In this article, the discrete-form time-variant multi-augmented Sylvester matrix problems, including discrete-form time-variant multi-augmented Sylvester matrix equation (MASME) and discrete-form time-variant multi-augmented Sylvester matrix inequality (MASMI), are formulated first. In order to solve the above-mentioned problems, in continuous time-variant environment, aided with the Kronecker product and vectorization techniques, the multi-augmented Sylvester matrix problems are transformed into simple linear matrix problems, which can be solved by using the proposed discrete-time recurrent neural network (RNN) models. Second, the theoretical analyses and comparisons on the computational performance of the recently developed discretization formulas are presented. Based on these theoretical results, a five-instant discretization formula with superior property is leveraged to establish the corresponding discrete-time RNN (DTRNN) models for solving the discrete-form time-variant MASME and discrete-form time-variant MASMI, respectively. Note that these DTRNN models are zero stable, consistent, and convergent with satisfied precision. Furthermore, illustrative numerical experiments are given to substantiate the excellent performance of the proposed DTRNN models for solving discrete-form time-variant multi-augmented Sylvester matrix problems. In addition, an application of robot manipulator further extends the theoretical research and physical realizability of RNN methods.

In this article, a robust $k$ -winner-take-all ( $k$ -WTA) neural network employing the saturation-allowed activation functions is designed and investigated to perform a $k$ -WTA operation, and is shown to possess enhanced robustness to disturbance compared to existing $k$ -WTA neural networks. Global convergence and robustness of the proposed $k$ -WTA neural network are demonstrated through analysis and simulations. An application studied in detail is competitive multiagent coordination and dynamic task allocation, in which $k$ active agents [among $m~(m > k)$ ] are allocated to execute a tracking task with the static $m-k$ ones. This is implemented by adopting a distributed $k$ -WTA network with limited communication, aided with a consensus filter. Simulation results demonstrating the system’s efficacy and feasibility are presented.

Controlling and processing of time-variant problem is universal in the fields of engineering and science, and the discrete-time recurrent neural network (RNN) model has been proven as an effective method for handling a variety of discrete time-variant problems. However, such model usually originates from the discretization research of continuous time-variant problem, and there is little research on the direct discretization method. To address the aforementioned problem, this article introduces a novel discrete-time RNN model for solving the discrete time-variant problem in a pioneering manner. Specifically, a discrete time-variant nonlinear system, which originates from the mathematical modeling of serial robot manipulator, is presented as a target problem. For solving the problem, first, the technique of second-order Taylor expansion is used to deal with the discrete time-variant nonlinear system, and the novel discrete-time RNN model is proposed subsequently. Second, the theoretical analyses are investigated and developed, which shows the convergence and precision of the proposed discrete-time RNN model. Furthermore, three distinct numerical experiments verify the excellent performance of the proposed discrete-time RNN model. In addition, a robot manipulator example further verifies the effectiveness and practicability of the proposed novel discrete-time RNN model.

In this paper, a new one-step-ahead numerical differentiation rule termed 5-instant discretization formula is proposed for the first-order derivative approximation with higher computational precision. Then, by exploiting the proposed formula to discretize the continuous-time zeroing neural network [or termed, continuous-time Zhang neural network (ZNN)] models, two new discrete-time zeroing neural network [or termed, discrete-time ZNN (DTZNN)] models are proposed, analyzed and investigated for solving systems of discrete time-variant inequalities, including the system of discrete time-variant linear inequalities and the system of discrete time-variant nonlinear inequalities. For comparative purposes, the recently developed Taylor-type DTZNN models and the widely used Euler-type DTZNN models are also presented. Theoretical analyses show that the proposed DTZNN models are convergent, and their steady-state residual errors have an O(g⁴) pattern with $ g$ denoting the sampling gap. Comparative numerical experimental results further substantiate the efficacy and superiority of the proposed DTZNN models for solving the systems of discrete time-variant inequalities.

Lexical simplification (LS) aims at replacing complex words with simpler alternatives. LS commonly consists of three main steps: complex word identification, substitute generation, and substitute ranking. Existing LS methods focus on the contextual information of the complex word in the last step (substitute ranking). However, they miss out the following two facts: (1) The word complexity of a polysemous word is very closely related to its context; (2) The step of substitute generation regardless of the context will inevitably produce a large number of spurious candidates. Therefore, we propose a novel LS system LSBert based on pretrained language model BERT to address the aforementioned issues, which is capable of making use of the wider context when both identifying the words in need of simplification and generating substitute candidates for the complex words.Specifically, LSBert consists of a network for complex word identification by fine-tuning BERT and a network for substitute generation based on BERT. Experimental results show that LSBert performs well in both complex word identification and substitute generation, achieving state-of-the-art results in three benchmarks. To facilitate reproducibility, the code of the LSBert system is available at https://github.com/qiang2100/BERT-LS .

In recent years, the cable-driven planar robot has made fruitful achievements in many fields, but the related researches are scarce yet in the industrial engineering field. In this article, as a powerful tool for solving discrete time-varying problems, the discrete-time recurrent neural network (DTRNN) is extended to drive the cable-driven planar robot for discrete real-time tracking control, which is derived by a new immediate discretization method, and thus, is termed as ID-DTRNN model. Specifically, first, we present the physical structure and mathematical model of the cable-driven planar robot. Then, the new ID-DTRNN model is proposed and applied for driving such cable-driven planar robot, which bases on the a different way of construction of the traditional DTRNN model. Through numerical experiments, the feasibility, validity, and physical reliability of the ID-DTRNN model for discrete real-time tracking control of the cable-driven planar robot are fully verified. In addition, in the real world, physical experiments of the cable-driven planar robot are presented, which successfully promote the development of physical application of the ID-DTRNN model, and fill the gap of such model in the industrial engineering field.