Presently, for the purpose of sustainable growth of the economy, it is a common choice to promote sectors’ digital transformation (DT). However, to credibly monitor the effect of DT on sectoral development, it is necessary to develop a systematic measure for the monitoring sector’s DT. This study provides a monitoring index system for sectors’ DT. First, an assessment framework for enterprises’ DT is introduced, which laid a foundation for the proposed monitoring index system for sectors’ DT. Secondly, a monitoring index system for sectors’ DT is established, which includes 13 monitoring indexes from four aspects, namely transformation stages, single-domain digitalization, integration and interconnection, and collaboration, interaction and mode innovation. A weighted method of interval hesitant fuzzy entropy is also given here. Finally, a panorama of sectors’ DT in China is derived by applying the proposed monitoring index system, and a prediction that the level of sectors’ DT in China will continue to grow in the next three years is made by gray predication.

In this article, the target tracking problem in a wireless sensor network with nonlinear Gaussian signal intensity attenuation model is considered. A Bayesian filter tracking algorithm is presented to estimate the locations of moving source that has unknown central signal intensity. This approach adopts a measurement conversion method to remove the measurement nonlinearity by the maximum likelihood estimator, and a linear estimate of the target position and its associated noise statistics obtained by the Newton–Raphson iterative optimization steps are applied into the standard Kalman filter. The Monte Carlo simulations have been conducted in comparison with the commonly used extended Kalman filter with an augmented state that consists of both the original target state and the augmentative central signal intensity. It is observed that the proposed measurement-converted Kalman filter can yield higher accurate estimate and nicer convergence performance over existing methods.

The target tracking problem in directional sensor networks (DSNs) is attracting increasing attention. Unlike the traditional omnidirectional sensor, a directional sensor has a special angle of view. It can offer direction information rather than just the sensing signal measurement with respect to the detected target. The existing tracking approaches in DSNs always separately consider the direction and measurement information; they hardly promise the tracking performance of minimum variance. In this paper, the field of view of directional sensor is approximated to a rectangle; as such the constrained area in which the target is bound to be is constructed. Then, the target tracking problem is formulated as a constrained estimation problem, and a constrained extended Kalman filter (CEKF) tracking algorithm integrating the direction and measurement information is presented; its structural and statistical properties are rigorously derived. It is proved that CEKF is the linear unbiased minimum variance estimator, and CEKF can yield a smaller error covariance than the unconstrained traditional extended Kalman filter using only sensor measurements. Simulation results show that the CEKF has superior tracking performance for directional wireless networks.

“Double-qualified” teachers are TVET instructors who combine pedagogical credentials with industry-recognized occupational competence or substantial workplace experience, linking teaching to authentic tasks and enterprise standards. Against the backdrop of quality improvement in vocational education, double-qualified teachers are widely regarded as pivotal for strengthening practical instruction and school–enterprise collaboration; however, student-perceived heterogeneity and the key drivers for the cultivation of double-qualified teachers remain insufficiently quantified. This study aims to use student questionnaire data to uncover the latent structure of double-qualified teaching experiences, identify heterogeneous learner segments, and determine the major qualities of teachers associated with students’ overall satisfaction and growth. Methodologically, we implement an integrated PCA–K-Means–Random Forest machine-learning framework: PCA reduces the dimensionality of highly correlated Likert-scale items and mitigates multicollinearity; K-Means clustering is performed in the PCA score space to segment students into distinct experiential profiles, with clustering quality assessed using metrics such as the Silhouette Score; and a Random Forest regression model is trained with dimension scores and background variables (e.g., grade level, major category, dual-teacher class exposure, and practical training experience) to estimate feature importance and identify key drivers. The results indicate a clearly stratified segmentation, with systematic differences across perceived teaching competence, practical guidance experience, school–enterprise interaction, and student satisfaction and growth; moreover, school–enterprise interaction and practical guidance emerge as the most influential components, suggesting that strengthening authentic task participation and the quality of collaboration should be prioritized. This work contributes a reproducible, data-driven “reduce–segment–explain” pathway that provides actionable quantitative evidence for cultivating and optimizing double-qualified teaching in a differentiated manner.

In this paper, a class of statistics named ART (the alternant recursive topology statistics) is proposed to measure the properties of correlation between two variables. A wide range of bi-variable correlations both linear and nonlinear can be evaluated by ART efficiently and equitably even if nothing is known about the specific types of those relationships. ART compensates the disadvantages of Reshef's model in which no polynomial time precise algorithm exists and the "local random" phenomenon can not be identified. As a class of nonparametric exploration statistics, ART is applied for analyzing a dataset of 10 American classical indexes, as a result, lots of bi-variable correlations are discovered.