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Complex Systems and Cognitive Processes by Roberto Serra

By Roberto Serra

This quantity describes our highbrow direction from the physics of advanced sys­ tems to the technology of man-made cognitive structures. It used to be fascinating to find that the various thoughts and techniques which achieve describing the self­ organizing phenomena of the actual international are proper additionally for comprehend­ ing cognitive approaches. a number of nonlinear physicists have felt the fascination of such discovery lately. during this quantity, we are going to 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 man made structures are vital in step with se; however, it may be anticipated that their learn will make clear a few normal ideas that are correct additionally to organic cognitive structures. the most function of this quantity is to teach that nonlinear dynamical structures have a number of homes which lead them to quite beautiful for achieving a few of the ambitions of man-made intelligence. the keenness which used to be pointed out above needs to even if be certified through a serious attention of the restrictions of the dynamical platforms strategy. figuring out cognitive tactics is an enormous clinical problem, and the achievements reached to this point let no unmarried approach to declare that it's the merely legitimate one. specifically, the procedure dependent upon nonlinear dynamical structures, that's our major subject, continues to be in an early degree of development.

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7a). The procedure for constructing such a set is as follows. A segment of unitary length is divided into three equal parts. The central part is removed, the operation is repeated on the other two, and so on. e. with a structure which replicates itself in all its substructures. For a self-similar set such as the Cantor one, the value of Do can be directly found from the construction algorithm. In fact, one can verify that R = (1/3)m, N = 2m. The Hausdorff fractal dimension for the Cantor set is thus .

A) A < 1/2: one stable fixed point x· (After Schuster, 1984) = OJ b) A = 1: two unstable fixed points. 38 3. Dynamical Behaviour of Complex Systems case where A = 1, with the corresponding unstable fixed points at 0 and 2/3. The instability is clear from the behaviour of the successive iterations corresponding to the initial conditions x(O) and x'(O) shown in the figure. In the absence of stable fixed points, the results of iterations corresponding to closely neighbouring initial conditions may progressively move away from one another.

A set of rules (the so-called meta-rules) which are used to decide which rules of inference to apply in a given computational stage. The meta-rules are of a more general nature than the production rules, and depend only to a limited extent upon the domain of application. Another aspect common to the various approaches to classical AI is the use of dedicated symbols to represent each concept (local representations). In this way, there must be a symbol for each concept. On the contrary to AI programs, dynamical systems reach their conclusions by applying evolutive rules to numerical variables, instead of applying inference rules to logical variables.

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