+1 914 945 3000 apte, ebibeln, nramesh, pednault, fateh @us.ibm.corn ABSTRACTFingerhut Business Intelligence (BI) has a long and successful history of building statistical models to predict consumer behavior. The models constructed are typically segmentationbased models in which the target audience is split into subpopulations (i.e., customer segments) and individually tailored statistical models are then developed for each segment. Such models are commonly employed in the direct-mail industry; however, segmentation is often performed on an ad-hoc basis without directly considering how segmentation affects the accuracy of the resulting segment models. Fingerhut BI approached IBM Research with the problem of how to build segmentation-based models more effectively so as to maximize predictive accuracy. The IBM Advanced Targeted MarketingSingle Events TM (IBM ATM-SE TM) solution is the result of IBM Research and Fingerhut BI directing their efforts jointly towards solving this problem. This paper presents an evaluation of ATM-SE's modeling capabilities using data from Fingerhut's catalog mailings.

Fingerhut mails up to 120 catalogs per year to each of its 7 million customers. With this dense mail plan and mailing decisions made independently for each catalog, many customers were receiving redundant and unproductive catalogs. To identify and eliminate this excessive operational expense, IBM and Fingerhut together developed an optimization system that selects the most profitable sequence of catalogs, called a mail stream, for each customer. With mail streams, Fingerhut makes better mailing decisions at the customer level, resulting in increased profits. Today, Fingerhut runs this application weekly to find the most profitable mail stream for each customer.

In this work we propose a new algorithm for the computation of statistical equilibrium quantities on a cubic lattice when both an energy and a statistical temperature are involved. We demonstrate that the pivot algorithm used in situations such as protein folding works well for a small range of temperatures near the polymeric case, but it fails in other situations. The new algorithm, using localized transformations, seems to perform well for all possible temperature values. Having reliably approximated the values of equilibrium energy, we also propose an efficient way to compute equilibrium entropy for all temperature values. We apply the algorithms in the context of suction or supercritical vortices in a tornadic flow, which are approximated by vortex filaments on a cubic lattice. We confirm that supercritical (smooth, "straight") vortices have the highest energy and correspond to negative temperatures in this model. The lowest-energy configurations are folded up and "balled up" to a great extent. The results support A. Chorin's findings that, in the context of supercritical vortices in a tornadic flow, when such high-energy vortices stretch, they need to fold.

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