Digital economy has emerged as one of the primary driving forces for economic globalization. However, assessing digital economy development in a robust and scientific manner remains a great challenge. This paper proposes an evaluation system with measurement errors correction to accurately research the regional differences in and the spatial-temporal evolution characteristics of digital economy development in the Yangtze River Economic Belt (YEB), combining the entropy method, the Dagum–Gini coefficient, an $\sigma$ convergence model and grey correlation analysis. The results present that the digital economy development index in the YEB rose from 2012 to 2021, with the greatest weight being social livelihood benefits. Meanwhile, there were noticeable regional differences in digital economy development in the YEB; in particular, the middle reaches showed obvious convergence. The grey correlation degree between the influence factors and the digital economy development ranged from 0.5286 to 0.9144, demonstrating a robust positive correlation. The theoretical framework of this paper integrates economic development models with advanced statistical analysis techniques, providing a robust analytical perspective for examining the complexities of digital economy evolution. The insights offer a blueprint for policymakers seeking to foster a robust and equitable digital economy, underscoring the potential of data-driven policy formulations in navigating the intricate landscape of economic globalization.

Post-traumatic stress disorder (PTSD) is a complex psychological disorder caused by multiple factors, which are not only related to individual psychological states but also closely linked to physiological responses, social environments, and personal experiences. Therefore, traditional single data source assessment methods are difficult to fully understand and evaluate the complexity of PTSD. To overcome this challenge, the focus of this study is on developing a PTSD risk assessment model based on multi-modal data fusion. The importance of multi-modal data fusion lies in its ability to integrate data from different dimensions and provide a more comprehensive PTSD risk assessment. For multi-modal data fusion, two sets of solutions are proposed: the first is to extract EEG features using B-spline basis functions, combined with questionnaire data, to construct a multi-modal Zero-Inflated Poisson regression model; the second is to build a multi-modal deep neural network fusion prediction model to automatically extract and fuse multi-modal data features. The results show that the multi-modal data model is more accurate than the single data model, with significantly improved prediction ability. Zero-inflated Poisson models are prone to over-fitting when data is limited, while deep neural network models show superior performance in both training and prediction sets, especially the Hybrid LSTM-FCNN model, which not only has high accuracy but also strong generalization ability. This study proves the potential of multi-modal data fusion in PTSD prediction, and the Hybrid LSTM-FCNN model stands out for its high accuracy and good generalization ability, providing scientific evidence for early warning of PTSD in rescue personnel. Future research can further explore model optimization and clinical applications to promote the mental health maintenance of rescue personnel.

The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit’s mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China.

By means of the method of quasi-lower and quasi-upper solutions and monotone iterative technique, we consider the nonlinear boundary value problems with Caputo fractional derivative and introduce two well-defined monotone sequences of quasi-lower and quasi-upper solutions which converge uniformly to the actual solution of the problem, and then the existence results of the solution for the problems are established. A numerical iterative scheme is introduced to obtain an accurate approximate solution and to give one example to demonstrate the accuracy and efficiency of the new approach.