Related papers: About Dynamical Systems Appearing in the Microscop…
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…
This paper proposes the theoretical grounds for emulating the Dynamic System Optimum with desired arrival times on regional networks, using aggregated traffic dynamics based on the Macroscopic Fundamental Diagram. We used a projection…
The basic interaction unit of many dynamical systems involves more than two nodes. In such situations where networks are not an appropriate modelling framework, it has recently become increasingly popular to turn to higher-order models,…
We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries…
Internet platforms' traffic defines important characteristics of platforms, such as pricing of services, advertisements, speed of operations. One can estimate the traffic with the traditional time series models like ARIMA, Holt-Winters,…
In this paper, we propose a kinetic model of traffic flow with uncertain binary interactions, which explains the scattering of the fundamental diagram in terms of the macroscopic variability of aggregate quantities, such as the mean speed…
This letter propose a new model for characterizing traffic dynamics in scale-free networks. With a replotted road map of cities with roads mapped to vertices and intersections to edges, and introducing the road capacity L and its handling…
Networks of dynamical systems play an important role in various domains and have motivated many studies on the control and analysis of linear dynamical networks. For linear network models considered in these studies, it is typically…
Our goal is to use overhead imagery to understand patterns in traffic flow, for instance answering questions such as how fast could you traverse Times Square at 3am on a Sunday. A traditional approach for solving this problem would be to…
Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the…
The main motivation of this work is to assess the validity of a LWR traffic flow model to model measurements obtained from trajectory data, and propose extensions of this model to improve it. A formulation for a discrete dynamical system is…
Traffic forecasting problem remains a challenging task in the intelligent transportation system due to its spatio-temporal complexity. Although temporal dependency has been well studied and discussed, spatial dependency is relatively less…
The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…
We consider stationary stochastic dynamical systems evolving on a compact metric space, by perturbing a deterministic dynamics with a random noise, added according to an arbitrary probabilistic distribution. We prove the maximal and…
There is a deep and interesting connection between the topological properties of a graph and the behaviour of the dynamical system defined on it. We analyse various kind of graphs, with different contrasting connectivity or degree…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Understanding the dynamics of road networks has theoretical implications for urban science and practical applications for sustainable long-term planning. Various generative models to explain road network growth have been introduced in the…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
A network as a substrate for dynamic processes may have its own dynamics. We propose a model for networks which evolve together with diffusing particles through a coupled dynamics, and investigate emerging structural property. The model…