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Realizing automatic recognition of coal gangue content during the top coal caving process is an important goal of fully mechanized mining automation. The existing methods for automatic recognition of coal gangue content have problems such as low accuracy and real-time performance. The coal gangue mixture generated during the top coal caving process is a three-phase medium formed by coal, gangue, and air. The electrical parameters of each phase medium are different. The propagation features of electromagnetic waves are also different in different components of the mixed three-phase medium. There is a significant difference in the dielectric constant between coal blocks and gangue. By studying the electrical parameters of coal gangue mixtures with different gangue contents, new ideas and methods can be provided for automatic recognition of gangue content in top coal caving working faces. In order to explore the electrical differences of coal gangue mixtures with different gangue contents, a bidirectional peak-valley search algorithm based on the divide and conquer strategy is proposed. Based on this algorithm, a multiphase discrete random medium model of coal gangue is established. Based on the Maxwell equations and their constitutive relationship equations, the electromagnetic wave forward simulation of the established model is performed using the finite difference time domain method. The analysis shows that after improving the bidirectional peak-valley search algorithm based on the divide and conquer strategy, there is a clear phase interface between the coal, gangue, and air phases in the coal gangue multiphase discrete random medium model. Moreover, there is a greater degree of dispersion of each phase and no aggregation phenomenon. Therefore, the local medium can also reflect the overall electrical parameters, which can meet the requirements of the medium model for electromagnetic wave forward modeling. The forward simulation results indicate the following points. ① The frequency of the excitation signal will affect the amplitude of the transmitted wave. In the 12 GHz range, the higher the frequency of the excitation signal, the greater the amplitude of the transmitted wave. Low frequency will reduce the robustness of the signal, and the excitation frequency should be higher than 2 GHz. ② The gangue content of the coal gangue mixture is positively correlated with the overall equivalent dielectric constant of the medium. The higher the gangue content, the greater the propagation loss of the electromagnetic wave signal. The smaller the amplitude of the signal received by the receiving plane, the longer the time it takes for the electromagnetic wave signal to penetrate the medium. There is a significant difference between different gangue contents, which can be used as a basis for the gangue content recognition of fully mechanized top coal caving.

We consider testing the mutual independency for high-dimensional data. It is known that $ L_2 $ L 2 -type statistics have lower power under sparse alternatives and $ L_\infty $ L ∞ -type statistics have lower power under dense alternatives in high dimensions. In this paper, we develop an adaptive test based on Kendall's tau to compromise both situations of the alternative, which can automatically be adapted to the underlying data. An adaptive test is very useful in practice as the sparsity or density for a data set is usually unknown. In addition, we establish the asymptotic joint distribution of $ L_2 $ L 2 -type and $ L_\infty $ L ∞ -type statistics based on Kendall's tau under mild assumptions and the asymptotic null distribution of the proposed statistic. Simulation studies show that our adaptive test performs well in either dense or sparse cases. To illustrate the usefulness and effectiveness of the proposed test, real data sets are also analysed. [ABSTRACT FROM AUTHOR]

Federated learning (FL) is an attractive paradigm for privacy-aware distributed machine learning, which enables clients to collaboratively learn a global model without sharing clients' data. Recently, many strategies have been proposed to improve the generality of the global model and thus improve FL effect. However, existing strategies either ignore the fairness among clients or sacrifice performance for fairness. They cannot ensure that the gap among clients is as small as possible without sacrificing federated performance. To address this issue, we propose ParetoFed, a new local information aggregation method dedicated to obtaining better federated performance with smaller gap among clients. Specifically, we propose to use multi-objective hyperparameter optimization (HPO) algorithm to gain global models that are both fair and effective. Then, we send Pareto Optimal global models to each client, allowing them to choose the most suitable one as the base to optimize their local model. ParetoFed not only make the global models more fair but also make the selection of local models more personalized, which can further improve the federated performance. Extensive experiments show that ParetoFed outperforms existing FL methods in terms of fairness, and even achieves better federated performance, which demonstrates the significance of our method. [ABSTRACT FROM AUTHOR]