An iterative algorithm for approximating the sign function of tensors with the einstein product

Alolyan, I., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2026). Pseudoinversion through an Innovative Finite-time Neutrosophic Logic activated Zeroing Neural Network: Applications to Robotic Motion Tracking. Journal of Computational and Applied Mathematics, 117695. Website Abstract

In recent years, the computation of the time-varying matrix (TVM) Moore–Penrose inverse, or pseudoinverse, has become increasingly important for addressing dynamic problems across various fields, including engineering, physics, and computer science. This work explores the application of the zeroing neural network (ZNN) methodology, a state-of-the-art technique, to efficiently compute the TVM pseudoinverse. A novel ZNN model is proposed for this purpose, representing the first such contribution in the literature. Its effectiveness is benchmarked against a widely adopted ZNN framework. Furthermore, the study introduces a high-performance finite-time neutrosophic logic/fuzzy adaptive activation function, derived from the commonly used sign-bi-power nonlinear activation function, and provides an in-depth investigation of its properties and advantages. Through three illustrative comparative numerical simulations and a real-world robotic motion tracking application, the proposed model and activation function demonstrate outstanding effectiveness in solving the TVM pseudoinversion problem for arbitrary-dimensional matrices.

Cao, X., Yang, Y., Li, S., & Katsikis, V. N. (2026). A Novel Stock Investment Strategy Based on Distributed k-WTA Dynamic Neural Network. Neural Networks, 108866. Website Abstract

This study addresses the problem of stock investment strategy, aiming to select the optimal k (k < n) stocks from a set of n stocks within a distributed topology to maximize investment returns. To this end, we propose a dynamic and adaptive neural network model based on the distributed k-winner-take-all (k-WTA) protocol. Firstly, we reformulate the k-WTA problem as a constrained quadratic programming problem and utilize the Sigmoid activation function to relax equality and inequality constraints. Secondly, by combining the simplified constraints with the graph-based topology of stock interactions, we construct a Lagrangian function and develop a time-evolving dynamic neural network whose neuron states update continuously until convergence, reflecting temporal adaptability and convergence dynamics. Unlike traditional centralized methods, the proposed network allows each stock node to communicate only with its connected neighbors, ensuring decentralized computation and scalability. We further present the hardware implementation and theoretically prove the model’s stability and convergence under connected graph topologies. Experiments include six static-input tests (different stock counts, parameters, and Gaussian noise) and dynamic validation using real-world stock data from 30 assets over 50 trading days. All seven experimental results confirm the feasibility, effectiveness, and robustness of the proposed model. Comparative analysis with existing WTA models also demonstrates superior adaptability and convergence performance.

Jerbi, H., Alateeq, A., Abbassi, R., Kchaou, M., Simos, T. E., Mourtas, S. D., Giannakopoulos, O. V., et al. (2026). Inflation Rate Prediction Using a Power-Activation Neural Network With Weight and Structure Determination. Mathematical Methods in the Applied Sciences, n/a(n/a). presented at the 2026, John Wiley & Sons, Ltd. Publisher's Version Abstract

ABSTRACT Inflation, defined as the trend of the continuous increasing of the general level of prices within a country's economy during a time period, affects both the private and public sectors of the economy. Policy makers have the need to control and stabilize the rate of inflation at low levels to achieve economic growth and prosperity. Particularly, they use the rate of inflation as a measure to diagnose economic problems and then to apply the corresponding macroeconomic policies. So, inflation rate forecasting must be accurate, and the measurement of the inflation rate, which is usually dependent on the consumer price index (CPI), should be as accurate as possible. Although there are many different ways to anticipate the CPI, the most accurate methods are those that use artificial neural network models. These methods usually outperform the traditional statistical-based forecasting techniques. This study spans the period from January 2015 to December 2024 using monthly, non-seasonally adjusted data from the Organization for Economic Co-operation and Development (OECD). Since WASD (weights and structure determination) neural networks have been demonstrated to address the drawbacks of traditional back-propagation neural networks, like poor training speed and local minimum, a three-layer power-activation WASD neural network model, termed WASDCPI, is taken into consideration. The WASDCPI model performs better than other well-known machine learning techniques for predicting the CPI of countries, including the USA, UK, Germany, France, India, Switzerland, Korea, and the Slovak Republic. All the data analysis is being conducted using the MATLAB environment.

