Due to its significance in science and engineering, time-varying linear matrix equation (LME) problems have received a lot of attention from scholars. It is for this reason that the issue of finding the minimum-norm least-squares solution of the time-varying quaternion LME (ML-TQ-LME) is addressed in this study. This is accomplished using the zeroing neural network (ZNN) technique, which has achieved considerable success in tackling time-varying issues. In light of that, two new ZNN models are introduced to solve the ML-TQ-LME problem for time-varying quaternion matrices of arbitrary dimension. Two simulation experiments and two practical acoustic source tracking applications show that the models function superbly.

The Markowitz model, a Nobel Prize winning model for portfolio analysis, paves the theoretical foundation in finance for modern investment. However, it remains a challenging problem in the high frequency trading (HFT) era to find a more time efficient solution for portfolio analysis, especially when considering circumstances with the dynamic fluctuation of stock prices and the desire to pursue contradictory objectives for less risk but more return. In this paper, we establish a recurrent neural network model to address this challenging problem in runtime. Rigorous theoretical analysis on the convergence and the optimality of portfolio optimization are presented. Numerical experiments are conducted based on real data from Dow Jones Industrial Average (DJIA) components and the results reveal that the proposed solution is superior to DJIA index in terms of higher investment returns and lower risks.

Defining efficient families of recurrent neural networks (RNN) models for solving time-varying nonlinear equations is an interesting research topic in applied mathematics. Accordingly, one of the underlying elements in designing RNN is the use of efficient nonlinear activation functions. The role of the activation function is to bring out an output from a set of input values that are supplied into a node. Our goal is to define new family of activation functions consisting of a fixed gain parameter and a functional part. Corresponding zeroing neural networks (ZNN) is defined, termed as varying-parameter improved zeroing neural network (VPIZNN), and applied to solving time-varying nonlinear equations. Compared with previous ZNN models, the new VPIZNN models reach an accelerated finite-time convergence due to the new time-varying activation function which is embedded into the VPIZNN design. Theoretical results and numerical experiments are presented to demonstrate the superiority of the novel VPIZNN formula. The capability of the proposed VPIZNN models are demonstrated in studying and solving the Van der Pol equation and finding the root $$\root m \of {a(t)}$$.

The efficient solution of the time-varying quaternion matrix inverse (TVQ-INV) is a challenging but crucial topic due to the significance of quaternions in many disciplines, including physics, engineering, and computer science. The main goal of this research is to employ the higher-order zeroing neural network (HZNN) strategy to address the TVQ-INV problem. HZNN is a family of zeroing neural network models that correlates to the hyperpower family of iterative methods with adjustable convergence order. Particularly, three novel HZNN models are created in order to solve the TVQ-INV both directly in the quaternion domain and indirectly in the complex and real domains. The noise-handling version of these models is also presented, and the performance of these models under various types of noises is theoretically and numerically tested. The effectiveness and practicality of these models are further supported by their use in robotic motion tracking. According to the principal results, each of these six models can solve the TVQ-INV effectively, and the HZNN strategy offers a faster convergence rate than the conventional zeroing neural network strategy.

Employee attrition, defined as the voluntary resignation of a subset of a company’s workforce, represents a direct threat to the financial health and overall prosperity of a firm. From lost reputation and sales to the undermining of the company’s long-term strategy and corporate secrets, the effects of employee attrition are multidimensional and, in the absence of thorough planning, may endanger the very existence of the firm. It is thus impeccable in today’s competitive environment that a company acquires tools that enable timely prediction of employee attrition and thus leave room either for retention campaigns or for the formulation of strategical maneuvers that will allow the firm to undergo their replacement process with its economic activity left unscathed. To this end, a weights and structure determination (WASD) neural network utilizing Fresnel cosine integrals in the determination of its activation functions, termed FCI-WASD, is developed through a process of three discrete stages. Those consist of populating the hidden layer with a sufficient number of neurons, fine-tuning the obtained structure through a neuron trimming process, and finally, storing the necessary portions of the network that will allow for its successful future recreation and application. Upon testing the FCI-WASD on two publicly available employee attrition datasets and comparing its performance to that of five popular and well-established classifiers, the vast majority of them coming from MATLAB’s classification learner app, the FCI-WASD demonstrated superior performance with the overall results suggesting that it is a competitive as well as reliable model that may be used with confidence in the task of employee attrition classification.

An improved activation function, termed extended sign-bi-power (Esbp), is proposed. An extension of the Li zeroing neural network (ELi-ZNN) based on the Esbp activation is derived to obtain the online solution of the time-varying inversion problem. A detailed theoretical analysis confirms that the new activation function accomplishes fast convergence in calculating the time-varying matrix inversion. At the same time, illustrative numerical experiments substantiate the excellent performance of the proposed activation function over the Li and tunable activation functions. Convergence properties and numerical behaviors of the proposed ELi-ZNN model are examined.

