A heuristic process on the existence of positive bases with applications to minimum-cost portfolio insurance in C [a, b]

Mourtas, S. D., Li, S., Cao, X., Liao, B., & Katsikis, V. N. (2025). Current Trends and Challenges in Applying Metaheuristics to the Innovative Area of Weight and Structure Determination Neuronets. Inventions, 10. Website Abstract

The weights and structure determination (WASD) neuronet (or neural network) is a single-hidden-layer feedforward neuronet that exhibits an excellent approximation ability, despite its simple structure. Thanks to its strong generalization, fast speed, and ease of implementation, the WASD neuronet has been the subject of many modifications, including metaheuristics, and applications in a wide range of scientific fields. As it has garnered significant attention in the last decade, the aim of this study is to provide an extensive overview of the WASD framework. Furthermore, the WASD has been effectively used in numerous real-time learning tasks like regression, multiclass classification, and binary classification due to its exceptional performance. In addition, we present WASD’s applications in social science, business, engineering, economics, and medicine. We aim to report these developments and provide some avenues for further research.

He, Y., Wang, X., Tie, Y., Yang, H., Simos, T. E., Mourtas, S. D., & Katsikis, V. N. (2025). Solving Lur'e equations through zeroing neural networks. Information Sciences, 718, 122418. Website Abstract

Solving Lur'e equations plays a critical role in addressing linear-quadratic optimal control (LQOC) problems, especially in cases where the control cost matrices are singular. This paper introduces, for the first time, two novel zeroing neural network (ZNN) models—ZNNLE and ZNNLE-LQOC—specifically designed to solve the Lur'e equation system and the LQOC problem, respectively. The proposed models extend the applicability of the ZNN methodology to these challenging scenarios by offering robust and efficient solutions to time-varying matrix equations. Theoretical analyses confirm the validity of both models, while numerical simulations and practical applications demonstrate their effectiveness. Moreover, a comparative study with an enhanced alternating-direction implicit (ADI) method highlights the superior performance of the ZNNLE-LQOC model in solving LQOC problems.

Katsikis, V. N., Liao, B., & Hua, C. (2025). Survey of Neurodynamic Methods for Control and Computation in Multi-Agent Systems. Symmetry, 17. Website Abstract

Neurodynamics is recognized as a powerful tool for addressing various problems in engineering, control, and intelligent systems. Over the past decade, neurodynamics-based methods and models have been rapidly developed, particularly in emerging areas such as neural computation and multi-agent systems. In this paper, we provide a brief survey of neurodynamics applied to computation and multi-agent systems. Specifically, we highlight key models and approaches related to time-varying computation, as well as cooperative and competitive behaviors in multi-agent systems. Furthermore, we discuss current challenges, potential opportunities, and promising future directions in this evolving field.

Yang, Y., Wu, P., Katsikis, V. N., Li, S., & Feng, W. (2025). A novel real-time noise-resilient zeroing neural network and its applications to matrix problem solving. Mathematics and Computers in Simulation. Website Abstract

Given the critical role of zeroing neural networks (ZNN) in various fields and the practical demand for models in effectively resisting real-time noise, this study introduces a novel anti-noise integral zeroing neural network (AN-IZNN) model alongside its enhanced counterpart (EAN-IZNN), for the applications of matrix problem solving. Theoretical analysis demonstrates their ability to achieve convergence even under different noise conditions. Both theoretical analyses and simulation validations highlight the superior performance of the proposed models over existing neural network models. Notably, the root mean square error of the proposed AN-IZNN and EAN-IZNN models is reduced by 92.6249% and 91.4178%, respectively, compared to scenarios without the proposed method, demonstrating the effectiveness of the solution.

Cao, X., Yang, Y., Li, S., Stanimirović, P. S., & Katsikis, V. N. (2025). Artificial Neural Dynamics for Portfolio Allocation: An Optimization Perspective. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 1-12.

Recent advancements in computational finance and business analytics. (Proceedings – ICCFBA-2024). (2024). Recent advancements in computational finance and business analytics. (Proceedings – ICCFBA-2024). (R. Gupta, Bartolucci, F., Katsikis, V. N., & Patnaik, S., Eds.) (2024th ed., pp. 616). Cham, Switzerland: Springer International Publishing. Publisher's Version

Katsikis, V. N., Mourtas, S. D., Sahas, R., & Balios, D. (2024). A Weights Direct Determination Neural Network for Credit Card Attrition Analysis. In L. A. Maglaras, Das, S., Tripathy, N., & Patnaik, S. (Eds.), Machine Learning Approaches in Financial Analytics (pp. 325–346). Cham: Springer Nature Switzerland. Website Abstract

Cost reduction is a component that contributes to both the profitability and longevity of a corporation, especially in the case of a financial institution, and can be accomplished through greater client retention. Particularly, credit card customers comprise a volatile subset of a bank's 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. Credit card attrition is generally a poorly investigated subtopic with a variety of challenges, like highly imbalanced datasets. This article utilizes neural networks to address the challenges of credit card attrition since they have found great application in many classification problems. More particularly, to overcome the shortcomings of traditional back propagation neural networks, we construct a multi-input trigonometrically activated weights and structure determination (MTA-WASD) neural network which incorporates structure trimming as well as other techniques that boost its training speed as well as diminish the danger and the subsequent detrimental effects of overfitting. When applied to three publicly available datasets, the MTA-WASD neural network demonstrated either superior or highly competitive performance across all metrics, compared to some of the best-performing classification models that MATLAB's classification learner app offers.

Cao, X., Li, S., Katsikis, V., Khan, A. T., He, H., Liu, Z., Zhang, L., et al. (2024). Empowering financial futures: Large language models in the modern financial landscape. EAI Endorsed Transactions on AI and Robotics, 3. presented at the Jul. Website

Stanimirović, P. S., Mourtas, S. D., Mosić, D., Katsikis, V. N., Cao, X., & Li, S. (2024). A Zeroing Neural Network Approach for Calculating Time-Varying G-Outer Inverse of Arbitrary Matrix. IEEE Transactions on Neural Networks and Learning Systems, 1-10.

Balios, D., Katsikis, V. N., Naoum, V. C., & Zaroulea, T. (2024). The effect of industry level characteristics and cross-country differences on earnings management: A European comparative perspective. Journal of Governance & Regulation, 13(2), 403-418. Publisher's Version

Vasilios Katsikis

Professor, Economics

A heuristic process on the existence of positive bases with applications to minimum-cost portfolio insurance in C [a, b]

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