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Bacterial wilt caused by Ralstonia solanacearum is a distributed and worldwide soilborne disease. The application of biocontrol microbes or agricultural chemicals has been widely used to manage tomato bacterial wilt. However, whether and how agricultural chemicals affect the antagonistic ability of biocontrol microbes is still unknown. Here, we combined potassium phosphite (K-Phite), an environmentally friendly agricultural chemical, and the biocontrol agent Bacillus amyloliquefaciens QPF8 (strain F8) to manage tomato bacterial wilt disease. First, K-Phite at a concentration of 0.05% (wt/vol) could significantly inhibit the growth of R. solanacearum. Second, 0.05% K-Phite enhanced the antagonistic capability of B. amyloliquefaciens F8. Third, the greenhouse soil experiments showed that the control efficiency for tomato bacterial wilt in the combined treatment was significantly higher than that of the application of B. amyloliquefaciens F8 or K-Phite alone. Overall, our results highlighted a novel strategy for the control of tomato bacterial wilt disease via application and revealed a new integrated pattern depending on the enhancement of the antagonistic capability of biocontrol microbes by K-Phite.

Deep learning models have been widely applied in various aspects of daily life. Many variant models based on deep learning structures have achieved even better performances. Attention-based architectures have become almost ubiquitous in deep learning structures. Especially, the transformer model has now defeated the convolutional neural network in image classification tasks to become the most widely used tool. However, the theoretical properties of attention-based models are seldom considered. In this work, we show that with suitable adaptations, the single-head self-attention transformer with a fixed number of transformer encoder blocks and free parameters is able to generate any desired polynomial of the input with no error. The number of transformer encoder blocks is the same as the degree of the target polynomial. Even more exciting, we find that these transformer encoder blocks in this model do not need to be trained. As a direct consequence, we show that the single-head self-attention transformer with increasing numbers of free parameters is universal. These surprising theoretical results clearly explain the outstanding performances of the transformer model and may shed light on future modifications in real applications. We also provide some experiments to verify our theoretical result.