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1982; Kendall et al., 1983). By the mid-1950s, Wigner s work (e.g., 1958, 1967) was followed by great interest in random matrices in some areas of mathematical physics, which continues until the present time (see, e.g., Soshnikov, 1998; Tracy and Widom, 1999; Davidson and Szarek, 2001). A third source of interest has been numerical analysis, motivated by the aforementioned condition number problems, which may have begun with a paper by Smale (1985). A very interesting survey of analytical methods, originally inspired by numerical analysis problems but including a diversity of applications, is that of Edelman and Rao (2005). In this chapter we are considering only a very small part of the subject, which concerns the condition number (A). One reason to include this topic here is that the methods we present are based on random elds and Rice formulas, which is the core of this book. In some cases, these methods do not give optimal results, as happens in the canonical case of matrices having i.i.d. standard normal entries. However, for noncentered Gaussian matrices, our methods still provide the best bounds for the tails of the probability distribution of (A) of which the authors are aware. We start in Section 13.1 with some elementary upper bounds for E(log (A)) when A is a random matrix with i.i.d. (not necessarily Gaussian) entries. The methods are ad hoc, but we are not aware of the existence of better general bounds. The remainder of the chapter concerns Gaussian matrices. Section 13.2 covers centered matrices and Section 13.3, noncentered matrices.

An optimal W(f) is needed, with minimal sidelobes and a very narrow main lobe width to make Z0 (k) as close as possible to U(f). Obviously, the optimal W(f) is d f , which means no windowing. A compromise is searched for, in which the window is nonzero for jnj N and its W(f) is as similar as possible to d f . In this search, the law of no free lunch exhibits itself. Sidelobes are removed at the expense of widening of the main lobe, and vice versa. Widening of the main lobe is equivalent to low-pass ltering, smoothing out the fast variations of U(f).

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Let us assume the wireless device has an IP address assigned either by hard coded, Network Address Translation (NAT) or Dynamic Host Con guration Protocol (DHCP) To prevent wireless traf cs that bypass the security perimeter or rewall to access the enterprise Intranet directly, the switch ports that the wireless APs are connecting to are either con gured on some virtual LANs (VLANs) or controlled and managed by the switches, a security appliance, or a centralized AP manager Hence, only certain precon gured and authorized IP subnet addresses are allowed to access the enterprise security perimeter while the rest traf cs will be refused for services In order to pass the enterprise security perimeter to access the enterprise Intranet, every user wireless device has to establish a SSL or IPSec VPN tunnel with the VPN server rst.

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To authenticate an authorized user, every mobile user is also issued with a hard or soft smart card that can generate a one-time-password when the user s key is entered If the one-time-password passes the AAA validation by the Radius server, the VPN server will then establish a tunnel that binds between the VPN client and server Once the mobile user is connected to the network, there may be more user logons required, depending on the type of network the application server is on and the application security requirements Hence, a centralized single sign-on requirement (eg, via XML signatures and SAML Security Assertions Markup Language protocol) is also on the horizon In addition to the wireless security issue, among the other known enterprise wireless network deployment concerns are the wireless QoS, IP mobility, application persistence, wireless LAN/WAN integration, and the constraint of mobile devices issues.

Government investigators began to put together cases, and at the time of this writing, a grand jury hearing was pending for one of the perpetrators. The scheme totaled more than $250,000 for USA Choice Payments, Inc., alone. There were elements of identity theft, shell company usage, debit card fraud, connections to organized crime and Internet fraud in this intriguing case. While it is impossible to be sure that all victims have been accounted for, the last dollar amount I heard involved in this scheme was upward of one million dollars in losses to individuals and businesses. These losses absorbed by the nancial intuitions, ultimately, and not the victims in this case are just a small piece of the total fraud costs every year. Our investigation revealed that Buzz and Felix had managed to obtain legitimate incorporation papers for a handful of shell companies from a state government of ce. Each company was set up using multiple stolen identities to complete the rst step of the scam. Next, they used these companies as a means to send payroll to their many different employees

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