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A topological index is a numeric quantity associated with a network or a graph that characterizes its whole structural properties. In [Javaid and Cao, Neural Computing and Applications, DOI 10.1007/s00521-017-2972-1], the various degree-based topological indices for the probabilistic neural networks are studied. We extend this study by considering the calculations of the other topological indices, and derive the analytical closed formulas for these new topological indices of the probabilistic neural network. Moreover, a comparative study using computer-based graphs has been carried out first time to clarify the nature of the computed topological descriptors for the probabilistic neural networks. Our results extend some known conclusions.
EN
Planting shrubs on sand land and degraded pasture are two main measures for desertification control particularly in northwest China. However, their effects on soil organic carbon (SOC) and its fractions remain uncertain. We assessed the changes in stocks of SOC, light fraction of SOC (LF–SOC) and heavy fraction of SOC (HF–SOC) after planting Artemisia ordosica (AO, 17 years), Astragalus mongolicum (AM, 5 years) and Salix psammophila (SP, 16 years) in sand land and planting Caragana microphylla (CM, 24 years) on degraded pasture. Results show that: 1) after planting AO, AM and SP on sand land, SOC stocks increased by 162.5%, 45.2% and 70.8%, respectively, and LF–SOC accounted for a large proportion in the increased SOC. Dry weights of LF–SOC, rather than carbon concentrations, were higher in shrublands than that in sand land; 2) after planting CM on degraded pasture, SOC stock decreased by 9.3% and all the loss was HF–SOC in 60–100 cm soil layer where both herbaceous fine root biomass (HFRB) and soil water content (SWC) also decreased. The results indicate that planting shrubs can result in an increase of SOC in sand land, whereas that can lead to a decrease of SOC in degraded pasture. The increase of SOC in sand land mainly bases on the accumulation of dry weight of LF–SOC. The loss of SOC in degraded pasture is caused by the decrease of carbon concentrations of HF–SOC, which can be related to the reduction of HFRB and SWC in deep soil layer. Therefore, shrub-planting for desertification control not always improve the quantity and stability of SOC in northwest China.
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