according to the value of the…

Most autonomous-vehicles (AVs) driving strategies are designed and analyzed at the vehicle level, yet their aggregate impact on macroscopic traffic flow is still not understood, particularly the flow heterogeneity that emerges when AVs…