Alexeev Nikita, Zograf Peter
1 Chebyshev Laboratory, St. Petersburg State University , St. Petersburg, Russia .
J Comput Biol. 2014 Aug;21(8):622-31. doi: 10.1089/cmb.2013.0066. Epub 2014 Mar 20.
The cycle graph introduced by Bafna and Pevzner is an important tool for evaluating the distance between two genomes, that is, the minimal number of rearrangements needed to transform one genome into another. We interpret this distance in topological terms and relate it to the random matrix theory. Namely, the number of genomes at a given 2-break distance from a fixed one (the Hultman number) is represented by a coefficient in the genus expansion of a matrix integral over the space of complex matrices with the Gaussian measure. We study generating functions for the Hultman numbers and prove that the two-break distance distribution is asymptotically normal.
Bafna和Pevzner引入的循环图是评估两个基因组之间距离的重要工具，即把一个基因组转化为另一个基因组所需的最小重排数。我们从拓扑学角度解释这个距离，并将其与随机矩阵理论联系起来。具体而言，与固定基因组具有给定2断点距离的基因组数量（Hultman数）由在具有高斯测度的复矩阵空间上的矩阵积分的亏格展开中的一个系数表示。我们研究Hultman数的生成函数，并证明2断点距离分布渐近正态。
