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首页> 外文期刊>Journal of Bioinformatics and Computational Biology >A RECURSIVE METHOD FOR SOLVING HAPLOTYPE FREQUENCIES WITH APPLICATION TO GENETICS
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A RECURSIVE METHOD FOR SOLVING HAPLOTYPE FREQUENCIES WITH APPLICATION TO GENETICS

机译：一种求解表型频率的递归方法在遗传学中的应用

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摘要

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(n2n) operations and the memory requirement is of O(2n) locations for the 2n-by-2n 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.
机译：随着生物学实验的先进发展，多基因座分析已变得流行。许多研究集中在这种多基因座分析的生物学和统计特性上。在本文中，我们研究了一个重要的计算问题：从大型线性系统Ax = b中求解单基因型类别的概率，该线性系统是从多个基因座分析中的重组事件得出的。由于重组矩阵A的大小相对于基因座数呈指数增长，因此需要快速求解器来处理分析中的大量基因座。通过利用矩阵A的良好结构，我们开发了一种有效的递归算法来求解这种结构化线性系统。特别是，针对n个基因座问题的算法的复杂度为O（n2n）个运算，而内存需求为2n x 2n矩阵A的O（2n）个位置。给出了数值示例来证明其有效性。我们高效的求解器。最后，我们应用我们提出的方法来分析Hapmap数据中一组单核苷酸多态性（SNP）的单倍型类别。

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