The ability to quickly calculate or query the shortest path distance between nodes on a road network is essential for many real-world applications. However, the traditional graph traversal shortest path algorithm methods, such as Dijkstra and Floyd–Warshall, cannot be extended to large-scale road networks, or the traversal speed on large-scale networks is very slow, which is computational and memory intensive. Therefore, researchers have developed many approximate methods, such as the landmark method and the embedding method, to speed up the processing time of graphs and the shortest path query. This study proposes a new method based on landmarks and embedding technology, and it proposes a multilayer neural network model to solve this problem. On the one hand, we generate distance-preserving embedding for each node, and on the other hand, we predict the shortest path distance between two nodes of a given embedment. Our approach significantly reduces training time costs and is able to approximate the real distance with a relatively low Mean Absolute Error (MAE). The experimental results on a real road network confirm these advantages.

The Soybean aphid (Aphis glycines) is a destructive pest that threatens soybeans. In order to develop green and effective control strategies, we propose an EQPAL epidemic model that integrates four developmental stages (1st–2nd stage nymphs, 3rd stage nymphs, 4th stage nymphs, and adults) and a ladybug (Harmonia axyridis) compartment. This model achieves green pest control by artificially releasing a natural enemy of soybean aphids to prey on adult soybean aphids. We analyzed the dynamic behavior of the model and derived the basic reproduction number ${\mathcal{R}}_0$. Using field monitoring data from Changchun City, Jilin Province, China in 2025, the segmented nonlinear least squares method was used for parameter estimation and fitting, resulting in an overall determination coefficient of $R^2=0.8204$. The numerical simulation results showed that the release of ladybugs significantly reduced the density and peak value of soybean aphid adults, and the predation rate $\beta$, predation conversion rate c, and ladybug migration rate $\omega$ were identified as key regulatory parameters. In addition, a cost–benefit analysis was conducted to determine the most cost-effective control measures.

Since the initiation of the highest-level public health emergency response in Jilin Province, China, on January 25, 2020, awareness of COVID-19 has remained high. However, in March 2022, an outbreak of COVID-19, attributed to imported cases, occurred in Changchun, China. Considering the psychological impact of COVID-19 on humans, we developed a SIQRS epidemic model. Dynamic analyses were conducted on both deterministic and corresponding stochastic models. By employing non-linear least squares to fit COVID-19 data, we analyzed the influence of psychological factors on the disease?s spread. Our aim was to explore effective prevention and control measures for COVID-19, taking into account the psychological dimension of the pandemic.