Download Complex Systems and Cognitive Processes by Roberto Serra PDF

By Roberto Serra

This quantity describes our highbrow course from the physics of advanced sys­ tems to the technology of synthetic cognitive structures. It used to be interesting to find that a number of the innovations and techniques which reach describing the self­ organizing phenomena of the actual global are proper additionally for comprehend­ ing cognitive tactics. a number of nonlinear physicists have felt the fascination of such discovery in recent times. during this quantity, we'll restrict our dialogue to synthetic cognitive structures, with out trying to version both the cognitive behaviour or the anxious constitution of people or animals. at the one hand, such synthetic structures are very important in line with se; nevertheless, it may be anticipated that their examine will make clear a few common rules that are correct additionally to organic cognitive structures. the most goal of this quantity is to teach that nonlinear dynamical structures have numerous homes which cause them to really appealing for attaining a number of the objectives of synthetic intelligence. the passion which used to be pointed out above needs to despite the fact that be certified via a serious attention of the constraints of the dynamical structures technique. realizing cognitive techniques is an enormous medical problem, and the achievements reached up to now let no unmarried technique to declare that it's the purely legitimate one. specifically, the procedure established upon nonlinear dynamical structures, that's our major subject, continues to be in an early level of development.

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1 shows a geometrical representation of the map. X(i+l) 11---------, A o 1 xli) fig. 1. The triangular map. (After Schuster, 1984) The stability criterion introduced above allows us to state that, for A < 1/2, the origin (x* = 0), which is the only fixed point of the map, is asymptotically stable. This may be immediately verified, as Fig. 2a shows, using a graphical representation of the results of successive iterations starting from an initial condition x(O) f:. O. In this interval of values for A, the origin is asymptotically stable for all possible initial conditions with 0 ~ x(O) ~ 1.

5 some networks are discussed whose cognitive behaviour is not associated with a truly asymptotic dynamics. This chapter will study first of all the case of discrete dynamical systems with only one state variable (Sect. 2). With reference to such systems, the study will include the relaxation towards fixed points, the appearance of periodic at tractors ("limit cycles") and the development of "chaotic" situations. The ideas will be brought into focus by referring to particular equations which, however, show a sufficient range and variety of behaviours: the "triangular map" and the "logistic map".

Using distributed representations it is not necessary to identify a priori every meaningful variable: even without any previous knowledge, the study of a certain number of specimens of a category can lead to the formation of co-activation patterns corresponding to that concept, given that the learning algorithm is adequate. It should be noted, however, that it is possible to obtain dynamical models for AI also by utilising a "formal neuron" for each concept (the so-called "grandmother neuron", which designates, in the jargon of neurophysiologists, the hypothesis that there is a specific neuron for every concept).

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