Diffraction, Fourier Optics and Imaging, by Okan K. Ersoy Copyright # 2007 John Wiley & Sons, Inc. in .NET

Drawer qrcode in .NET Diffraction, Fourier Optics and Imaging, by Okan K. Ersoy Copyright # 2007 John Wiley & Sons, Inc.

The expectation in Equation (19.4) is with respect to the conditional density Z ^ f j 1jIi u di u ^j 1 u = ^j 1 s ds f f
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Public key or asymmetric key cryptography is a form of protecting data in which a pair of mathematically bound keys are derived from the same functions. At the same time the function reduces the possibility of deducting one from the other. Whitfield Diffie and Martin Hellman pioneered this concept in 1976. Any user or system involved in the communication will have a pair of keys: one is called the private key and the other is the public key. If the user or system wants to receive encrypted information, the sender will be provided with a copy of the public key. This can be transferred using any technology. It is not dangerous to send the public key using insecure channels as the private key cannot be obtained on the basis of the public key (with appropriate key lengths the complexity is so high that it is considered impossible to guess the private key). Content encrypted with the public key of the recipient by the sender can only be decrypted using the private key from the sender. Asymmetric key encryption has some clear advantages including key management and distribution and scalability of the infrastructure. Some disadvantages are that it is resource intensive compared with a symmetric key, which reduces the speed of the process. Both symmetric and asymmetric encryption can be easily combined within an IPTV environment. Content can be encrypted using a symmetric key that is encrypted using the public key of recipients who in turn are the only ones allowed to open the key. The same network can be used to send the content and the key as it would be encrypted.
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as to the future. Borrowing from standard nance theory, it depends on two variables (standard deviations and correlations) that only make existential sense under normality. It paints a picture of how dispersed (volatile) nancial markets have been during a prespeci ed prior period, and then translates that estimate into expected results going forward, using a very large degree of con dence but not quite yet 100 percent. That is, VaR does not capture the more unlikely setbacks. The problem with this is not just that the effects of rare events may be devastating, but that the normal world of VaR assumes an unrealistically low chance that those happenstances will happen. In other words, the VaR number (generally purported to be a reliable guide to the market risks faced by a nancial institution) excludes the potentially most troublesome scenarios and assigns an unseemly high probability to the (selected) past repeating itself. No wonder, then, that VaR models failed during the crisis. Markets spectacularly revealed themselves to be non-normal, and the historical sample periods used in the calculation (which range from a few months to several years, depending on the institution) did not contain some of the things that uniquely took place beginning in the second half of 2007. Both volatility and correlation behaved in insultingly different ways from the recent past. The risk forecast proved spectacularly lacking. The of cial guiding light misguided aplenty. Neither the likelihood nor the speed or the severity of the downfall were predicted. But before we delve deep into the actual details of how VaR did not succeed during the crisis, let s anticipate a central theme of this book: VaR not only fails at measuring, preventing, or predicting humongous risks, it can actually help create them. By leaving aside the extremes and operating from a philosophical platform that vastly underestimates the (real) probability of rare events, VaR can yield numbers that are so low that complacency is unmitigatingly bred and risk taking runs amok. Trades can be shown to be almost negligibly risky at the 95 or 99 percent (or even 99.9 percent) con dence level, thus affording the perfect stamp of approval. Not only would the trade be executed, little capital would be set against it, creating in effect a largely leveraged position for the institution. In other words, the mathematics of VaR would have encouraged the rm to enter into situations where bad news (even slightly so) can cause a lot of damage and manufacture enormous losses, certainly way above those indicated by the glori ed risk radar. These types of
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It follows that spreading of waves increases as f and M are reduced. In the telescopic system, C 0 0, and the input spreading of waves coming from an aperture is increased at the output by a factor of 1/M. In order to nd the size of the virtual hologram apertures, both magni cation and diffraction effects need to be considered. The size of a virtual hologram aperture dv can be written as dv Mdr D 16:2-23
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Figure 4.1. Realization of the detection process and its smoothing with 2 = 10 3 . There are 100 markers on a chromosome of size 1 morgan, and 500 individuals are observed.
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Logging & Recovery Mechanism
The excess return or alpha, L, of the long side of the long-plus-short portfolio will equal the alpha of the short side, S, which will equal the alpha of the long-only portfolio, LO. Furthermore, the residual risk of the long side of the long-plus-short portfolio, L, will equal the residual risk of the short side, S, which will equal the residual risk of the longonly portfolio, LO. These equivalencies re ect the fact that all the portfolios, the longonly portfolio and the long and short components of the long-plus-short portfolio, are constructed relative to a benchmark index. Each portfolio is active in pursuing excess return relative to the underlying benchmark only insofar as it holds securities in weights that depart from their benchmark weights. However, departures from benchmark weights introduce residual risk. Controlling portfolio risk thus involves balancing expected excess (to benchmark) returns against the added risk they introduce. In this balancing act, the investor faces the probability of having to forgo some increment of expected return in order to reduce portfolio residual risk. Portfolio construction is benchmark-constrained.8 Consider, for example, an investor who does not have the ability to discriminate between good and bad oil stocks, or who believes that no oil stock will signi cantly out- or underperform the underlying benchmark in the near future. In long-plus-short, this investor may have to hold some oil stocks in the long portfolio and short some oil stocks in the short portfolio, if only to control each portfolio s residual risk relative to the benchmark. In long-plus-short, the advantage offered by the exibility to short is also curtailed by the need to control risk by holding or shorting securities in benchmark-like weights. The ratio of the performance of the long-plus-short portfolio to that of the long-only portfolio can be expressed as follows: IR L + S ---------------- = IR LO 2 ---------------------1 + L + S
wooden spoon, stir the beef until it is browned, about 3 minutes. Add the salt, pepper, and broth, and simmer, covered, over low heat for 10 minutes.
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