Asymptotic Laplacian-Energy-Like Invariant of Lattices

Let $\mu_1\ge \mu_2\ge\cdots\ge\mu_n$ denote the Laplacian eigenvalues of $G$ with $n$ vertices. The Laplacian-energy-like invariant, denoted by $LEL(G)= \sum_{i=1}^{n-1}\sqrt{\mu_i}$, is a novel topological index. In this paper, we show that the Laplacian-energy-like per vertex of various lattices is independent of the toroidal, cylindrical, and free boundary conditions. Simultaneously, the explicit asymptotic values of the Laplacian-energy-like in these lattices are obtained. Moreover, our approach implies that in general the Laplacian-energy-like per vertex of other lattices is independent of the boundary conditions.Comment: 6 pages, 2 figure

The Effect of Crowdsourced Police Enforcement Data on Traffic Speed:A Case Study of The Netherlands

The proliferation of smartphones and internet connectivity has provided the opportunity to use crowdsourced data in traffic management. Nowadays, many people use navigation apps such as Google Maps, Waze, and Flitsmeister to obtain real-time travel information and provide feedback on road conditions, such as reporting police speed checks. As an accurate traffic speed prediction is of great significance for road users and traffic managers, different models have been proposed and widely used to predict traffic speed considering the spatio-temporal dependence of traffic data and external factors such as the weather, accidents and points of interest. This study investigates the impact of crowdsourced data about police enforcement from navigation apps on traffic speed. In addition, we examine whether the police enforcement report affects the accuracy of the deep learning prediction model. The authors extract crowdsourced police enforcement information from navigation apps, collect the corresponding historical traffic speed data, and predict traffic speed in several corridors in The Netherlands using a GCN-GRU traffic speed prediction model. The results show that the crowdsourced data for police enforcement cause the average vehicle speed to drop between 1 [km/h] and 3 [km/h] when passing the road segments marked with police activity. Moreover, the prediction performance of the GCN-GRU model during the periods without police enforcement is better than the periods with reported police activity, showing that police speed check reports can decrease the accuracy of speed prediction models