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But a blog is more than the published musings of an individual. Blogs can be interactive as well. The owner of a blog may post an opinion, and if permitted, others may post their own thoughts on the same topic in response. Some blogs are restricted to allow only the owner to make postings, others allow moderated discussion, and still others are wide open. Thus a blog can be thought of not so much as a solitary diary, but more like a cross between a diary and an e-mail thread. A number of online tools allow authors to design, create, and maintain blogs. I use one called Blogger, at www.blogger.com, because I found it very easy to use and it provided me with the help I needed back when I knew nothing about blogs. Blogger.com is also free, which certainly helps, especially when you are just getting started. Of course, Blogger.com is by no means the only blogging tool; you can find a wide variety of available tools with a simple web search.

Exhibit 3.4 Sample Analysis of Prescription Drug Costs and Utilization within an Employee Population

156 A1 a1,1 . . . a1,m1 . . . . . . . . . A2 . . . a2,1 . . . a2,m2 . . . . . . An . . . . . . . . . an,1 . . .

(5.43)

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process, 2 transition, 146 inventory modeling, 206 inverse Gaussian density, 61, 104 MGF, 60 Kaplan Meier estimator de nition, 79 HIV transfusion data, 79 kernel density estimate, 223 comparison to exact, 223 comparison to saddlepoint, 224 M/G/1 queue, 235 kidney disease progression analytical solution, 44 Bayes predictive density, 108 Gibbs sampling, 109 likelihood construction, 190 maple code, 47 MGF, 21 pointwise prediction bounds, 109 saddlepoint approximation, 58 series model, 12 solved owgraph, 20 Kirkoff s Laws, 29, 30 Laplace transform, 12, 47 bilateral, 12, 249 exact inversion, maple, 250 Laplace s method, 103, 111 reliability repair model, 112 saddlepoint based, 111 likelihood approximate, 188 constructed, 188, 191 Bayesian, 189, 193 cellular telephone network, 229 diabetic retinopathy, 192 frequentist, 189 hydraulic pump system, 216 MLE, 193 M/M/3 queue, 229 diabetic retinopathy, 160 Markov model, 152 M/G/1 queue, 234 separable, 100 likelihood function, 90 Little s law, 210 loop de nition, 17 rst order, 36, 155, 182 higher order, 36 second order, 36, 182

Often labeled simply as middleware, the software infrastructure that supports a Grid is complex. Its architectural complexity increases when the network is elevated to the status of a first-class Grid-managed resource like other Grid resources, such as computation cycles and storage. This chapter avoids the use of the word middleware, because it is too vague for the topics discussed. It introduces definitions for Grid network services and Grid network infrastructure. It then profiles representative examples both for Grid infrastructure in general and for Grid network infrastructure specifically, while reviewing their salient characteristics. The chapter continues with a description of Grid network infrastructure components, such as network bindings, virtualization, access control and policy, and scheduling. The chapter concludes with the challenges and opportunities in federating multiple instances of Grid network infrastructures, each representing a different, independently managed network domain. Clearly, Grid network infrastructures are at an early developmental stage and predate interoperability standards. Although there are no firm foundations in these areas, the chapter attempts to highlight design points, characterize alternate views, and provide references to literature.

We can now prove that sticky sampling meets the goals in the de nition of the frequent items problem with probability at least 1 using space independent of n. Theorem 2 [51] For any , , (0, 1), with < , sticky sampling solves the frequent items problems with probability at least 1 using a sample of expected size (2/ ) log( 1 1 ). Proof. We rst note that the estimated frequency of a sample element x is an underestimate of the true frequency, that is, fe (x) f (x). Thus, if the true frequency is smaller than ( )n, the algorithm will not return x, since it must also be fe (x) < ( )n. We now prove that there are no false negatives with probability 1 . Let k be the number of elements with frequency at least , and let y1 , ..., yk be those elements. Clearly, it must be k 1/ . There are no false negatives if and only if all the elements y1 , ..., yk are returned by the algorithm. We now study the probability of the complementary event, proving that it is upper bounded by .

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