基因组重排模型的一种新的代数方法
A new algebraic approach to genome rearrangement models
摘要：
我们提出了一个统一的框架，在基因组代数建模基因组及其重排，同时将所有的物理对称性的元素。建立在以前的工作，利用对称群的群代数，我们明确地构建了无符号的圆形基因组二面角对称的情况下的基因组代数，并表明，基因组重排距离的最大似然估计（MLE），可以有效地和更有效地进行在这种设置。然后，我们构建的基因组代数更一般的情况下，也就是说，基因组，可以表示为任意组和对称群的元素，并表明，MLE计算可以完全在这个框架内进行。在这个框架中没有规定的模型;也就是说，它允许任何保留区域集合的重排选择，以及任意的权重。此外，由于似然函数是从路径概率（路径计数的概括）构建的，因此该框架可以用于基于路径概率的任何距离度量。
英文摘要：
We present a unified framework for modelling genomes and their rearrangements in a genome algebra, as elements that simultaneously incorporate all physical symmetries. Building on previous work utilising the group algebra of the symmetric group, we explicitly construct the genome algebra for the case of unsigned circular genomes with dihedral symmetry and show that the maximum likelihood estimate (MLE) of genome rearrangement distance can be validly and more efficiently performed in this setting. We then construct the genome algebra for a more general case, that is, for genomes that may be represented by elements of an arbitrary group and symmetry group, and show that the MLE computations can be performed entirely within this framework. There is no prescribed model in this framework; that is, it allows any choice of rearrangements that preserve the set of regions, along with arbitrary weights. Further, since the likelihood function is built from path probabilities -- a generalisation of path counts -- the framework may be utilised for any distance measure that is based on path probabilities.
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