Natural language programming of robotic systems presents significant challenges in bridging high-level intent with low-level motion planning, particularly for redundant manipulators in artistic or spatially constrained tasks. We present \textbf{BeetleBrush}, a novel LLM-powered robotic drawing framework that combines large-scale language understanding with bio-inspired optimization for trajectory execution. Natural language prompts are processed using Google Gemini 2.5 Flash within a Retrieval-Augmented Generation (RAG) system enhanced by a curated database of over 200 drawing examples. The resulting stroke sequences are translated into target end-effector trajectories, which are executed using a 7-DOF KUKA manipulator through an enhanced Beetle Antennae Search (BAS) algorithm operating in forward kinematics space-circumventing the need for analytical inverse kinematics. Our system achieves accurate, safe, and expressive robot drawings with real-time performance and high workspace compliance. Across 12 representative prompts of varying complexity, BeetleBrush achieved mean end-effector errors of 0.0048–0.0051 meters and RMSE values below 0.0051 meters in most cases, with maximum errors under 0.0173 meters. The system also exhibited stable convergence behavior and successfully executed 94.4\% of strokes across tasks, including geometrically constrained figures like cubes, cones, and composite scenes. BeetleBrush demonstrates how LLM-guided generation and bio-inspired control can be effectively integrated for robust, intuitive, and geometry-aware robot programming.

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.

Discrete-form time-dependent quadratic programming (DF-TDQP) problem, as a type of time-dependent problems, is prevalent in science and engineering. Currently, there are many studies on the discretization of continuous time-dependent problems despite the fact that researchers have made different breakthroughs using recurrent neural networks (RNNs) in dealing with discrete-form time-dependent problems, relatively limited research has been devoted to the direct discretization approach. To solve the DF-TDQP problem, a novel direct discretization approach is introduced. Based on this approach, the corresponding discrete-form recurrent neurodynamics (DFRN) model is developed. Furthermore, on this basis, a novel enhanced discrete-form recurrent neurodynamics (E-DFRN) model is further established to obtain high-accuracy optimal solutions for such DF-TDQP problems. The accuracy and convergence of both the DFRN model and E-DFRN model are explained through theoretical analysis, and their effectiveness and superiority are validated based on numerical experiments. Finally, the applicability of these models to the tracking tasks of planar manipulators is verified.

Recurrent neural network (RNN) is a neurodynamic method designed to tackle time-varying problems in various technical domains, which are widely derived from scientific research and practical applications. It should be noted that traditional models often lack an effective capability to suppress nonlinear time-varying noise during the design process, and thus may encounter many difficulties in practical applications. This article presents a novel RNN model for solving the continuous time-varying matrix pseudoinverse, which has a significant characteristic of double integral-reinforcing (DIR) term and is termed DIR continuous-time RNN (DIR-CT-RNN) model. Correspondingly, using the discretization formula, a DIR discrete-time RNN (DIR-DT-RNN) is presented for solving the discrete time-varying matrix pseudoinverse. The theoretical results present that the DIR-DT-RNN model converges toward the theoretical solution under the discrete time-unvarying constant (DTU-C) noise or discrete time-varying linear (DTV-L) noise interference. Under the discrete time-varying quadratic (DTV-Q) noise interference, the proposed model converges to a constant that relates to the design parameters. In addition, simulation results, including an application for trajectory tracking of three-link robotic manipulator, which come from practical engineering background, verify the effectiveness and superiority of DIR-DT-RNN model for solving the time-varying matrix pseudoinverse under various types of noise interference.

ABSTRACT The zeroing neural network (ZNN), a canonical recurrent neural network, was developed in previous studies to address time‐varying problem‐solving scenarios. Numerous practical applications involve time‐varying linear equations and inequality systems that demand real‐time solutions. This article proposes a ZNN model specifically designed to solve such time‐varying linear systems. Innovatively, it incorporates a new non‐negative slack variable that transforms complex time‐varying inequality systems into more easily solvable time‐varying equation systems. By using an exponential decay formula and establishing an indefinite error function, the ZNN model is built. The suggested ZNN model's convergence properties are validated by theoretical research. Results from comparative simulations further support the superiority and effectiveness of the ZNN model in resolving inequality systems and time‐varying linear equations.

ABSTRACT This paper proposes a robust dual‐integral structure zeroing neural network (ZNN) design framework, effectively overcoming the limitations of existing single‐integral enhanced ZNN models in completely suppressing linear noise. Based on this design framework, a complex‐type dual‐integral structure ZNN (DISZNN) model with inherent linear noise suppression capability is constructed for computing dynamic complex matrix inversion (DCMI) online. The stability, convergence, and robustness of the proposed DISZNN model are ensured via rigorous theoretical analyses. In three distinct experiments involving DCMI (including cases with only imaginary parts, both real and imaginary parts, and high‐dimensional scenarios), the state trajectories of the DISZNN model are well and quickly fitted to the dynamic trajectories of the theoretical solutions with very low residual errors in various linear noise environments. More specifically, the residual errors of the DISZNN model for online computation of DCMI under linear noise environments are consistently below the order of , representing one‐thousandth of the residual errors in existing noise‐tolerant ZNN models. Finally, the DISZNN design framework is applied to construct a controlled chaotic system of a permanent magnet synchronous motor (PMSM) with uncertainties and external disturbances based on real‐world modeling. Experimental results demonstrate that the three state errors of the controlled PMSM chaotic system converge to zero quickly and stably under various conditions (system parameters, external disturbances, and uncertainties), further highlighting the superiority and generalizability of the DISZNN design framework.

