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1883). He believed those at the high end of the scale had much more to contribute than did those at the low end. The same kinds of judgments do not pervade the literatures of, say, sensation or memory. This tendency to con ate intelligence with some kind of economic or social value to society and perhaps beyond society has continued to the present day (e.g., Herrnstein & Murray, 1994; Schmidt & Hunter, 1998). Intelligence Is Complex: Binet s Theory of Judgment In 1904, the minister of Public Instruction in Paris named a commission charged with studying or creating tests that would ensure that mentally defective children (as they then were called) would receive an adequate education. The commission decided that no child suspected of retardation should be placed in a special class for children with mental retardation without rst being given an examination from which it could be certi ed that because of the state of his intelligence, he was unable to pro t, in an average measure, from the instruction given in the ordinary schools (Binet & Simon, 1916a, p. 9). Binet and Simon devised a test based on a conception of intelligence very different from Galton s and Cattell s. They viewed judgment as central to intelligence. At the same time, they viewed Galton s tests as ridiculous. They cited Helen Keller as an example of someone who was very intelligent but who would have performed terribly on Galton s tests. Binet and Simon s (1916a) theory of intelligent thinking in many ways foreshadowed later research on the development of metacognition (e.g., Brown & DeLoache, 1978; Flavell & Wellman, 1977; Mazzoni & Nelson, 1998). According to Binet and Simon (1916b), intelligent thought comprises three distinct elements: direction, adaptation, and control. Direction consists in knowing what has to be done and how it is to be accomplished. When we are required to add three numbers, for example, we give ourselves a series of instructions on how to proceed, and these instructions form the direction of thought. Adaptation refers to one s selection and monitoring of one s strategy during task performance. For example, in adding to numbers, one rst needs to decide on a strategy to add the numbers. As we add, we need to check (monitor) that we are not repeating the addition of any of the digits we already have added. Control is the ability to criticize one s own thoughts and actions. This ability often occurs beneath the conscious level. If one notices that the sum one attains is smaller than either number (if the numbers are positive), one recognizes the need to add the numbers again, as there must have been a mistake in one s adding.

In essence, by minimizing (3.6) we invoke a computing process in which we split the i0-th cluster into two clusters, maintaining a balance of the membership grades of the original cluster. Here zi are the prototypes and F [fik] denotes a partition matrix that satis es constraint (3.7), meaning that the split is driven by the data and membership grades of the most diversi ed cluster. The term conditional clustering comes from the fact that we require that the resulting membership degrees fik are distributed according to the membership values available for the cluster to be split. The detailed calculations of the partition matrix F and the two prototypes z1 and z2 are carried out iteratively according to the two formulas fik ui0 k 2 X kxk zi k1= m 1

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Newman, M. (1972). Integral Matrices. Academic Press, New York. Ortega, J.M. (1987). Malrix Theory, a Second Coursr. Plenum Press. New York. Perlis, S. (1952). Thcory of Matrices. Addison- Wesley, Reading, ~1 ass. Pissanetsky, S. (1984). Sparse Matrix Technology. Academic Press. London. Pollock. D.S.G. (1979). The Algebra of Econometrics. \~,1ilcy, Chichester. Pringle, R. M. & A. A. Rayner (1971). Generalized Inl.'t rse :\fatricrs lI ilh Applicatioll,y to Statistics. Griffin. London. Rao. C. R. (1973). Linear Statisti :al Inference and its Applications. 2nd edn, John Wilev, New York. Rao, C'.R. & S.K. Mitra (1971). Generalized Inverse of Malnces and its AppllcatlOlls. Wilev. New York. Rogers: G.S. (1980). MCllrix DerivCltives. Marcel Dekker. New York. Searle, S.R. (1982) . .lfCltrix Algebra Useful for Statlsti",. Wiley. New ) ork. Seber, G.A.F. (1981). Multivariate Observations. Wilf>Y. ;-,rew York, SenE'/,a, E. (1973). Nonnegative Matrices. Wiley, New York. Stewart, G.W. (1973). Introduction to Matrix ComputatIOns. Academic Press. New York. Suprenenko, D.A. & R.I. Tyshkevich (1968). Comrnutatit'e Malrice.i. Academir Press, New )"ork. Turnbull, H,\\'. (19.')0), The Theory of DeterminCltlls. Matricfs and 1111'ariol1t8, Blackie, London. Turnbull. H,W. & A.C. Aitken (1932). An IntroductlOrJ 10 the Throry of CarlOrli('(l/ .\fatrices. Blackie. London. Varga, R.S. (1962) . .Vatrix iterative A nalysis. Prentice-II all, Englewood Cliffs. :; ..1. \Vilkinson, J. H. ( 1965). The Algebraie Eigenvalue Problem. Clarendon Press. Oxford. Zurmiihl. R. & S. Falk (1981). Matrizfn lind ihre Anwendtmgen. Tell I: Gt'twd/agfrl. Springer, Berlin, Zurmiihl, R. & S. Falk (1986). Molnzen und ihrf' Anwendungen. Tfil 2: NUt7lfri$,h, .tlc/hoden. Springer. Berlin.

when the limit exists. The two quantities H (X) and H (X) correspond to two different notions of entropy rate. The rst is the per symbol entropy of the n random variables, and the second is the conditional entropy of the last random variable given the past. We now prove the important result that for stationary processes both limits exist and are equal. Theorem 4.2.1 For a stationary stochastic process, the limits in (4.10) and (4.14) exist and are equal: H (X) = H (X). We rst prove that lim H (Xn |Xn 1 , . . . , X1 ) exists. Theorem 4.2.2 For a stationary stochastic process, H (Xn |Xn 1 , . . . , X1 ) is nonincreasing in n and has a limit H (X). Proof H (Xn+1 |X1 , X2 , . . . , Xn ) H (Xn+1 |Xn , . . . , X2 ) = H (Xn |Xn 1 , . . . , X1 ), (4.16) (4.17) (4.15)

ord = (val & 0xFF00); ord = ((val & 0xFF00) << 8); ord = ((val & 0xFF00) > 8); ord = (val << 8); ord = (val > 8);