Pooling Design and Nonadaptive Group Testing Important Tools for DNA Sequencing Series on Applied Mathematics Series on Applied Mathematics 1st Edition by Dingzhu Du, Frank K Hwang ISBN 978-9812568229 9812568220
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Product details:
ISBN 10: 9812568220
ISBN 13: 978-9812568229
Author: Dingzhu Du, Frank K Hwang
Table of contents:
Chapter 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
Chapter 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
Chapter 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 d2 Case
References
Chapter 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
Chapter 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 r2 and d = 3
5.10 Some Trivial 2-Stage Pooling Designs
References
Chapter 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
References
Chapter 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
Chapter 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
Chapter 9 Hyperplane Designs
9.1 Introduction
9.2 m-Dimensional Arrays
9.3 A K, x K. Decomposition of Kn
9.4 Efficiency
9.5 Other Transversal Designs
9.6 Two Recent Applications
References
Chapter 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
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Tags: Dingzhu Du, Frank K Hwang, Pooling Design, Nonadaptive Group, Important Tools