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.

The efficient calculation of the time-varying matrix (TVM) pseudoinverse, or Moore–Penrose inverse, is a fundamental requirement for solving dynamic problems in diverse fields. To address this issue, this research proposes a novel zeroing neural network model, termed ZMPC, that is specifically designed for TVM pseudoinverse computation. The ZMPC model, in contrast to traditional frameworks, simultaneously enforces all four Penrose equations to ensure that the computed solution remains the unique TVM pseudoinverse with improved tracking accuracy and reduced computational load. Another significant theoretical contribution of this research is the integration of a novel finite-time noise-resilient adaptive activation function (NAF), which uses neutrosophic logic principles to enhance convergence and robustness. To evaluate these developments, the proposed NAF-based ZMPC framework is compared with state-of-the-art formulations through three numerical examples and a practical mobile object localization task. The results demonstrate that the proposed framework achieves improved effectiveness, consistent finite-time convergence, and high noise robustness across arbitrary matrix dimensions, outperforming prevalent methodologies in TVM pseudoinversion.

Calculation of the time-varying (TV) matrix generalized inverse has grown into an essential tool in many fields, such as computer science, physics, engineering, and mathematics, in order to tackle TV challenges. This work investigates the challenge of finding a TV extension of a subclass of inner inverses on real matrices, known as generalized-outer (G-outer) inverses. More precisely, our goal is to construct TV G-outer inverses (TV-GOIs) by utilizing the zeroing neural network (ZNN) process, which is presently thought to be a state-of-the-art solution to tackling TV matrix challenges. Using known advantages of ZNN dynamic systems, a novel ZNN model, called ZNNGOI, is presented in the literature for the first time in order to compute TV-GOIs. The ZNNGOI performs excellently in performed numerical simulations and an application on addressing localization problems. In terms of solving linear TV matrix equations, its performance is comparable to that of the standard ZNN model for computing the pseudoinverse.

Thek-winner-takes-all (k-WTA) problem involves selecting the topkagents with the highest inputs from a set ofncandidates. This problem plays a fundamental role in modeling competitive behaviors in social systems and economic environments. In this article, we propose a structurally simplified dynamic neural network to solve thek-WTA problem efficiently. The originalk-WTA task is first reformulated as a constrained quadratic programming (QP) problem. A smooth sigmoid function is then introduced to encode inequality constraints implicitly, simplifying the representation. Based on this formulation, we develop a continuous-time neural dynamic model capable of solving the problem in real time. The proposed model is theoretically proven to achieve global convergence and optimality with respect to thek-WTA solution. Extensive numerical experiments, including tests on real-world data, validate the effectiveness of the proposed approach, demonstrating fast convergence, robustness, and practical applicability.

Real-time high-frequency trading poses a significant challenge to the classical portfolio allocation problem, demanding rapid computational efficiency for constructing Markowitz model-based portfolios. Building on the principles of arbitrage pricing theory (APT), this study introduces a dynamic neural network model aimed at minimizing investment risk, optimizing portfolio allocation within predefined constraints, and maximizing returns. First, a convex optimization objective function incorporating risk constraints is formulated based on APT principles. This is followed by the introduction of a novel dynamic neural network model designed to solve the convex optimization problem, accompanied by comprehensive theoretical analysis and rigorous proofs. The study uses two distinct datasets sourced from Yahoo Finance, consisting of 30 selected stocks, covering a span of 250 valid trading days to validate the proposed methodology. The results of 30 different stock market scenario experiments indicate that, when the upper limit for investment risk is set at$3.285 \times 10^{-4}$, the expected maximum investment return exceeds the Dow Jones Industrial Average (DJIA) index by 16.2816%. These empirical findings highlight the viability, stability, and efficacy of the proposed approach and framework, demonstrating its potential applicability for real-time, high-frequency trading scenarios. Furthermore, the outcomes suggest policy implications for risk management and portfolio optimization in dynamic financial environments.

High-frequency trading proposes new challenges to classical portfolio selection problems. Especially, the timely and accurate solution of portfolios is highly demanded in financial market nowadays. This article makes progress along this direction by proposing novel neural networks with softmax equalization to address the problem. To the best of our knowledge, this is the first time that softmax technique is used to deal with equation constraints in portfolio selections. Theoretical analysis shows that the proposed method is globally convergent to the optimum of the optimization formulation of portfolio selection. Experiments based on real stock data verify the effectiveness of the proposed solution. It is worth mentioning that the two proposed models achieve 5.50% and 5.47% less cost, respectively, than the solution obtained by using MATLAB dedicated solvers, which demonstrates the superiority of the proposed strategies.

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.

The problem of solving algebraic Riccati equations (AREs) and certain linear matrix equations which arise from the ARE frequently occur in applied and pure mathematics, science, and engineering applications. In this article, by considering the nonsymmetric ARE (NARE) as a general form of ARE, the time-varying NARE (TV-NARE) problem is proposed and investigated. As a particular case of TV-NARE, the time-invariant NARE (TI-NARE) problem is investigated too. Then, by employing the zeroing (or Zhang) neural dynamics (ZND) design, a ZND TV-NARE (ZNDTV-NARE) model and a ZND TI-NARE (ZNDTI-NARE) model are proposed and investigated. Also, by combining the ZNDTV-NARE model with the frozen-time Riccati equation (FTRE) approach to optimal control of linear time-varying (LTV) systems based on the state-dependent Riccati equation (SDRE) process, a hybrid ZND FTRE control (HZND-FTREC) model is developed and investigated. The effectiveness of the proposed dynamical systems is proven in ten numerical experiments, three of which include applications to LTV and nonlinear systems.

A correlation between fuzzy logic systems (FLS) and zeroing neural networks (ZNN) design is investigated. It is shown that the gain parameter included in ZNN design can be dynamically adjusted over time by means of an appropriate value derived as the output of a properly defined FLS, which includes appropriately defined membership functions and fuzzy logic rules. Dynamical systems which are applicable to time-varying rank-deficient matrices are proposed. Convergence properties are investigated and illustrative simulation experiments are performed. Presented simulation experiments confirm the superiority of the FLS proposed in this article with respect to previously proposed FLS for dynamic adjustment of gain parameters. Furthermore, the superiority of the FLS-based ZNN model over the corresponding ZNN models based on the classical approach in defining the varying-gain parameter is demonstrated.

The problem of solving linear equations is considered as one of the fundamental problems commonly encountered in science and engineering. In this article, the complex-valued time-varying linear matrix equation (CVTV-LME) problem is investigated. Then, by employing a complex-valued, time-varying QR (CVTVQR) decomposition, the zeroing neural network (ZNN) method, equivalent transformations, Kronecker product, and vectorization techniques, we propose and study a CVTVQR decomposition-based linear matrix equation (CVTVQR-LME) model. In addition to the usage of the QR decomposition, the further advantage of the CVTVQR-LME model is reflected in the fact that it can handle a linear system with square or rectangular coefficient matrix in both the matrix and vector cases. Its efficacy in solving the CVTV-LME problems have been tested in a variety of numerical simulations as well as in two applications, one in robotic motion tracking and the other in angle-of-arrival localization.