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The scientific judgement of the structural abrupt transition characteristics of the carbon market price is an important means to comprehensively analyze its fluctuation law and effectively prevent carbon market risks. However, the existing methods for identifying structural changes of the carbon market based on carbon price data mostly regard the carbon price series as a deterministic time series and pay less attention to the uncertainty implied by the carbon price series. We propose a framework for identifying abrupt transitions in the carbon market from the perspective of a complex network by considering the influence of random factors on the carbon price series, expressing the carbon price series as a sequence of probability density functions, using the distribution of probability density to reveal the uncertainty information implied by carbon price series and constructing a recurrence network of carbon price probability density. Based on the community structure, the break index and statistical test method are defined. The simulation verifies the effectiveness and superiority of the method compared with traditional methods. An empirical analysis uses the carbon price data of the European Union carbon market and seven pilot carbon markets in China. The results show many abrupt transitions in the carbon price series of the two markets, whose occurrence period is closely related to major events. [ABSTRACT FROM AUTHOR]

Through the K-means clustering analysis, it divides the regions of China into four clusters according to the differences in high-tech industry development level between 2008 and 2016. Considering "environmental pollution" and "innovation failure", an improved SBM-DEA efficiency measurement model was constructed to measure the green technology innovation efficiency of China's high-tech industry clusters. Lasso regression was used to screen out the factors affecting the green technology innovation efficiency of high-tech industry in each cluster area. On this basis, quantile regression method is used to study the influence degree and regional differences of various influencing factors on green innovation efficiency of high-tech industry at different quantile. Meanwhile, DEA-tobit model is used for robustness test. The research shows that in each cluster area, the factors that significantly affect the green innovation efficiency of high-tech industry are different, and the degree of influence of each factor on the innovation efficiency at different quantile is also different. Combining the empirical results with the reality of high-tech industries in various regions, the corresponding policy recommendations are put forward. [ABSTRACT FROM AUTHOR]

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China., (© 2024. The Author(s), under exclusive licence to the Society for Mathematical Biology.)