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particular algorithms assume, in effect, that arithmetic operations are of in nite precision (This is not the same as assuming that the inputs are of in nite length) To illustrate this point, consider the following algorithm for computing the average of n of numbers: SumSimple(S) x=0 for i = 1 to n { x = x + S[i] } x = x/n; return(x); Although this is a correct and ef cient algorithm, it does not lend itself particularly well to accurate implementation in current standard computer languages For example, suppose that the input S[i] was produced by the function S[i] = i 2 ; then x grows in magnitude at every iteration while S[i] shrinks.

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Knowledge networks depend for their success on the right social environment. We have worked within many such respectful, trusting, nurturing, and educational social environments, and those experiences have led us to write this book. We both spent many years learning together with hundreds of others in building a small, self-sufficient community in Tennessee. We applied what we learned in that challenging social experiment to the work we did in the early days of our first online communities at The WELL and Women.com. The members of those communities showed us the value of lowering the communications boundaries between management and customers. In those and in subsequent positions at AOL, Digital City, Salon.com, and PlanetRX, we observed the value of informal knowledge sharing through the Net. And so we thank the innumerable people we worked with and did our best to serve for being our teachers in collaboration in those virtual but still very personal environments. We would not have traveled our respective paths toward community interaction were it not for the support and example of our families. And so we each acknowledge their parts in our development as leaders who look for the ways in which people agree rather than ways in which they disagree. Nancy: I want to thank my mother and father, Bill and Dorothy Gerard, who have always exemplified the essential best practices of granting people the benefit of the doubt regardless of age, race, gender, or social standing. I have learned from them that 99 percent of the time people not only prove worthy of

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Be upfront with your customers. Make it clear when you are collecting data and what you will use it for. Post a comprehensive statement about your corporate privacy policy on your home page. Remind visitors about your policy whenever they disclose additional information. This low-cost disclosure presents a real opportunity to do well by being good. Enable access. Let customers see their pro les and, where possible, view the data that you have collected. Allow them to edit their pro les or even opt out of your database. Few companies do this today, largely because the most commonly used personalization and content management software do not support it (IBM and NCR have made headway on creating this next generation of software). Give your customers a reason to share data. You can overcome discomfort about disclosing personal data with incentives such as loyalty points, access to more information or personalized sites, or special discounts. Provide customers with good reasons for volunteering information.

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In the idealized human genetics research of the past, individual professors worked with families that suffered from a high incidence of a particular disease, searching for genetic links that would allow testing for, and, it was hoped, ultimately prevention or treatment for, that family s genetic disease The professors were motivated by altruism, the families hoped, ultimately, for prevention of or treatment for that family s genetic disease This picture was never entirely true Pharmaceutical companies, and then biotechnology rms, have long played some role in genetic research Professors, even the most idealistic, no doubt were interested in research not just for altruism but for tenure, grants, and the Nobel Prize And research subjects often would receive small cash payments for travel or other expenses However accurate the idealistic picture may once have been, it clearly is much less common today.

In cases like this, implementations of the SumSimple algorithm exhibit signi cant round-off error, because small numbers added to large numbers tend to drop off the end of the addition operator s precision and fail to contribute to the sum (see Higham 2002, pp 14 17) (For a precise explanation of the mechanics of rounding error, see Section 2421) Altering the algorithm to sort S before summing reduces rounding error and leads to more accurate results (This is generally true, not true only for the previous example) Applying this concept, we can create a wrapper algorithm, given by SumAccurate(S) Sort(S) return(SumSimple(S)); Concerning the overall purpose of accuracy in computer implementations, Wilkinson (1994) claims that [t]he results matter more than the algorithm There is certainly some truth in this simpli cation Implementation matters.

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