Abstract The conditional edge-connectivity is an important parameter to evaluate the reliability and fault tolerance of multi-processor systems. The $n$-dimensional bijective connection networks $B_{n}$ contain hypercubes, crossed cubes, Möbius cubes and twisted cubes, etc. The conditional edge-connectivity of a connected graph $G$ is the minimum cardinality of edge sets, whose deletion disconnects $G$ and results in each remaining component satisfying property $\mathscr{P}$. And let $F$ be the edge set as desired. For a positive integer $a$, if $\mathscr{P}$ denotes the property that the average degree of each component of $G-F$ is no less than $a$, then the conditional edge-connectivity can be called the $a$-average degree edge-connectivity $\overline{\lambda }_{a}(G)$. In this paper, we determine that the exact value of the $a$-average degree edge-connectivity of an $n$-dimensional bijective connection network $\overline{\lambda }_{a}(B_{n})$ is $(n-a)2^a$ for each $0\leq a \leq n-1 $ and $n\geq 1$. 1

Multilevel converters play an important role in power electronic systems. In recent years, data-driven fault diagnosis technologies for multilevel converters have rapidly developed and are generally based on feature engineering and intelligent classification algorithms. However, the fault detection rate, speed, and stability still need to be improved, especially for complex converter systems. In this article, based on a probabilistic autoencoder architecture, an affine-invariant Riemannian metric autoencoder (AIRMAE) is proposed for feature extraction, and combined with classifiers, a supervised learning fault diagnosis method for multilevel converters is constructed. The proposed AIRMAE is able to investigate low-dimensional representations from high-dimensional data manifolds while preserving sufficient valid information. Based on a five-level nested neutral-point piloted converter, the effectiveness of the proposed method is verified by experiments. The performance is superior to that of existing state-of-the-art fault diagnosis methods, with high detection accuracy, good stability, and strong waveform reconstruction ability.

Satellite hyperspectral remote sensing is a useful technology to extract soil heavy metal content. This paper introduces an inversion method of soil copper (Cu) content using AHSI/ZY1-02D data and assesses the inversion accuracy with field investigation data. Different spectral pretreatments are compared and then an inversion model of soil Cu content based on random frog leaping and regression tree ensemble is established. Compared with the original spectrum, the utilized spectral transformations can significantly increase the number of sensitive bands for soil Cu inversion, and the correlation between Cu content and spectrum can be improved as well. We also find the reciprocal spectrum and its differential transformations have the highest correlation with the soil Cu content. Moreover, the R2 and RMSE of the inversion model are 0.826 and 596.79 mg/kg, respectively, indicating that AHSI/ZY1-02D hyperspectral data can be used to estimate the total Cu content in the soil at mining area.

Soil organic matter content (SOM-C) is an important evaluation index of soil quality. Hyperspectral remote sensing inversion method of SOM-C is a popular approach. However, the lack of satellite hyperspectral data limits the application of this technology. This study took Shuyang County, Jiangsu Province as the research area. To analyze the application potential of AHSI/ZY1-02D data in the extraction of SOM-C information, we compared the correlation between SOM-C and pixel reflectance spectrum, transformed spectrum and spectral indices, and then built a SOM-C inversion model based on spectral indices with RMSE of 5.97 g/kg. The results showed good correlation between the transformed hyperspectral satellite data and actual SOM-C in the mid-range between 20–35 g/kg region, which indicated the satellite hyperspectral images can provide significant data support for soil quality evaluation.