Title Pooling designs and nonadaptive group testing : important tools for DNA sequencing / Ding-Zhu Du, Frank K. Hwang

Published New Jersey : World Scientific, ©2006

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Description 1 online resource (ix, 237 pages) : illustrations Series Series on applied mathematics ; v. 18 Series on applied mathematics ; v. 18. Contents Ch. 1. Introduction. 1.1. Group testing. 1.2. Nonadaptive group testing. 1.3. Applications in molecular biology. 1.4. Pooling designs for two simple applications. 1.5. Pooling designs and mathematics. 1.6. An outline of the book. References -- ch. 2. Basic theory on separating matrices. 2.1. d-Separable and d-separable matrices. 2.2. d-disjunct matrices. 2.3. The minimum number of pools for given d and n. 2.4. Combinatorial bounds for d-disjunct matrices with constant weight. 2.5. Asymptotic lower and upper bounds. 2.6. (d, r)-disjunct matrices. 2.7. Error-tolerance. References -- ch. 3. Deterministic designs. 3.1. t-designs and t-packing. 3.2. Direct construction. 3.3. Explicit construction of selectors. 3.4. Grid designs. 3.5. Error-correcting code. 3.6. Transversal designs. 3.7. The d = 2 case. References -- ch. 4. Deterministic designs from partial orders. 4.1. Subset containment designs. 4.2. Partial order of faces in a simplicial complex. 4.3. Monotone graph properties. 4.4. Partial order of linear spaces over a finite field. 4.5. Atomic poset. References -- ch. 5. Random pooling designs and probabilistic analysis. 5.1. Introduction to random designs. 5.2. A general approach to compute probabilities of unresolved clones. 5.3. Random incidence designs. 5.4. Random k-set designs. 5.5. Random r-size designs. 5.6. Random distinct k-set designs. 5.7. Intersection pooling designs. 5.8. Subset containment designs in extended use. 5.9. Edge-representative decoding with r = 2 and d = 3. 5.10. Some trivial 2-stage pooling designs. References -- ch. 6. Pooling designs on complexes. 6.1. Introduction. 6.2. A construction of (H : d; z)-disjunct matrix. 6.3. (d, r; z]-disjunct matrix. 6.4. Constructions for (d, r; z]-disjunct matrices. 6.5. Random designs. 6.6. Trivial two-stage pooling designs for complete r-graphs. 6.7. Sequential algorithms for H[symbol]. References -- ch. 7. Contig sequencing. 7.1. Introduction. 7.2. Some probability analysis of a k-subset. 7.3. Sequential algorithms. 7.4. Nonadaptive algorithms for matching. 7.5. The 3-stage procedure. References -- ch. 8. The inhibitor model. 8.1. Introduction. 8.2. 1-round algorithm. 8.3. Sequential and k-round algorithms. 8.4. Some other inhibitor models. References -- ch. 9. Hyperplane designs. 9.1. Introduction. 9.2. m-dimensional arrays. 9.3. A K[symbol] x K[symbol] decomposition of K[symbol]. 9.4. Efficiency. 9.5. Other transversal designs. 9.6. Two recent applications. References -- ch 10. Non-unique probe selection. 10.1. Introduction. 10.2. Complexity of pooling designs. 10.3. Complexity of minimum pooling designs. 10.4. Approximations of minimum pooling designs. References Bibliography Includes bibliographical references and index Notes Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL Print version record Subject Molecular biology -- Mathematics Nucleotide sequence -- Mathematics Combinatorial group theory. Mathematical models. Sequence Analysis, DNA -- methods Models, Theoretical mathematical models. SCIENCE -- Life Sciences -- Genetics & Genomics. Mathematical models Combinatorial group theory Molecular biology -- Mathematics Nucleotide sequence -- Mathematics Form Electronic book Author Hwang, Frank. LC no. 2006046417 ISBN 9789812773463 9812773460 9789812568229 9812568220

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