Learning Korobov Functions by Correntropy and Convolutional Neural Networks.

Combining information-theoretic learning with deep learning has gained significant attention in recent years, as it offers a promising approach to tackle the challenges posed by big data. However, the theoretical understanding of convolutional structures, which are vital to many structured deep learning models, remains incomplete. To partially bridge this gap, this letter aims to develop generalization analysis for deep convolutional neural network (CNN) algorithms using learning theory. Specifically, we focus on investigating robust regression using correntropy-induced loss functions derived from information-theoretic learning. Our analysis demonstrates an explicit convergence rate for deep CNN-based robust regression algorithms when the target function resides in the Korobov space. This study sheds light on the theoretical underpinnings of CNNs and provides a framework for understanding their performance and limitations.

Potassium Phosphite Enhances the Antagonistic Capability of Bacillus amyloliquefaciens to Manage Tomato Bacterial Wilt.

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.

Generalization analysis of deep CNNs under maximum correntropy criterion.

Convolutional neural networks (CNNs) have gained immense popularity in recent years, finding their utility in diverse fields such as image recognition, natural language processing, and bio-informatics. Despite the remarkable progress made in deep learning theory, most studies on CNNs, especially in regression tasks, tend to heavily rely on the least squares loss function. However, there are situations where such learning algorithms may not suffice, particularly in the presence of heavy-tailed noises or outliers. This predicament emphasizes the necessity of exploring alternative loss functions that can handle such scenarios more effectively, thereby unleashing the true potential of CNNs. In this paper, we investigate the generalization error of deep CNNs with the rectified linear unit (ReLU) activation function for robust regression problems within an information-theoretic learning framework. Our study demonstrates that when the regression function exhibits an additive ridge structure and the noise possesses a finite pth moment, the empirical risk minimization scheme, generated by the maximum correntropy criterion and deep CNNs, achieves fast convergence rates. Notably, these rates align with the mini-max optimal convergence rates attained by fully connected neural network model with the Huber loss function up to a logarithmic factor. Additionally, we further establish the convergence rates of deep CNNs under the maximum correntropy criterion when the regression function resides in a Sobolev space on the sphere.

Theory of deep convolutional neural networks II: Spherical analysis.

Deep learning based on deep neural networks of various structures and architectures has been powerful in many practical applications, but it lacks enough theoretical verifications. In this paper, we consider a family of deep convolutional neural networks applied to approximate functions on the unit sphere Sd-1 of Rd. Our analysis presents rates of uniform approximation when the approximated function lies in the Sobolev space W∞r(Sd-1) with r>0 or takes an additive ridge form. Our work verifies theoretically the modelling and approximation ability of deep convolutional neural networks followed by downsampling and one fully connected layer or two. The key idea of our spherical analysis is to use the inner product form of the reproducing kernels of the spaces of spherical harmonics and then to apply convolutional factorizations of filters to realize the generated linear features.

Biological Potential of Bioorganic Fertilizer Fortified with Bacterial Antagonist for the Control of Tomato Bacterial Wilt and the Promotion of Crop Yields.

The application of Bacillus sp. in the biological control of plant soilborne diseases has been shown to be an environmentally friendly alternative to the use of chemical fungicides. In this study, the effects of bioorganic fertilizer (BOF) fortified with Bacillus amyloliquefaciens SQY 162 on the suppression of tomato bacterial wilt were investigated in pot experiments. The disease incidence of tomato wilt after the application of BOF was 65.18% and 41.62% lower at 10 and 20 days after transplantation, respectively, than in the control condition. BOF also promoted the plant growth. The SQY 162 populations efficiently colonized the tomato rhizosphere, which directly suppressed the number of Ralstonia solanacearum in the tomato rhizosphere soil. In the presence of BOF, the activities of defense-related enzymes in tomato were lower than in the presence of the control treatment, but the expression levels of the defense-related genes of the plants in the salicylic acid and jasmonic acid pathways were enhanced. It was also found that strain SQY 162 could secrete antibiotic surfactin, but not volatile organic compounds, to suppress Ralstonia. The strain could also produce plant growth promotion compounds such as siderophores and indole-3-acetic acid. Thus, owing to its innate multiple-functional traits and its broad biocontrol activities, we found that this antagonistic strain isolated from the tobacco rhizosphere could establish itself successfully in the tomato rhizosphere to control soilborne diseases.

Pectin Enhances Bio-Control Efficacy by Inducing Colonization and Secretion of Secondary Metabolites by Bacillus amyloliquefaciens SQY 162 in the Rhizosphere of Tobacco.

Bacillus amyloliquefaciens is a plant-beneficial Gram-positive bacterium involved in suppressing soil-borne pathogens through the secretion of secondary metabolites and high rhizosphere competence. Biofilm formation is regarded as a prerequisite for high rhizosphere competence. In this work, we show that plant extracts affect the chemotaxis and biofilm formation of B. amyloliquefaciens SQY 162 (SQY 162). All carbohydrates tested induced the chemotaxis and biofilm formation of the SQY 162 strain; however, the bacterial growth rate was not influenced by the addition of carbohydrates. A strong chemotactic response and biofilm formation of SQY 162 were both induced by pectin through stimulation of surfactin synthesis and transcriptional expression of biofilm formation related matrix genes. These results suggested that pectin might serve as an environmental factor in the stimulation of the biofilm formation of SQY 162. Furthermore, in pot experiments the surfactin production and the population of SQY 162 in the rhizosphere significantly increased with the addition of sucrose or pectin, whereas the abundance of the bacterial pathogen Ralstonia decreased. With increased production of secondary metabolites in the rhizosphere of tobacco by SQY 162 and improved colonization density of SQY 162 in the pectin treatment, the disease incidences of bacterial wilt were efficiently suppressed. The present study revealed that certain plant extracts might serve as energy sources or environmental cues for SQY 162 to enhance the population density on tobacco root and bio-control efficacy of tobacco bacterial wilt.