In many cases, the correlation between time series has a certain lag effect. To study the lag correlation between two time series variables, we select London Metal Exchange (LME) nickel futures and spot prices from 3 January 2008 to 29 December 2017 as sample data to carry out stationarity tests, cointegration tests and Granger causality tests to determine the stationarity and correlation of two time series. Then, we use the method of combining the distributed lag model and sliding window method to construct a network. We select the best sliding window length through a sensitivity test. The time series is reconstructed into a complex network by taking the types of patterns as the nodes and the conduction relationship between the patterns as the edges. The number of transitions between patterns is defined as the weight of the edge. The results show that the spot price changes are caused by the change in nickel futures price and that the optimal sliding window length is 64. Additionally, 12 types of patterns account for a large proportion of the patterns in the network. Six patterns are the main intermediaries of pattern transmission and appear centrally with the change in the market environment. Therefore, the relationship model between these futures and spot prices has remained stable for a long time. Combining the positive and negative news of the market, we identify the timing of the change in the relationship model and can use this approach to improve the accuracy of early warning methods. This study provides a method to construct a complex network using a distributed lag model, which can help analyze two real time series variables with lag correlation.

As COVID-19 spread globally in 2020, the interaction between the traffic dynamics and the spread of the epidemic has attracted much attention. However, controlling the spread of the epidemic remains a challenging issue. In this paper, we have investigated the relationships between link-closure strategies and the traffic-driven epidemic spreading. It is found that the epidemic spreading can be suppressed by the targeted closing of links between small-degree nodes. In contrast, closing links between large-degree nodes can accelerate the outbreak of the epidemic. These findings have significance for controlling the spread of the epidemic.

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With the accelerated development of smart cities, the construction and development of smart grids have an increasing impact on the safe and stable operation of power systems. The benefit evaluation of smart grids can find out the problems of smart grids more comprehensively, which is of great practical significance for the further development of smart cities. In order to ensure accuracy and real-time evaluation, this paper proposes a new hybrid intelligent evaluation model using an improved technique for order preference by similarity to an ideal solution (TOPSIS) and long–short-term memory (LSTM) optimized by a modified sparrow search algorithm (MSSA). First, a set of smart grid benefit evaluation index systems is established in the context of considering smart city development. Then, aiming at the reverse order problem existing in TOPSIS, an improved evaluation model with entropy weight and modified TOPSIS is established. Finally, an intelligent evaluation model based on LSTM with MSSA optimization is designed. The example analysis verifies the accuracy of the model proposed, points out the important factors affecting the benefits of smart grids, and provides a new idea to achieve effective evaluation and rapid prediction, which can help to improve the benefit level of smart grids.

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