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The use of combinatorial chemistry has become commonplace within the pharmaceutical industry. Less widespread but gaining in popularity is the derivation of activity models from the high-throughput assays of these libraries. Such models are then used as filters during the design of refined daughter libraries. The design of these second generation libraries,… (More)

This paper describes methods for counting the number of non-negative integer solutions of the system Ax = b when A is a non-negative totally unimodular matrix and b an integral vector of fixed dimension. The complexity (under a unit cost arithmetic model) is strong in the sense that it depends only on the dimensions of A and not on the size of the entries… (More)

- William Gasarch, Joesph P S Kung, Gian-Carlo Rota, Catherine H Yan Review, John Mount, Hsu +1 other
- 2010

In this column we review the following books. Can you really use analytic techniques in combinatorics? Yes! And this book tells you how! More than that-it takes the informal term Analytic Combinatorics and defines the term and the field. How did Rota do combinatorics? He tried to refine mere tricks into general techniques. This book shows combinatorics as a… (More)

- David Bruce Wilson, Richard P Stanley, David Aldous, Henry Cohn, Persi Diaconis, Jim Fill +7 others
- 2007

Random sampling has found numerous applications in computer science, statistics, and physics. The most widely applicable method of random sampling is to use a Markov chain whose steady state distribution is the probability distribution r from which we wish to sample. After the Markov chain has been run for long enough, its state is approximately distributed… (More)

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