title: A construction of pooling designs with some happy surprises.
abstract: The screening of data sets for "positive data objects" is essential to modern technology. A (group) test that indicates whether a positive data object is in a specific subset or pool of the dataset can greatly facilitate the identification of all the positive data objects. A collection of tested pools is called a pooling design. Pooling designs are standard experimental tools in many biotechnical applications. In this paper, we use the (linear) subspace relation coupled with the general concept of a "containment matrix" to construct pooling designs with surprisingly high degrees of error correction (detection.) Error-correcting pooling designs are important to biotechnical applications where error rates often are as high as 15%. What is also surprising is that the rank of the pooling design containment matrix is independent of the number of positive data objects in the dataset.
authors.affiliation: Department of Probability Theory, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia. agd-msu@yandex.ru
authors.forename: A
authors.initials: A
authors.lastname: D'Yachkov
authors.forename: Frank
authors.initials: F
authors.lastname: Hwang
authors.forename: Antony
authors.initials: A
authors.lastname: Macula
authors.forename: Pavel
authors.initials: P
authors.lastname: Vilenkin
authors.forename: Chih-Wen
authors.initials: CW
authors.lastname: Weng
mesh_terms: D019295:Computational Biology / Q000379:methods*; D004247:DNA / Q000032:analysis*; D015342:DNA Probes; D015698:Genomic Library; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical
chemical_list: D015342:DNA Probes; D004247:DNA