Xue, Q., Wu, C., Nie, J., Zhou, S., Liu, H., & Katsikis, V. N. (2026). An improved multi-objective animated oat optimization algorithm for resource-constrained construction project organization design. Scientific Reports . presented at the 2026. Publisher's Version Abstract

Global urbanization has promoted to an increasing scale of construction projects, thereby making the optimization of construction project organization design a critical task in engineering management. However, conventional methods relying on empirical decision-making suffer from issues like low resource allocation efficiency, many difficulties in coordinating multi-objective conflicts and insufficient dynamic adjustment capabilities. To address these issues, we propose the first multi-objective extension of the Animated Oat Optimization algorithm (MOAOO), which represents a pioneering contribution in transforming the single-objective AOO into a multi-objective optimizer for construction project organization design. The developed algorithm fundamentally extends the biological mechanism of Animated Oat Optimization introducing several key innovations: (a) a novel hybrid position update rule combining Elite Reference Points and stochastic perturbations to prevent premature convergence; (b) an innovative three-layer constraint processing mechanism ensuring the generation of feasible solutions; and (c) a dual-threshold convergence monitoring system for early termination. Notably, we establish MOAOO as the inaugural multi-objective variant of AOO, integrating dynamic elite retention strategies, non-dominated sorting, and dynamic archive mechanisms to enable effective collaborative optimization of three conflicting goals. Enough experiments on ZDT test functions demonstrate that the designed MOAOO method shows competitive performance compared to advanced algorithms such as Pre-DEMO, MOEA/D-OED, and Pi-MOEA in terms of hypervolume inverted generational distance and the Spacing metrics. The indicator is improved in certain configurations. In an engineering case study, MOAOO reduces resource fluctuation by 72.7% in the compromise solution while achieving a balanced duration (279 days) and cost ($1.34 M). Moreover, the proposed algorithm converges in 118 iterations on average, thereby verifying its practical value in construction scheduling.

Kansal, M., Katsikis, V., & Sharma, P. (2026). An iterative algorithm for approximating the sign function of tensors with the einstein product. Quaestiones Mathematicae, 1–24. Taylor & Francis. Website

Jerbi, H., Aoun, S. B., Abbassi, R., Kchaou, M., Simos, T. E., Mourtas, S. D., Katsikis, V. N., et al. (2026). An innovative neutrosophic logic adaptive high-order zeroing neural network for solving linear matrix equations: Applications to acoustic source tracking. Journal of Computational and Applied Mathematics, 475, 117058. Publisher's Version Abstract

Scholars have put a lot of emphasis on time-varying linear matrix equations (LMEs) problems because of its importance in science and engineering. The problem of determining the time-varying LME’s minimum-norm least-squares solution (MLLE) is therefore tackled in this work. This is achieved by the use of NHZNN, a recently developed neutrosophic logic/fuzzy adaptive high-order zeroing neural network technique. The NHZNN is an advancement on the conventional zeroing neural network (ZNN) technique, which has shown great promise in solving time-varying tasks. To address the MLLE task for arbitrary-dimensional time-varying matrices, three novel ZNN models are presented. The models perform exceptionally well, as demonstrated by two simulation studies and two real-world applications to acoustic source tracking.

Cao, X., Yang, Y., Li, S., Katsikis, V. N., & Stanimirović, P. S. (2025). A novel competition model for dynamic winner-take-all. International Journal of Systems Science, 1–23. Taylor & Francis. Website

Khan, A. H., Cao, X., Luo, C., Zhang, S., Guo, W., Katsikis, V. N., & Li, S. (2025). Spiking Neural Networks: A Comprehensive Survey of Training Methodologies, Hardware Implementations and Applications. Artificial Intelligence Science and Engineering, IEEEXplore, 1, 175-207.

Cao, X., Yang, Y., Li, S., & Katsikis, V. N. (2025). k-Winner-Take-All Competition Based on Novel Dynamic Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-11.

Gupta, R., Bartolucci, F., Katsikis, V. N., & Patnaik, S. (2025). Recent Developments in Computational Finance and Business Analytics: Proceedings of the 3rd International Conference on Computational Finance and Business Analytics. Learning and Analytics in Intelligent Systems. Springer. Website

Vasilios Katsikis

Professor, Economics

An iterative algorithm for approximating the sign function of tensors with the einstein product

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