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In this work, we present a new proximal gradient algorithm based on Tseng’s extragradient method and an inertial technique to solve the convex minimization problem in real Hilbert spaces. Using the stepsize rules, the selection of the Lipschitz constant of the gradient of functions is avoided. We then prove the weak convergence theorem and present the numerical experiments for image recovery. The comparative results show that the proposed algorithm has better efficiency than other methods.

Objective: To develop and evaluate a technique using convolutional neural networks (CNNs) for the computer-assisted diagnosis of cervical spine fractures from radiographic x-ray images. By leveraging deep learning techniques, the study might potentially lead to improved patient outcomes and clinical decision-making. Methods: This study obtained 500 lateral radiographic cervical spine x-ray images from standard open-source dataset repositories to develop a classification model using CNNs. All the images contained diagnostic information, including normal cervical radiographic images (n=250) and fracture images of the cervical spine fracture (n=250). The model would classify whether the patient had a cervical spine fracture or not. Seventy percent of the images were training data sets used for model training, and 30% were for testing. Konstanz Information Miner (KNIME)'s graphic user interface-based programming enabled class label annotation, data preprocessing, CNNs model training, and performance evaluation. Results: The performance evaluation of a model for detecting cervical spine fractures presents compelling results across various metrics. This model exhibits high sensitivity (recall) values of 0.886 for fractures and 0.957 for normal cases, indicating its proficiency in identifying true positives. Precision values of 0.954 for fractures and 0.893 for normal cases highlight the model's ability to minimize false positives. With specificity values of 0.957 for fractures and 0.886 for normal cases, the model effectively identifies true negatives. The overall accuracy of 92.14% highlights its reliability in correctly classifying cases by the area under the receiver operating characteristic curve. Conclusion: We successfully used deep learning models for computer-assisted diagnosis of cervical spine fractures from radiographic x-ray images. This approach can assist the radiologist in screening, detecting, and diagnosing cervical spine fractures. [ABSTRACT FROM AUTHOR]

This paper introduces a new algorithm that combines the forward–backward splitting algorithms with a double inertial technique, utilizing the previous three iterations. The weak convergence theorem is established under certain mild conditions in a Hilbert space, including a relaxed inertial method in real numbers. An example of infinite dimension space is given with numerical results to support our proposed algorithm. The algorithm is applied to an asymmetrical educational dataset of students from 109 schools, utilizing asymmetric inputs as nine attributes to predict the output as students' mathematical integrated skills. The algorithm's performance is compared with other algorithms in the literature to demonstrate its effectiveness. The proposed algorithm demonstrates comparable precision, recall, accuracy, and F1 score but performs a relatively lower number of iterations. The contributions of each performance aspect to the mathematical integration skill of students are discussed to improve students' mathematical learning. [ABSTRACT FROM AUTHOR]

This paper presents a two inertial technique with a projection Mann forward-backward splitting algorithm for solving variational inclusion problems that exhibit weak convergence under suitable conditions in Hilbert spaces. Furthermore, we provide a numerical example in infinitely dimensional spaces to support the main result. Finally, we provide an application for data classification using an extreme learning machine. According to data provided by theWorld Health Organization (WHO), stroke is recognized as the predominant contributor to mortality and disability on a global scale. To appraise the efficacy of our algorithm, we procured a dependable dataset for stroke prediction from the Kaggle website. The best algorithm that performed this task is ours compared to other machine learning methods. [ABSTRACT FROM AUTHOR]

This study investigates the weak convergence of the sequences generated by the inertial relaxed [Math Processing Error] C Q algorithm with Mann's iteration for solving the split feasibility problem in real Hilbert spaces. Moreover, we present the advantage of our algorithm by choosing a wider range of parameters than the recent methods. Finally, we apply our algorithm to solve the classification problem using the heart disease dataset collected from the UCI machine learning repository as a training set. The result shows that our algorithm performs better than many machine learning methods and also extreme learning machine with fast iterative shrinkage-thresholding algorithm (FISTA) and inertial relaxed [Math Processing Error] C Q algorithm (IRCQA) under consideration according to accuracy, precision, recall, and F1-score. [ABSTRACT FROM AUTHOR]