An evaluation index system for the coupled and coordinated development of China’s digital economy and rural revitalization, including a total of 46 indicators for the digital economy and rural revitalization subsystems, was constructed and combined with the entropy weight method, the coupling coordination degree model, Zhou’s constraint identification index, the Dagum Gini coefficient decomposition method, and the panel spatial econometric model to analyze the level of coupled and coordinated development of China’s digital economy and rural revitalization. The results found that: (1) the coupling and coordination between the two have gradually improved. The constraints of the digital economy on rural revitalization were gradually alleviated from 2011 to 2015, but after the 19th Party Congress, the development trend of rural revitalization has significantly outstripped the digital economy. (2) the spatial differences in the degree of coupling and coordination between the two are dominated by inter-regional differences and show significant spatial convergence and spatial correlation. Differentiated digital economy development strategies and more radiation in polarized areas are important for reducing regional differences in the level of coupling and coordination between the digital economy and rural revitalization. This will help China’s digital countryside grow more efficiently.

The paper constructs an evaluation index system of China’s digital economy and rural revitalization development, including 46 indicators of digital economy and rural revitalization subsystem, and analyzes the impact of China’s digital economy on rural revitalization by combining spatial Markov analysis method and spatial econometric model, and finds that:① The spatial heterogeneity of rural revitalization pattern is obvious, and the difference between north and south is more prominent, and the spatial clustering characteristic of rural revitalization pattern The spatial clustering characteristics are obvious, and the degree of clustering decreases with the increase of the spatial distance threshold. ② Digital economic development can significantly promote the level of rural revitalization in the region, and this finding is found to be robust by introducing the exogenous policy shock test of the Outline of Digital Rural Development Strategy, and digital economic development has a significant spatial siphon effect and can influence the level of rural revitalization in neighboring regions. Considering spatial heterogeneity, the regression results based on the multi-distance economic circle show that the siphoning effect of digital economy on rural revitalization in other regions peaks at 700 km ③Main contribution: It reveals that implementing a differentiated digital economy development strategy and enhancing the radiation of polarized regions are important for reducing regional differences in digital economy and rural revitalization to realize the coordinated development of China’s digital countryside.

Clarifying the sources of the digital finance inclusive development gap helps profoundly understand the regional characteristics of inclusive digital finance and benefits and formulate and implement specific policies scientifically and reasonably. Based on the 2011–2020 “Peking University Digital Finance Inclusive Index,” this study explores the regional disparity in digital finance inclusive development and its sources in the Yangtze River Delta economic cluster using the methods of the center of gravity shift, standard deviation ellipse, nested Theil index difference decomposition, and Kernel density. We found that inclusive digital finance shows a rising trend year by year, with evident heterogeneity and spatial agglomeration characteristics; interprovincial differences are the primary sources of the overall differences in inclusive digital finance in the Yangtze River Delta. The spatial effect of digital inclusion finance between the Yangtze River Delta regions has continuity. Because of the significant positive spatial correlation of digital inclusion finance between regions, digital inclusion finance in this region is vulnerable to potential shocks from neighboring regions. Moreover, with or without the spatial lag term, the level of inclusive digital finance in all regions of the Yangtze River Delta shows a leap forward. This paper looks at the regional gap of inclusive digital finance and its structural decomposition in the Yangtze River Delta city cluster from three perspectives: time trend, spatial structure, and dynamic evolution. This gives an empirical basis for the different kinds of digital finance inclusive development policies and a guide for making decisions to speed up the formation of a regional digital finance inclusive synergistic development path.

PM2.5 concentration is an important indicator to measure air quality. Its value is affected by meteorological factors and air pollutants, so it has the characteristics of nonlinearity, irregularity, and uncertainty. To accurately predict PM2.5 concentration, this paper proposes a hybrid prediction system based on the Synchrosqueezing Wavelet Transform (SWT) method, Quantum Particle Swarm Optimization (QPSO) algorithm, and Long Short-Term Memory (LSTM) model. First, the original data are denoised by the SWT method and taken as the input of the prediction model. Then, the main parameters of the LSTM model are optimized by global search based on the QPSO algorithm, which solves the problems of slow convergence and local extremum of traditional parameter training algorithms. Finally, the PM2.5 daily concentration data of Chengdu, Shijiazhuang, Shenyang, and Wuhan are predicted by the proposed SWT-QPSO-LSTM model, and the prediction results are compared with those of single prediction models and hybrid prediction models. The experimental results show that the proposed model achieves higher prediction precision and lower prediction error than other models.