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Thus, the beam-splitting activity of the condenser prism is exactly matched and undone by the beam-recombing action of the objective prism Note that the axes of beam splitting and beam recombination of both DIC prisms are parallel to each other and fixed at a 45 angle with respect to the transmission axes of the crossed polarizer and analyzer This axis is called the shear axis because it defines the axis of lateral displacement of the O and E wavefronts at the specimen and at all locations between the specimen and the image If, however, the O- and E-ray pair encounters a phase gradient in an object, the two beams will have different optical paths and become differentially shifted in phase.

We have some bad news for you. Look again at Exhibit 2.4. In the case of equity portfolios, we note that a fully diversi ed portfolio can be achieved with a limited number of equities. The number of assets needed to create a fully diversi ed portfolio of loans or other credit assets is much larger. It is certainly bigger than 100 assets and it may be larger than 1,000 assets. But we have some good news for you as well. The diversi cation effect for portfolios of loans or other credit assets will be larger than the diversi cation effect for portfolios of equities. Remember that the bedrock risk the risk that cannot be diversi ed away is average covariance. As before, I nd it easier to think about correlations than covariances, so, since both of them are telling me about the same thing, I switch and talk about correlation. The typical correlation of equity returns is 20% 70%. However, the typical correlation of defaults is much smaller 5% to 15%. So the risk that cannot be diversi ed away will be smaller. The bad news is that it is going to take many more assets in the portfolio to achieve a fully diversi ed portfolio. The good news is once you have a fully diversi ed portfolio, you re going to get a much larger diversi cation effect.

where Bbest = theoretical best rate, Bsend = chosen send rate, Stotal = total data size to send (i.e., payload), and RTT=round-trip time. This ratio shows that, in order to maximize throughput, an application should strive to minimize RTT Bsend /Stotal by maximizing the size of the payload to be delivered. For example, given that RTT for Chicago to Amsterdam is 100 ms, and Bsend is 600 Mbps, if one wishes to achieve a throughput of 90% of the sending rate, then the payload, Stotal needs to be at least 67.5 MB.

We treat the situation the same as we do in standard light microscopy: Waves emanating from the same object particle in the specimen meet at their conjugate location in the image plane, with the difference that the waves must first pass through the objective DIC prism and analyzer These waves emerge from the prism as elliptically polarized light (Fig 10-5c) The E vector of the resultant ray is not planar, but sweeps out an elliptical pathway in three-dimensional space These rays partially pass through the analyzer, resulting in a linearly polarized component with a finite amplitude This information.

where = 10 6 and log L( |D) = 383.21. The Bayes predictive density based on m = 400 samples is given in Figure 5.10. The density is very heavy-tailed, due primarily to the distributions chosen. The small kink near t = 0 is due to the mixture distribution: namely, that the 0 2 exponential will tend to 1 while the 0 1 inverse Gaussian tends to 0 as t 0. Rejection sampling is very inef cient; in this case, only 3% of the samples are accepted. A generalization of rejection sampling is to use importance sampling to sample from a complicated high-dimensional posterior. Importance sampling is dif cult to implement with complicated owgraphs, especially so in the presence of censored data where choosing an envelope function can become dif cult. Two other popular methods, Gibbs sampling and the Metropolis Hastings algorithm, also

public key encryption and hashing systems are explained, together with their use in common digital certi cation and secure data transmission applications. On-line services such as Napster and gnutella have threatened copyright protection. Some relief may be had through use of digital watermarking but this is not foolproof. Providing access rights to legitimate users can be enabled by means of smart-cards and biometric systems. The latter are a special class of pattern recognition applications. Some basic theory is reviewed, particularly with regard to what makes a good classi er and a range of biometric alternatives are assessed.