Investor sentiment is an important factor that affects stock prices, stock market returns, and asset pricing. However, the fluctuation patterns and factors influencing investor sentiment have received less attention from scholars. This study uses text messages from stock investors' social networks and natural language processing techniques to reveal sentiment fluctuation laws of stock market investors. An investor confidence index (ICI) is constructed by quantifying sentiment in investor messages on social networks. By taking this index as a proxy for sentiment, we measure the candidate fluctuation periods of investor sentiment using a Fourier transform. The significance test then determines the significant cycle of investor sentiment within seven days. Based on this, cluster analysis further reveals that investor sentiment in the 7-day cycle has a 5 + 2 cycle of variability. That is, from Monday to Friday, investor sentiment is disturbed by stock market sentiment showing profit-seeking and risk-averse preferences, while during the weekend holiday, stock market disturbance to investor sentiment becomes lower, investor sentiment is substantially higher, and volatility is narrowed, showing a typical holiday effect. The analysis also shows that the recurring cycle of 5-day trading days and 2-day holidays is a direct exogenous factor contributing to the 7-day cycle of investor sentiment. This study provides a new perspective for studying "investor sentiment," "day of the week effect," and "behavioral finance."

This paper analyzes the efficiency of the input and output of R&D activity and the status of its development and management in universities in each region of China and proposes suggestions for improvement. The DEA–Malmquist model was used to analyze the static and dynamic science and technology statistics for universities in each region during 2006–2019 to reveal changes in the input and output of R&D activity. The overall efficiency of the R&D activity of universities in all regions of China was low. Among the 27 regions studied, DEA revealed effective efficiency in 20 regions in 2006, accounting for 74.07%, and in 19 regions in 2019, accounting for 70.37%. The Malmquist index was greater than 1 in 17 regions in 2006–2019, with an average value of 1.023 during 2006–2019. The technological progress of R&D activity in universities in each region plays a major role in the improvement of the overall efficiency. Conclusions: The efficiency of the R&D activity of Chinese universities in all regions is low in general, with large disparities between regions. The R&D activity of Chinese universities lacks scientific management. It is necessary to optimize the allocation of research resources, construct an evaluation system for the efficiency of R&D activity, and offer incentives for research to improve the output and promote the transformation of results in Chinese universities.

The convolutional neural network (CNN) is an important network model for processing time series classification tasks. However, there can be a lot of noise in the data itself. The clarity of spatial feature expression of time‐series samples and the freeness and balance of data samples both have a big effect on how well CNNs can handle time series classification (TSC) tasks. This paper proposes a multi‐pose marking learning algorithm (MPML), which optimizes the spatial representation of data samples through multiple graphical representations of time series data and then solves the problems of freeness and heterogeneity of data samples through labeling and preferential learning of poorly trained sample data. The algorithm improves the model's robustness to noise by improving the spatial expression sentiment of the time series and the labeling learning of the feature data, thereby improving the convolutional neural network's performance to perform the TSC task. We show how well the algorithm works by testing it on 46 datasets from the UCR Time Series Classification Archive and comparing the results.

In this paper, a reaction-diffusion model is proposed to describe the dynamics of rumor propagation among ignorant (who have not heard the rumor and are susceptible to be informed), spreader (who are spreading the rumor) and stifler (who know the rumor but that are no longer spreading it). The rumor is assumed to spread on a one-dimensional area called ‘street’. Numerical simulation is used to investigate the evolution of these three groups. The effects of the coefficients in this model, including the spreading rate α , decay rate β and self-diffusion coefficients ( D 1 , D 2 and D 3 ), are discussed. Our conclusions have the potential to explain phenomena in financial markets, information dissemination, communication networks, replicated database maintenance and disease transmission.

Rural revitalization hinges on the rural agriculture–industry–services (AIS) integration and urban-rural coordinated development, with improved market-oriented allocation of rural factors serving as a key economic lever for advancing both. Based on national panel data from 2009 to 2022, our analysis suggests that rural AIS integration exerts a positive income-increasing effect on rural residents. Further quantile regression reveals that rural AIS integration exhibits a stronger positive association with farmers’ income growth at higher income quantiles. Both the dynamic System GMM and the difference GMM indicate that the rural AIS integration can narrow the urban-rural income gap. Non-farm employment plays a partial mediating role in the impact of rural AIS integration on reducing the income gap. The threshold model test results reveal that the income-increasing effect of the rural AIS integration showed an inverted U-shaped marginal convergence trend with the increase of urbanization rate. Therefore, deepening the reform of the rural land system, exploring multifunctional agriculture for higher non-farm employment, enriching the financial and fiscal support, and advancing phased coordination between urbanization and rural AIS integration are appropriate choices to promote the rural AIS integration, which aims to narrow the urban-rural income gap by creating new pathways to increase rural residents’ property income, operating income and wage income. The findings enrich the theoretical foundation for understanding how the rural AIS integration boosts residents’ income and narrows the urban-rural gap, with two specific contributions: first, clarifying that its marginal income-increasing effect is more pronounced across higher quantiles of rural income distribution; second, deriving policy implications for leveraging urbanization’s non-linear impact to strengthen this effect.