Symbolic Computation of the Aluthge Transform

Kovalnogov, V. N., Fedorov, R. V., Demidov, D. A., Malyoshina, M. A., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2023). Computing quaternion matrix pseudoinverse with zeroing neural networks. Aims Mathematics, 8(10). Publisher's Version Abstract

Cao, X., Francis, A., Pu, X., Zhang, Z., Katsikis, V., Stanimirovic, P., Brajevic, I., et al. (2023). A novel recurrent neural network based online portfolio analysis for high frequency trading. Expert Systems with Applications, 233, 120934. Website Abstract

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.

Behera, R., Gerontitis, D., Stanimirović, P., Katsikis, V., Shi, Y., & Cao, X. (2023). An efficient zeroing neural network for solving time-varying nonlinear equations. Neural Computing and Applications. presented at the 2023. Publisher's Version Abstract

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 $$\root m \of {a(t)}$$.

Simos, T. E., Katsikis, V. N., Mourtas, S. D., & Stanimirović, P. S. (2023). Solving Time-Varying Nonsymmetric Algebraic Riccati Equations With Zeroing Neural Dynamics. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-13.

Abbassi, R., Jerbi, H., Kchaou, M., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2023). Towards Higher-Order Zeroing Neural Networks for Calculating Quaternion Matrix Inverse with Application to Robotic Motion Tracking. Mathematics, 11. Website Abstract

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.

Kovalnogov, V. N., Fedorov, R. V., Demidov, D. A., Malyoshina, M. A., Simos, T. E., Katsikis, V. N., Mourtas, S. D., et al. (2023). Zeroing neural networks for computing quaternion linear matrix equation with application to color restoration of images. AIMS Mathematics, 8, 14321-14339. Publisher's Version

Alharbi, H., Alshammari, O., Jerbi, H., Simos, T. E., Katsikis, V. N., Mourtas, S. D., & Sahas, R. D. (2023). A Fresnel Cosine Integral WASD Neural Network for the Classification of Employee Attrition. Mathematics, 11. Website Abstract

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.

Gerontitis, D., Mo, C., Stanimirović, P. S., Tzekis, P., & Katsikis, V. N. (2023). A novel extended Li zeroing neural network for matrix inversion. Neural Computing and Applications. presented at the 2023. Publisher's Version Abstract

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.

Zhang, D., Zhao, Y., Mosić, D., & Katsikis, V. N. (2023). Exact expressions for the Drazin inverse of anti-triangular matrices. Journal of Computational and Applied Mathematics, 428, 115187. Website Abstract

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.

Mourtas, S. D., Stanimirovic, P. S., & Katsikis, V. N. (2023).

A neutrosophic adaptive recurrent neural network for time-varying matrix inversion Publisher's Version

. European Proceedings of Computers and Technology. HMMOCS 2022 International Workshop "Hybrid methods of modeling and optimization in complex systems.

Vasilios Katsikis

Professor, Economics

Symbolic Computation of the Aluthge Transform

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