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where we are omitting the time index i for compactness of notation. Introduce the symbols 8 = 1-6, = E lw(i)16, where the scalars {(:,<:} denote the fourth and sixth-order respectively. The data { d ( i ) , i v ( i ) } assumed to satisfy model (15.16). u, are moments of v(i),

These equations characterize the solution of the regularized least-squares problem (29.28). When 8 = 0, the equations reduce to

= af (1 SNR)

for some given matrices Li. For example, if La is chosen as the identity matrix, Li = I, then the problem amounts to that of estimating w o itself. If, on the other hand, Li = u, i then the problem amounts to estimating uiwo, which is the uncorrupted part of d ( i ) . Different choices for Li lead to different interpretations for si. The derivation that follows is for arbitrary Li. Clearly, whenever we say that the observations { d ( i ) } satisfy a model of the form (45.1), there is the implicit assumption that such a woexists and, furthermore, that we know its

1 5 0

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with their entries separated by multiples of some delay D. The choice D = 1corresponds to E-APA and PRA, but larger values for D can also be employed. One motivation for using D > 1is to increase the separation, and consequently reduce the correlation, among the regressors in Ui. As we are going to see in our studies on the performance of adaptive filters, starting in 15, the performance of LMS-type filters tends to be sensitive to the correlation of its regression data. And E-APA filters, with D = 1 or D > 1, address some of these deficiencies albeit at an increased computational cost over NLMS. Finally, it is worth mentioning that the APA form (13.5), with E = 0, can be rewritten in an equivalent form in terms of orthogonalized regressors {Gi} that are obtained from the original regressors { u i } via a Gram-Schmidt orthogonalization procedure (see Rob. III.43). The details are carried out in Rob. III.44 and they lead to the following statement.

dollars and a history of on-time payments could show the news media thousands of dollars charged in a few days, all obvious fraud Financial institutions also found they could pass the losses off to their customers in the form of higher interest rates It was not until the losses from fraud cut into the banking institutions profits that changes occurred and proactive fraud prevention became routine In the early 1980s, a bank investigator for a major financial institution in New York decided that he would create his own fraud detection process for the increasing number of fraudulent credit card applications his bank was receiving These applications were being submitted using stolen identities and contained the names, birth dates, Social Security numbers, and employment histories of the victims.

This bank investigator correctly assumed that the bulk of these thousands of fraudulent applications were being submitted by members of Nigerian Criminal Enterprises who were a plague on the credit card industry at the time At this point, credit card applications were completed by hand and mailed in for processing After finding that the fraudsters had a very distinctive style of handwriting, this investigator began to manually review each submitted application looking for these handwriting characteristics They included the signature being underlined, periods on both sides of middle initials in names, period after signatures, reversal of first and last names, European-style date, a colon used in place of decimals, dashes or slashes, letters A and E connected to the next letter, dashes between names or nouns, as well as other misspelled words and strange abbreviations.

The hardware configuration of the PC is stored in the computer s CMOS memory. This data is managed through the BIOS setup program. This section discusses how to access the setup program and each of the menu types it displays.

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