By Hermann Haken
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Additional info for Synergetic Computers and Cognition: A Top-Down Approach to Neural Nets
2 Reminder of the Basic C oncepts and Mathematical Tools of Synergetics 35 f(q) f(q) q q Fig. 13. The probability distribution for a particle which moves in the potentials of Fig. 6. 63) can easily be visualized when we think of the interpretation of V as a potentiallandscape. The minima of V, where the particle will be found most frequently, are at the sametime the maxima of j. For example, the distribution functions corresponding to the one-dimensional potentials of Fig. 6 are given in Fig. 13.
The selection of a specific roll system (cf. Fig. 2). At the same time it describes multistability because any direction k oftheroll pattern can be realized. 49) was represented in Fig. 3 for various stochastic initial conditions of the velocity field v. As we shall show in Chap. 5, this property of specific mode selection remains valid if Ck , k ' is replaced by Ck,k ' = A B>A for for k=k' k*-k' . 51) This means that the functional dependence on k , k' is now given by Fig. 10. Let us summarize the results of this chapter.
A} The faces that are stored as the prolotype patterns used in this book. The letters encode the names or identify the figures. In addition to the faces other figures were also included to check how the synergetic computer responds and what properlies it displays when recognizing these patterns. From Fuchs and Haken (1988 a). (b) The prototype patterns corresponding to the adjoint vectors v + . From Fuchs and Haken ( 1988 a) Fig. 2. When part of a face is presented to the computer, whose attention parameter 1s set to a negative value, the face eventually disappears from the computer screen.
Synergetic Computers and Cognition: A Top-Down Approach to Neural Nets by Hermann Haken