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we see that the schema  is assigned rank 3 by the three instances A3, A4, A7, while the schema  is assigned rank 4 using A4 Îx and A7 Îx with two other instances, and  is assigned rank 3 using A7 Îx and two other instances. |
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If we set M = 32 then the above calculation for r(8, 1, 32) indicates that some sets of size 32 drawn from  (randomly generated ones in this case) can assign a rank m ³ 8 to 9000 distinct schemata (for k = 2, l = 32). The problem then is one of using this potential to represent the relative ranking of the sample averages  for a large set of observed schemata. Once again we must wait upon the discussion of reproductive plans in chapter 6 to see that this can be done. |
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Summarizing: Given a set of detectors  the elements  each have a representation (d1(A), . . . , d1(A)) in terms of the ordered set of l attributes di(A) Î Vi, i = 1,. . . ,l.  designates a particular subset of , namely all elements of for which the corresponding representations match all positions in x which are not '' "s. Given a set of observations  from , the average payoff  of the observed instances  is apportioned to x as its credit for the performances of the possessing the corresponding set of attributes. Since each is an instance of 2l schemata it constitutes a valid sample point of 2l distinct subsets of (or events on) . This suggests the existence of algorithms which, by testing many possibilities with a single trial, are intrinsically parallel and which store the relative rankings of for a great many schemata by selecting a small set  . The algorithms introduced in chapter 6 will realize these possibilities. Later (chapter 8) dependence on the detectors {di} will be eliminated by subjecting the detectors themselves to adaptation. |
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