Real-time online optimisation plays a crucial role in high-frequency trading (HFT) strategies. The Markowitz model, as a Nobel Prize-winning framework, is widely used for portfolio management optimisation by framing the problem as a constrained quadratic programming task. While conventional analytical methods are typically effective for solving quadratic programming problems with linear constraints, the introduction of both linear equality and inequality constraints in the Markowitz model necessitates the use of numerical methods. The complexity of these numerical solutions presents technical challenges for real-time online optimisation, especially in HFT environments where computational speed and efficiency are critical. To address this challenge, we propose a simplified model that decomposes the problem into analytically solvable and unsolvable components, alongside an innovative dynamic neural network designed to quickly solve the unsolvable components. Overall, this method helps reduce computational load and is well-suited for real-time online computations in HFT settings. Furthermore, we conducted a theoretical analysis and proof of the optimality and global convergence of the solutions obtained using this method. Finally, based on a large set of real stock data, we performed three numerical experiments to validate its effectiveness. Notably, in an experiment using Dow Jones Industrial Average (DJIA) stock data, our approach reduced total costs by 5.54% compared to the commonly used MATLAB quadprog() solver, demonstrating the potential of this method as an efficient tool for portfolio management in HFT scenarios.

Discrete time-variant equation systems represent a typical and complex problem across various disciplines. With the increasing complexity of systems in various fields, traditional methods have been unable to effectively deal with the current discrete time-variant equation systems, especially in the dynamic engineering problem. Generally speaking, traditional methods are typically limited to considering discrete time-variant equation systems in ideal state, and there is a lack of deep research about more intricate disturbance states. This paper introduces a new recurrent neural network (RNN) algorithm, termed the discrete-time double-integration-enhanced RNN (DT-DIE-RNN) algorithm, for handling discrete time-variant equation systems (including discrete time-variant linear and nonlinear equation system) under discrete square-time-variant disturbance. Firstly, the continuous-time double-integration-enhanced RNN (CT-DIE-RNN) algorithm is presented for solving discrete time-variant linear and nonlinear equation systems by using double-integral-type error function. Secondly, the corresponding discrete-time RNN algorithm is presented, and the convergence and precision of such an algorithm are theoretically analyzed. Finally, the effectiveness and superiority of the proposed DT-DIE-RNN algorithm for solving discrete time-variant linear and nonlinear equation systems are supported by comparative numerical experiments, and these theoretical results are further verified by robot manipulator applications.Note to Practitioners—Generally speaking, previous algorithms are unable to guarantee the operation of robot manipulator stably with discrete square-time-variant disturbance. In this study, we design a new RNN algorithm which possesses stronger anti-disturbance capability for solving discrete time-variant equation systems, and such the algorithm is applied to the tracking control of robot manipulator. In the discrete-time environment, in order to solve the discrete time-variant problem smoothly and stably, it is necessary to ensure that the error in each time period is within an acceptable range. The basic guidelines of this paper are as follows. First of all, a double-integration RNN algorithm is constructed, i.e., discrete-time double-integration-enhanced RNN (DT-DIE-RNN) algorithm. Then the effectiveness and superiority of the DT-DIE-RNN algorithm are verified by numerical experiment and engineering simulation, respectively. In summary, the proposed RNN algorithm can be seen as a new breakthrough in the research field of discrete-time RNN algorithm.

With the rapid development of the multi-robot systems, formation control has become a fundamental challenge. Traditional approaches focus mainly on the design of control algorithms to realize specific formation patterns, while neglecting how to determine the desired formation. In this paper, the optimal formation problem based on shape theory is reformulated as a convex optimization problem. A predetermined time convergent zeroing neural dynamics (PDTZND) approach, derived from zeroing neural networks (ZNN), is proposed to efficiently solve this problem. The PDTZND approach ensures that the system error converges in a strict and predetermined time, which provides an efficient, accurate solution for optimal formation. In addition, the convergence of the proposed approach is rigorously analyzed by means of Lyapunov theory, and its validity and superiority are verified by numerical simulations and physical experiments.

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.

This paper reports on the experience collecting a number of corpora of Nordic languages spoken by children. The aim of the data collection is providing annotated data to develop and evaluate computer assisted pronunciation assessment systems both for non-native children learning a Nordic language (L2) and for L1 children with speech sound disorder (SSD). The paper presents the challenges encountered recording and annotating data for Finnish, Swedish and Norwegian, as well as the ethical considerations related with making this data publicly available. We hope that sharing this experience will encourage others to collect similar data for other languages. Of the different data collections, we were able to make the Norwegian corpus publicly available in the hope that it will serve as a reference in pronunciation assessment research.

