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1 A V Aho, R Sethi, and J D Ullman, Compiler Design: Principles, Techniques, and Tools, Addison-Wesley, Reading, Mass, 1986 2 C N Fischer and R J LeBlanc, Crafting a Compiler with C, BenjaminICummings, Redwood City, Calif, 1991 3 R W Floyd, "Syntactic Analysis and Operator Precedence," Journal of the ACM 10:3 (1963), 3 16-333

derivation of the as/w correction until Section 11.7, where it will emerge as a by-product of the study of the three-jet events e - e + -> qqg.

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In this chapter we discuss two utility applications of data structures: data compression and cross-referencing Data compression is an important technique in computer science It can be used to reduce the size of files stored on disk (in effect increasing the capacity of the disk) and also to increase the effective rate of transmission by modems (by transmitting less data) Virtually all newer modems perform some type of compression Cross-referencing is a scanning and sorting technique that is done, for example, to make an index for a book In this chapter, we show: an implementation of a file-compression algorithm called Huffman's algorithm; and an implementation of a cross-referencing program that lists, in sorted order, all identifiers in a program and gives the line numbers on which they occur

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If the hypothesis is rejected, then the ordinary leastsquares estimates of the regression coefficients are used If the hypothesis is accepted, then {3 q + I, .. , {3 p are estimated to be 0 and {31"'" {3 q are estimated by least squares in the reduced model Rather than choose between least squares in the full model and least squares in the reduced model on the basis of a test statistic F, subspace-Stein estimation takes a weighted average of the two, with the weights depending on the value of F Principal Components Regression To deal with regression data having collinearities among the explanatory variables, another technique one can use, besides ridge regression, is principal components regression The first principal component is the standardized linear combination of the explanatory variables that shows the most variability (A linear combination is.

The ASCII character set consists of roughly 100 printable characters To distinguish these characters, [log I001 = 7 bits are required Seven bits allow the representation of 128 characters, so the ASCII character set adds some other "unprintable" characters An eighth bit is added to allow parity checks The important point, however, is that if the size of the character set is C, then log C 1 bits are needed in a standard fixed-length encoding Suppose that you have a file that contains only the characters a, e, i, s, and t, blank spaces ( s p ) ,and newlines (nl) Suppose further that the file has 10 a's, 15 e's, 12 i's, 3 s's, 4 t's, 13 blanks, and 1 newline As Figure 131 shows, representing this file requires 174 bits because there are 58 characters and each character requires 3 bits

So far, we have not faced the problem of how the quarks turn into the hadrons that hit the detector. It was sufficient to state that the quarks must fragment into hadrons with unit probability. This gives (11.4). For more detailed calculations, this problem cannot be sidestepped. In the center-of-mass frame, the produced quark and antiquark separate with equal and opposite 'momentum and materialize into two back-to-back jets of hadrons which have momenta roughly collinear with the original q and q directions. The hadrons may be misaligned by a momentum transverse to the q or q direction by an amount not exceeding about 300 MeV. In 1, we visualized jet formation as hadron bremsstrahlung once the q and q separate by a distance of around 1 fm. Then, as becomes large, and strong color forces pull on the separating q and q. The potential energy becomes so large that one or more qq pairs are created (see Fig. 1.14). Eventually, all the energy is degraded into two jets of hadrons moving more or less in the direction of the q. and q. To describe the fragmentation of quarks into hadrons, we use an analogous formalism to that introduced in 9 to describe the quarks inside hadrons. Figure 11.4 shows the observation of a hadron h, whose energy is measured to be E h The corresponding differential cross section can be written as (11.8 )

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