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By D.E. Johnson, etc.

ISBN-10: 0133724093

ISBN-13: 9780133724097

Hardcover with gilt lettering with out dirt jacket

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This can be seen as follows. Let the absolutely stable (maximum E) pattern of b and w cells be b enclosed by w, and similarly that of w and χ cells be a pattern of w enclosed by X, Let e denote the medium common to both the systems. The question we 42 Robert Rosen then ask is whether this implies anything about the maximum Ε pattern of b and X. The first two observations and the previous discussion imply Abb - 2Abw + Awe + Abw > Aee - 2A,e + Aww - > Abe + 0, (21b) 0, (2lc) A^w > 2A,, + 0, A,. e + A , , > Awe + Aee - 2A,e + A,, > (21a) A^w, (22a) A,,, (22b) 0.

Therefore, N^^,, A^bei and A^ee cauttot be maximum simultaneously and, hence, we will not have an absolutely stable pattern if the coefficients of N^^, A^be. and A^ee in Eq. (20) are positive. On the other hand, if we require both A^bb and A^ee to be maximal and A^be to be minimal, we obtain an onion pattern with the b cells forming the inner layer, the w cells surrounding them, and these in turn being surrounded by the e cells. This pattern will be absolutely stable if M, > 0, M l + Λ/3 < M 2 , M, > 0.

In some sense this requirement is implied by the experimental results: configurations of maximum Ε do not change into submaximal configurations with time. As far as elementary permutations are concerned, this restriction may be interpreted to mean that the requirement is global: that is, the Ε of the overall pattern must increase even if some moves are locally energetically unfavorable. Since this implies that individual cells have some way of detecting and responding to informa­ tion as to the global pattern of which they are a part, this does not seem very plausible.

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