Biographical Dictionary of Modern Egypt by Jr. Goldschmidt Arthur

By Jr. Goldschmidt Arthur

Offers biographical sketches and resource fabric for roughly four hundred women and men who've performed an enormous position in Egypt's nationwide lifestyles. Entries variety in size from part a web page to 2 pages, and describe the contributions of politicians, writers, diplomats, spiritual leaders, and students, in addition to founders of newspapers, shops, theatrical troupes, and leading edge options of visible illustration. Earliest figures profiled are from the overdue 18th and early nineteenth centuries.

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Too. 16 1. Mathematical Preliminaries Direction Cosines. If the relevant information in patterns or signals is contained only in the relative magnitudes of their components, then similarity can often be better measured in terms of direction cosines defined in the following way. 42) Ilx1111Y11 is by definition the direction cosine of their mutual angle, with (x, y) the scalar product of x and y, and Ilxll the Euclidean norm of x. 42), or cos 0 = C. 42) complies with the traditional definition of correlation coefficient in statistics, provided that we understand the vectors x and y as sequences of stochastic numbers {~i} and {1]j}, respectively.

Consider a finite set of vectorial or other samples {xd. Let dij = d(Xi' Xj) be the distance of Xi and Xj in some metric. ij . Let Ti E ~2 be the location or coordinate vector of the image of Xi on a display plane. The principle is to place the Ti, i = 1,2, ... ,k, onto the plane in such a way that all their mutual Euclidean distances Ih - Tj II have as closely as possible the corresponding values d ij . Clearly this can only be made approximately. To approximate the d ij by the IITi - Tj II one may make iterative corrections.

More often, however, it must be estimated on the basis of exemplary samples selected in preliminary studies. The theories of decision processes are centrally based on the concept of a loss function or cost function, the value of which depends on factors set up heuristically, or after extensive experience, for instance, on the importance of detection of a particular occurrence, or on a miss to detect it. Let C(Si, Sk) be the unit cost of One decision that indicates the punishment of classification of a pattern to Si when it was actually from Sk.

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