{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,29]],"date-time":"2022-03-29T14:26:54Z","timestamp":1648564014919},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Bioinform. Comput. Biol."],"published-print":{"date-parts":[[2006,12]]},"abstract":"<jats:p> Multiple loci analysis has become popular with the advanced developments in biological experiments. A lot of studies have been focused on the biological and the statistical properties of such multiple loci analysis. In this paper, we study one of the important computational problems: solving the probabilities of haplotype classes from a large linear system Ax = b derived from the recombination events in multiple loci analysis. Since the size of the recombination matrix A increases exponentially with respect to the number of loci, fast solvers are required to deal with a large number of loci in the analysis. By exploiting the nice structure of the matrix A, we develop an efficient recursive algorithm for solving such structured linear systems. In particular, the complexity of the proposed algorithm for the n loci problem is of O(n2<jats:sup>n<\/jats:sup>) operations and the memory requirement is of O(2<jats:sup>n<\/jats:sup>) locations for the 2<jats:sup>n<\/jats:sup>-by-2<jats:sup>n<\/jats:sup> matrix A. Numerical examples are given to demonstrate the effectiveness of our efficient solver. Finally, we apply our proposed method to analyze the haplotype classes for a set of single nucleotides polymorphisms (SNPs) from Hapmap data. <\/jats:p>","DOI":"10.1142\/s0219720006002454","type":"journal-article","created":{"date-parts":[[2007,1,23]],"date-time":"2007-01-23T11:41:58Z","timestamp":1169552518000},"page":"1269-1285","source":"Crossref","is-referenced-by-count":0,"title":["A RECURSIVE METHOD FOR SOLVING HAPLOTYPE FREQUENCIES WITH APPLICATION TO GENETICS"],"prefix":"10.1142","volume":"04","author":[{"given":"MICHAEL K.","family":"NG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China"}]},{"given":"ERIC S.","family":"FUNG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China"}]},{"given":"YIU-FAI","family":"LEE","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China"}]},{"given":"WAI-KI","family":"CHING","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong, China"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1994.tb00725.x"},{"key":"rf2","volume-title":"Matrix Computations","author":"Golub G.","year":"1989"},{"key":"rf3","first-page":"299","volume":"8","author":"Haldane J. B. S.","journal-title":"Journal of Genetic"},{"key":"rf4","first-page":"1212","volume":"56","author":"Kruglyak L.","journal-title":"American Journal of Human Genetics"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1943.tb02321.x"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0040-5809(84)90013-3"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-185X.1938.tb00516.x"},{"key":"rf8","volume-title":"Statistics in Human Genetics","author":"Sham P.","year":"1998"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1111\/j.1469-1809.1976.tb00175.x"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1159\/000154123"},{"key":"rf11","first-page":"255","volume":"47","author":"Zhao L. P.","journal-title":"American Journal of Human Genetics"}],"container-title":["Journal of Bioinformatics and Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219720006002454","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T02:44:25Z","timestamp":1565145865000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219720006002454"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,12]]},"references-count":11,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2006,12]]}},"alternative-id":["10.1142\/S0219720006002454"],"URL":"https:\/\/doi.org\/10.1142\/s0219720006002454","relation":{},"ISSN":["0219-7200","1757-6334"],"issn-type":[{"value":"0219-7200","type":"print"},{"value":"1757-6334","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,12]]}}}