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This paper provides a thorough exploration of the absolute value equations $Ax-|x|=b$, a seemingly straightforward concept that has gained heightened attention in recent years. It is an NP-hard and nondifferentiable problem and equivalent with the standard linear complementarity problem. Offering a comprehensive review of existing literature, the study delves into theorems concerning the existence and nonexistence of solutions to the absolute value equations, along with numerical methods for effectively addressing this complex equation. Going beyond conventional approaches, the paper investigates strategies for obtaining solutions with minimal norms, techniques for correcting infeasible systems, and other pertinent topics. By pinpointing challenging issues and emphasizing open problems, this paper serves as a valuable guide for shaping the future research trajectory in this dynamic and multifaceted field.

This paper provides an overview of the necessary and sufficient conditions for guaranteeing the unique solvability of absolute value equations. In addition to discussing the basic form of these equations, we also address several generalizations, including generalized absolute value equations and matrix absolute value equations. Our survey encompasses known results as well as novel characterizations proposed in this study.

XAI refers to the techniques and methods for building AI applications which assist end users to interpret output and predictions of AI models. Black box AI applications in high-stakes decision-making situations, such as medical domain have increased the demand for transparency and explainability since wrong predictions may have severe consequences. Model explainability and interpretability are vital successful deployment of AI models in healthcare practices. AI applications' underlying reasoning needs to be transparent to clinicians in order to gain their trust. This paper presents a systematic review of XAI aspects and challenges in the healthcare domain. The primary goals of this study are to review various XAI methods, their challenges, and related machine learning models in healthcare. The methods are discussed under six categories: Features-oriented methods, global methods, concept models, surrogate models, local pixel-based methods, and human-centric methods. Most importantly, the paper explores XAI role in healthcare problems to clarify its necessity in safety-critical applications. The paper intends to establish a comprehensive understanding of XAI-related applications in the healthcare field by reviewing the related experimental results. To facilitate future research for filling research gaps, the importance of XAI models from different viewpoints and their limitations are investigated.

Multi-task learning (MTL) has emerged as a promising topic of machine learning in recent years, aiming to enhance the performance of numerous related learning tasks by exploiting beneficial information. During the training phase, most of the existing multi-task learning models concentrate entirely on the target task data and ignore the non-target task data contained in the target tasks. To address this issue, Universum data, that do not correspond to any class of a classification problem, may be used as prior knowledge in the training model. This study looks at the challenge of multi-task learning using Universum data to employ non-target task data, which leads to better performance. It proposes a multi-task twin support vector machine with Universum data (UMTSVM) and provides two approaches to its solution. The first approach takes into account the dual formulation of UMTSVM and tries to solve a quadratic programming problem. The second approach formulates a least-squares version of UMTSVM and refers to it as LS-UMTSVM to further increase the generalization performance. The solution of the two primal problems in LS-UMTSVM is simplified to solving just two systems of linear equations, resulting in an incredibly simple and quick approach. Numerical experiments on several popular multi-task data sets and medical data sets demonstrate the efficiency of the proposed methods.

The first known case of Coronavirus disease 2019 (COVID-19) was identified in December 2019. It has spread worldwide, leading to an ongoing pandemic, imposed restrictions and costs to many countries. Predicting the number of new cases and deaths during this period can be a useful step in predicting the costs and facilities required in the future. The purpose of this study is to predict new cases and deaths rate one, three and seven-day ahead during the next 100 days. The motivation for predicting every n days (instead of just every day) is the investigation of the possibility of computational cost reduction and still achieving reasonable performance. Such a scenario may be encountered in real-time forecasting of time series. Six different deep learning methods are examined on the data adopted from the WHO website. Three methods are LSTM, Convolutional LSTM, and GRU. The bidirectional extension is then considered for each method to forecast the rate of new cases and new deaths in Australia and Iran countries. This study is novel as it carries out a comprehensive evaluation of the aforementioned three deep learning methods and their bidirectional extensions to perform prediction on COVID-19 new cases and new death rate time series. To the best of our knowledge, this is the first time that Bi-GRU and Bi-Conv-LSTM models are used for prediction on COVID-19 new cases and new deaths time series. The evaluation of the methods is presented in the form of graphs and Friedman statistical test. The results show that the bidirectional models have lower errors than other models. A several error evaluation metrics are presented to compare all models, and finally, the superiority of bidirectional methods is determined. This research could be useful for organisations working against COVID-19 and determining their long-term plans.

COVID-19 has caused many deaths worldwide. The automation of the diagnosis of this virus is highly desired. Convolutional neural networks (CNNs) have shown outstanding classification performance on image datasets. To date, it appears that COVID computer-aided diagnosis systems based on CNNs and clinical information have not yet been analysed or explored. We propose a novel method, named the CNN-AE, to predict the survival chance of COVID-19 patients using a CNN trained with clinical information. Notably, the required resources to prepare CT images are expensive and limited compared to those required to collect clinical data, such as blood pressure, liver disease, etc. We evaluated our method using a publicly available clinical dataset that we collected. The dataset properties were carefully analysed to extract important features and compute the correlations of features. A data augmentation procedure based on autoencoders (AEs) was proposed to balance the dataset. The experimental results revealed that the average accuracy of the CNN-AE (96.05%) was higher than that of the CNN (92.49%). To demonstrate the generality of our augmentation method, we trained some existing mortality risk prediction methods on our dataset (with and without data augmentation) and compared their performances. We also evaluated our method using another dataset for further generality verification. To show that clinical data can be used for COVID-19 survival chance prediction, the CNN-AE was compared with multiple pre-trained deep models that were tuned based on CT images.

In binary classification, kernel-free linear or quadratic support vector machines are proposed to avoid dealing with difficulties such as finding appropriate kernel functions or tuning their hyper-parameters. Furthermore, Universum data points, which do not belong to any class, can be exploited to embed prior knowledge into the corresponding models so that the generalization performance is improved. In this paper, we design novel kernel-free Universum quadratic surface support vector machine models. Further, we propose the L1 norm regularized version that is beneficial for detecting potential sparsity patterns in the Hessian of the quadratic surface and reducing to the standard linear models if the data points are (almost) linearly separable. The proposed models are convex such that standard numerical solvers can be utilized for solving them. Nonetheless, we formulate a least squares version of the L1 norm regularized model and next, design an effective tailored algorithm that only requires solving one linear system. Several theoretical properties of these models are then reported/proved as well. We finally conduct numerical experiments on both artificial and public benchmark data sets to demonstrate the feasibility and effectiveness of the proposed models.

In this study, calculations necessary to solve the large scale linear programming problems in two operating systems, Linux and Windows 7 (Win), are compared using two different methods. Relying on the interior-point methods, linear-programming interior point solvers (LIPSOL) software was used for the first method and relying on an augmented Lagrangian method-based algorithm, the second method used the generalized derivative. The performed calculations for various problems show the produced random in the Linux operating system (OS) and Win OS indicate the efficiency of the performed calculations in the Linux OS in terms of the accuracy and using of the optimum memory., Comment: 8 pages; This paper will be published in Appl. Math. Inf. Sci. Vol. 7 No. 1 (2013)