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One crucial problem for applying machine learning algorithms to real-world datasets is missing data. The objective of data imputation is to fill the missing values in a dataset to resemble the completed dataset as accurately as possible. Many methods are proposed in the literature that mostly differs on the objective function and types of the variables considered. The performance of traditional machine learning methods is low when there is a nonlinear and complex relationship between features. Recently, deep learning methods are introduced to estimate data distribution and generate values for missing entries. However, these methods are originally developed for large datasets and custom data types such as image, video, and text. Thus, adopting these methods for small and structured datasets that are prevalent in real-world applications is not straightforward and often yields unsatisfactory results. Also, both types of methods do not consider uncertainty in the imputed data. We address these issues by developing a simple neural network-based architecture that works well with small and tabular datasets and utilizing a novel adversarial strategy to estimate the uncertainty of imputed data. The estimated uncertainty scores of features are then passed to the imputer module, and it fills the missing values by paying more attention to more reliable feature values. It results in an uncertainty-aware imputer with a promising performance. Extensive experiments conducted on some realworld datasets confirm that the proposed methods considerably outperform state-of-the-art imputers. Meanwhile, their execution time is not costly compared to peer state-of-the-art methods.

Nonlinear differential equations extensively used mathematical models for many interesting and important phenomena observed in numerous areas of science and technology. They are inspired by problems in diverse fields such as economics, biology, fluid dynamics, physics, differential geometry, engineering, control theory, materials science, and quantum mechanics. This special issue aims to highlight recent developments in methods and applications of nonlinear differential equations. In addition, there are papers analyzing equations that arise in engineering, classical and fluid mechanics, and finance. In this paper, we present a new numerical approach, which is concerned with the solutions of Nonlinear Differential Equations determined by a new approximation system based on inverse Laplace transforms using Chebyshev polynomials functional matrix of integration. The obtained solutions are novel, and previous literature lacks such derivations. The reliability and accuracy of our approach were shown by comparing our derived solutions with solutions obtained by other existing methods. The efficiency of the proposed numerical technique is exhibited through graphical illustrations and results drafted in tabular form for specific values of the parameters to validate the numerical investigation. The system capability is clarified through several standard nonlinear differential equations: Duffing, Van der Pol, Blasius, and Haul. The numerical results illustrate that the estimated result is in good agreement with exact or numerical styles available in literature whenever the exact results are unknown. Errors estimation to the corresponding numerical scheme also is carried out.

Genetic algorithms (GAs) represent a method that mimics the process of natural evolution in effort to find good solutions. In that process, crossover operator plays an important role. To comprehend the genetic algorithms as a whole, it is necessary to understand the role of a crossover operator. Today, there are a number of different crossover operators that can be used , one of the problems in using genetic algorithms is the choice of crossover operator Many crossover operators have been proposed in literature on evolutionary algorithms, however, it is still unclear which crossover operator works best for a given optimization problem. This paper aims at studying the behavior of different types of crossover operators in the performance of genetic algorithm. These types of crossover are implemented on Traveling Salesman Problem (TSP); Whitley used the order crossover (OX) depending on specific parameters to solve the traveling salesman problem, the aim of this paper is to make a comparative study between order crossover (OX) and other types of crossover using the same parameters which was Whitley used.

This article aims at studying the behavior of different types of crossover operators in the performance of Genetic Algorithm. We have also studied the effects of the parameters and variables (crossover probability (pc), mutation probability (pm), population size (pop-size) and number of generation (NG)) for controlling the algorithm. This research accumulated most of the types of crossover operators these types are implemented on evolving weights of Neural Network problem. The article investigates the role of crossover in GAs with respect to this problem, by using a comparative study between the iteration results obtained from changing the parameters values (crossover probability, mutation rate, population size and number of generation). From the experimental results, the best parameters values for the Evolving Weights of XOR-NN problem are NG = 1000, pop-size = 50, pm = 0.001, pc = 0.5 and the best operator is Line Recombination crossover.