Portfolio analysis is a crucial subject within modern finance. However, the classical Markowitz model, which was awarded the Nobel Prize in Economics in 1991, faces new challenges in contemporary financial environments. Specifically, it fails to consider transaction costs and cardinality constraints, which have become increasingly critical factors, particularly in the era of high-frequency trading. To address these limitations, this research is motivated by the successful application of machine learning tools in various engineering disciplines. In this work, three novel dynamic neural networks are proposed to tackle nonconvex portfolio optimization under the presence of transaction costs and cardinality constraints. The neural dynamics are intentionally designed to exploit the structural characteristics of the problem, and the proposed models are rigorously proven to achieve global convergence. To validate their effectiveness, experimental analysis is conducted using real stock market data of companies listed in the Dow Jones Index (DJI), covering the period from November 8, 2021 to November 8, 2022, encompassing an entire year. The results demonstrate the efficacy of the proposed methods. Notably, the proposed model achieves a substantial reduction in costs (which combines investment risk and reward) by as much as 56.71% compared with portfolios that are averagely selected.

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.

Data augmentation is a technique which enhances the size and quality of training data such that deep learning or machine learning models can achieve better performance. This paper proposes a novel way of applying data augmentation for child speech recognition in the low data resource scenario. Data augmentation is achieved by modifying existing adult speech signals. The procedure consists of two main parts, resampling, and time scaling. The experiment involves both speech from children aged from kindergarten to grade 10, and adults’ speech. We test the proposed method using both a TDNN-HMM and a GMM-HMM acoustic model. The results show that the proposed data augmentation scheme achieves a relative 7.95% reduction of WERs compared with 4.56% relative reduction when using a traditional bilinear frequency warping approach.

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 Markowitz model, a portfolio analysis model that won the Nobel Prize, lays the theoretical groundwork for modern finance. The transaction cost and the cardinality restriction, which were not covered in Markowitz model, are becoming increasingly important with the advent of high-frequency trading era. However, it remains a challenging problem to consider those constraints due to the nonconvex nature of the problem. A novel dynamic neural network, inspired by its successes in machine learning, is developed to tackle this difficult issue. Theoretical analysis is provided for the convergence of the designed neural network. Experimental results using real stock market data confirm the effectiveness of the proposed model. With the proposed model, the cost function characterizing the overall risks, and rewards is reduced by 123.6% from$-4.549\times 10^{-5}$to$-1.0173\times 10^{-4}$. This indicates that the proposed strategy is successful in reducing risks and increasing rewards.

In this article, we computationally model the social behavior of beetles and apply it to the tracking control of manipulators. The beetles demonstrate excellent skills to forage food in a previously unknown environment by merely using their olfactory senses. The goal of the beetle is to search the region with the maximum smell. Therefore, the actions of the beetle can be characterized as an optimization algorithm. This article mathematically models this behavior in the form of a recurrent neural network (RNN) with a temporal-feedback connection. We apply the formulated RNN controller for the redundancy resolution and tracking control of the redundant manipulators with an unknown kinematic model. Most of the industrial robots have redundant manipulators, and kinematic trajectory tracking is a fundamental problem for any industrial task. The behavior of the beetle allows us to formulate a position-level controller without relying on the manipulation of the Jacobian matrix. It is in contrast with the conventional velocity-level controllers, which require an accurate kinematic model of the manipulator and calculation of pseudoinverse of Jacobian, a computationally expensive task. The proposed algorithm, called Beetle Antennae Olfactory Recurrent Neural Network (BAORNN) algorithm, is capable of driving the manipulator by only using the feedback from the position and orientation sensors. The stability and convergence of the proposed algorithm are theoretically proved, and the simulations results using a seven-degree-of-freedom (DOF) industrial robotic arm, KUKA LBR IIWA14, are presented to demonstrate the performance of the proposed algorithm.

Nowadays, industrial redundant manipulators have been playing important roles in manufacturing fields, such as welding and assembling, by performing repetitive and dull work. Such long-term industrial operations usually require redundant manipulators to keep good working conditions and maintain steadiness of joint actuation. However, some joints of redundant manipulators may fall into fault status after enduring long-period heavy manipulations, causing that the desired industrial tasks cannot be accomplished accurately. In this article, we propose a novel fault-tolerant method with simultaneous fault-diagnose function for motion planning and control of industrial redundant manipulators. The proposed approach is able to adaptively localize which joints run away from the normal state to be fault, and it can guarantee to finish the desired path tracking control even when these fault joints lose their velocity to actuate. Simulation and experiment results on a Kuka LBR iiwa manipulator demonstrate the efficiency of the proposed fault-tolerant method for motion control of the redundant manipulator.