symbolic computation
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The study and understanding of human behaviour is relevant to computer science, artificial intelligence, neural computation, cognitive science, philosophy, psychology, and several other areas. Presupposing cognition as basis of behaviour, among the most prominent tools in the modelling of behaviour are computational-logic systems, connectionist models of cognition, and models of uncertainty. Recent studies in cognitive science, artificial intelligence, and psychology have produced a number of cognitive models of reasoning, learning, and language that are underpinned by computation. In addition, efforts in computer science research have led to the development of cognitive computational systems integrating machine learning and automated reasoning. Such systems have shown promise in a range of applications, including computational biology, fault diagnosis, training and assessment in simulators, and software verification. This joint survey reviews the personal ideas and views of several researchers on neural-symbolic learning and reasoning. The article is organised in three parts: Firstly, we frame the scope and goals of neural-symbolic computation and have a look at the theoretical foundations. We then proceed to describe the realisations of neural-symbolic computation, systems, and applications. Finally we present the challenges facing the area and avenues for further research.

Abstract Of current interest, in nonlinear optics, fluid dynamics and plasma physics, the paper commented (i.e., Phys. Scr. 95, 095207, 2020) has investigated a (2+1)-dimensional extended Calogero-Bogoyavlenskii-Schiff system. Hereby, we make the issue raised in that paper more complete. Using the Hirota method and symbolic computation, we construct three sets of the bilinear auto-Bäcklund transformations for that system, along with some analytic solutions. As for the amplitude of the relevant wave in nonlinear optics, fluid dynamics or plasma physics, our results depend on the coefficients in that system.

In this paper, we propose a novel solution strategy to explicitly describe the design space in which no recourse is considered for the realization of the parameters. First, to smooth the boundary of the design space, the Kreisselmeier-Steinhauser (KS) function is applied to aggregate all inequality constraints, and project them into the design space. Next, for creating a surrogate polynomial model of the KS function, we focus on finding the sampling points on the boundary of KS space. After testing the feasibility of Latin hypercube sampling points, two methods are presented to efficiently extend the set of boundary points. Finally, a symbolic computation method, cylindrical algebraic decomposition, is applied to transform the surrogate model into a series of explicit and triangular subsystems that can be further converted to describe the KS space. Two case studies are considered to show the efficiency of the proposed algorithm.

Abstract The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau (GL) equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors’ knowledge, the results reported in the current study, classified as bright and kink solitons, are new and have been acquired for the first time.