Searching Genome-Wide Multi-Locus Associations for Multiple Diseases Based on Bayesian Inference.

Taking the advantage of high-throughput single nucleotide polymorphism (SNP) genotyping technology, large genome-wide association studies (GWASs) have been considered to hold promise for unraveling complex relationships between genotypes and phenotypes. Current multi-locus-based methods are insufficient to detect interactions with diverse genetic effects on multifarious diseases. Also, statistic tests for high-order epistasis ( ≥ 2 SNPs) raise huge computational and analytical challenges because the computation increases exponentially as the growth of the cardinality of SNPs combinations.

On the parameterized complexity of pooling design.

Pooling design is a very helpful tool for reducing the number of tests in DNA library screening, which is a key process to obtain high-quality DNA libraries for studying gene functions. Three basic problems in pooling design are, given an m x n binary matrix and a positive integer d, to decide whether the matrix is d-separable (d-separable, or d-disjunct). The three problems are all known to be coNP-complete.

New constructions of one- and two-stage pooling designs.

The study of gene functions requires a DNA library of high quality, such a library is obtained from a large mount of testing and screening. Pooling design is a very helpful tool for reducing the number of tests for DNA library screening. In this paper, we present new one- and two-stage pooling designs, together with new probabilistic pooling designs.

Identifying d positive clones in the presence of inhibitors.

Farach et al. introduced the inhibitor model in pooling design, where existence of a single inhibitor clone in a pool dictates its outcome to be negative regardless of the existence of positive clones in the pool. Various sequential or multiround pooling designs have been given to identify all the positive clones under the inhibitor model.

Efficient constructions of disjunct matrices with applications to DNA library screening.

The study of gene functions requires a DNA library of high quality, such a library is obtained from a large mount of testing and screening. Pooling design is a very helpful tool for reducing the number of tests for DNA library screening. In this paper, we present two Las Vegas algorithms for efficient constructions of d-disjunct and (d ; z)-disjunct matrices respectively.

New construction for transversal design.

The study of gene functions requires the development of a DNA library of high quality through much of testing and screening. Pooling design is a mathematical tool to reduce the number of tests for DNA library screening. The transversal design is a special type of pooling design, which is good in implementation.