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In this work, we relied on a particular exact method to solve NP-Hard problem of determining a horizontal fragmentation scheme in relational data warehouses. The method used is that of linear programming which is distinguished by other methods by the existence of practical methods that facilitate the resolution of problems that may be described in linear form. We quote the Simplex method and the interior points. To meet the linearity of the objective function and constraints, we used initially “De Morgan” theorem, which is based on properties of sets to transform and optimize decision queries, from any form to a linear one. In addition to designing and solving the selection problem of horizontal fragmentation technique, we considered the problem in two simultaneous objectives, namely: the number of Inputs/Outputs needed to run the global workload, and number of fragments generated to identify the best solutions compared to the concept of Pareto dominance. In addition, to carry out our work, we used the Benchmark APB1 invoked by a workload, to achieve satisfactory results.

Several studies have invested in machine learning classifiers to protect plants from diseases by processing leaf images. Most of the proposed classifiers are trained and evaluated with small datasets, focusing on the extraction of hand-crafted features from image to classify the leaves. In this study, we have used a large dataset compared to the state-of-the art. Here, the dataset contains 14,828 images of tomato leaves infected with nine diseases. To train our classifier, we have introduced the Convolutional Neural Network (CNN) as a learning algorithm. One of the biggest advantages of CNN is the automatic extraction of features by processing directly the raw images. To analyze the proposed deep model, we have used visualization methods to understand symptoms and to localize disease regions in leaf. The obtained results are encouraging, reaching 99.18% of accuracy, which ourperforms dramatically shallow models, and they can be used as a practical tool for farmers to protect tomato against disease.