In this case study a fully symbolic design and modeling method are presented for blood glucose control of diabetic patients under intensive care using Mathematica. The analysis is based on a modified two-compartment model proposed by Bergman et al. The applied feedback control law decoupling even the nonlinear model leads to a fully symbolic solution of the closed loop equations. The effectivit...

A hybrid dynamical system is a mathematical model suitable for describing an extensive spectrum of multi-modal, time-series behaviors, ranging from bouncing balls to air traffic controllers. This paper describes multi-modal symbolic regression (MMSR): a learning algorithm to construct non-linear symbolic representations of discrete dynamical systems with continuous mappings from unlabeled, time...

Tools for performing automated analyses of data communication protocols are frequently based on symbolic execution algorithms that search the behavior of finite state machine models. The symbolic execution algorithms, however, are inherently restricted in the size of the models that they can handle. They work well for models that generate up to 100,000 system states. Beyond that the time and sp...

An important achievement in modeling online language comprehension is the discovery of the relationship between processing difficulty and surprisal (Hale, 2001; Levy, 2008). However, it is not clear how structural uncertainty can be represented and updated in a continuoustime continuous-state dynamical system model, a reasonable abstraction of neural computation. In this study, we investigate t...

The dominating models of information processes have been based on symbolic representations of information and knowledge. During the last decades, a variety of non-symbolic models have been proposed as superior. The prime examples of models within the non-symbolic approach are neural networks. However, to a large extent they lack a higher-level theory of representation. In this paper, conceptual...

Traditional connectionist networks are sharply limited as general accounts of human perception and cognition because they are unable to represent relational ideas such as loves (John, Mary) or bigger-than (Volkswagen, breadbox) in a way that allows them to be manipulated as explicitly relational structures. This paper reviews and critiques the four major responses to this problem in the modelin...

Complex nonlinear dynamics arise in many fields of science and engineering, but uncovering the underlying differential equations directly from observations poses a challenging task. The ability to symbolically model complex networked systems is key to understanding them, an open problem in many disciplines. Here we introduce for the first time a method that can automatically generate symbolic e...

We consider the problem of tracing algebraic curves by computer, using a numerical technique augmented by symbolic computations. In particular, all singularities are analyzed cOITectly. The methods presented find application in solid modeling and robotics.

Human thought is remarkably flexible: we can think about infinitely many different situations despite uncertainty and novelty. Probabilistic models of cognition (Chater, Tenenbaum, & Yuille, 2006) have been successful at explaining a wide variety of learning and reasoning under uncertainty. They have borrowed tools from statistics and machine learning to explain phenomena from perception (Yuill...

Важнейшей задачей современной начальной школы является развитие личности через формирование универсальных учебных действий (далее –УУД), которые выступают основой образовательного процесса. Особую группу УУД составляют знаково-символические действия. На уровне начального образования основным показателем развития знаково-символических становится овладение моделированием. Знаково-символическое мо...