The main contribution of this paper is to develop explicit expressions for the Drazin inverse of two kinds of anti-triangular block complex matrices under new assumptions. Further, we apply our results to obtain new formulae for the Drazin inverse of a 2 × 2 block complex matrix. We present a list of well-known results which are recovered in this paper. We give three examples to illustrate our new explicit expressions.

Credit card customers comprise a volatile subset of a banks' client base. As such, banks would like to predict in advance which of those clients are likely to attrite, so as to approach them with proactive marketing campaigns. Neuronets have found great application in many classification problems. Credit card attrition is a poorly investigated subtopic that poses many challenges, such as highly imbalanced datasets. The goal of this research is to construct a feed-forward neuronet that can overcome such obstacles and thus accurately classify credit card attrition. To this end, we employ a weights and structure determination (WASD) algorithm that facilitates the development of a competitive and all around robust classifier whilst accounting for the shortcomings of traditional back propagation neuronets. This is supported by the fact that when compared with some of the best performing classification models that MATLAB's classification learner app offers, the power softplus activated WASD neuronet demonstrated either superior or highly competitive performance across all metrics.

The core components of both traditional and contemporary control systems are the proportional–integral–derivative (PID) control systems, which have established themselves as standards for technical and industrial applications. Therefore, the tuning of the PID controllers is of high importance. Utilizing optimization algorithms to reduce the mean square error of the controller’s output is one approach of tuning PID controllers. In this paper, an appropriately modified metaheuristic optimization algorithm dubbed beetle antennae search (BAS) is employed for robust tuning of PID controllers. The findings of three simulated experiments on stabilizing feedback control systems show that BAS produces comparable or higher performance than three other well-known optimization algorithms while only consuming a tenth of their time.

This paper presents a dynamic model based on neutrosophic numbers and a neutrosophic logic engine. The introduced neutrosophic logic/fuzzy adaptive Zeroing Neural Network dynamic is termed NSFZNN and represents an improvement over the traditional Zeroing Neural Network (ZNN) design. The model aims to calculate the matrix pseudo-inverse and the minimum-norm least-squares solutions of time-varying linear systems. The improvement of the proposed model emerges from the advantages of neutrosophic logic over fuzzy and intuitionistic fuzzy logic in solving complex problems associated with predictions, vagueness, uncertainty, and imprecision. We use neutrosphication, de-fuzzification, and de-neutrosophication instead of fuzzification and de-fuzzification exploited so far. The basic idea is based on the known advantages of neutrosophic systems compared to fuzzy systems. Simulation examples and engineering applications on localization problems and electrical networks are presented to test the efficiency and accuracy of the proposed dynamical system.

The computation of the time-varying matrix pseudoinverse has become crucial in recent years for solving time-varying problems in engineering and science domains. This paper investigates the issue of calculating the time-varying pseudoinverse based on full-rank decomposition (FRD) using the zeroing neural network (ZNN) method, which is currently considered to be a cutting edge method for calculating the time-varying matrix pseudoinverse. As a consequence, for the first time in the literature, a new ZNN model called ZNNFRDP is introduced for time-varying pseudoinversion and it is based on FRD. FourFive numerical experiments investigate and confirm that the ZNNFRDP model performs as well as, if not better than, other well-performing ZNN models in the calculation of the time-varying pseudoinverse. Additionally, theoretical analysis and numerical findings have both supported the effectiveness of the proposed model.

The influence of neutrosophy on many fields of science and technology, as well as its numerous applications, are evident. Our motivation is to apply neutrosophy for the first time in order to improve methods for solving unconstrained optimization. Particularly, in this research, we propose and investigate an improvement of line search methods for solving unconstrained nonlinear optimization models. The improvement is based on the application of symmetry involved in neutrosophic logic in determining appropriate step size for the class of descent direction methods. Theoretical analysis is performed to show the convergence of proposed iterations under the same conditions as for the related standard iterations. Mutual comparison and analysis of generated numerical results reveal better behavior of the suggested iterations compared with analogous available iterations considering the Dolan and Moré performance profiles and statistical ranking. Statistical comparison also reveals advantages of the neutrosophic improvements of the considered line search optimization methods.

It is well known that minimum-cost portfolio insurance (MPI) is an essential investment strategy. This article presents a time-varying version of the original static MPI problem, which is thus more realistic. Then, to solve it efficiently, we propose a powerful recurrent neural network called the linear-variational-inequality primal-dual neural network (LVI-PDNN). By doing so, we overcome the drawbacks of the static approach and propose an online solution. In order to improve the performance of the standard LVI-PDNN model, an adaptive fuzzy-power LVI-PDNN (F-LVI-PDNN) model is also introduced and studied. This model combines the fuzzy control technique with LVI-PDNN. Numerical experiments and computer simulations confirm the F-LVI-PDNN model’s superiority over the LVI-PDNN model and show that our approach is a splendid option to accustomed MATLAB procedures.