Download or read book Pooling Designs with Geometry of Classical Gropus and Random Pooling Designs on Complexex written by James Yu and published by . This book was released on 2009 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Group testing techniques have been in existence for decades. However, recent applications of group testing to molecular biology experiments and DNA library screening in particular have attracted many attentions and revived people's interest in non-adaptive group testing now often known as pooling designs. These molecular biology applications are revolutionizing modern medicine and having a major impact on science and society today. Due to their unique characteristics, these applications have brought forward a new set of problems for group testing to tackle and many challenges for group testing theory to face. As a result, many efforts have been spent in recent years in search of efficient error-tolerant pooling designs, which are of great importance to molecular biology applications. An interesting class of deterministic pooling designs discovered in recent years is based on the inclusion properties of certain mathematical structures. The general framework for these structures is known as pooling space. The pooling designs from pooling spaces exhibit great potential because of their simplicity and the wide range of design parameters they can handle. However, these designs often suffer from low test efficiencies. We give three new error-tolerant pooling designs in this category using concepts from geometry of classical groups over finite fields and give v proof of the correctness and error-tolerance of these designs. We use different types of spaces and subspace in the pooling design to improve the test efficiencies. A comparative study with several existing pooling designs found in the literature shows that our new constructions have improved test efficiencies. In addition, we present three error-tolerant random trivial two-stage pooling designs for complexes and prove the correctness of these designs. The pooling design for complexes has important applications in drug discovery and other biology experiments. We propose the concepts of almost separable and almost disjunct matrices. By intersecting a random matrix with the complements of these almost separating matrices, we construct the random pooling designs for complexes. Correctness proofs are given for the decoding algorithms. The expected values are derived for these designs to detect any complexes.