Title: A symmetry-inclusive algebraic approach to genome rearrangement Show Chinese title

Title: 包含对称性的代数方法用于基因组重排

Abstract: Of the many modern approaches to calculating evolutionary distance via models of genome rearrangement, most are tied to a particular set of genomic modelling assumptions and to a restricted class of allowed rearrangements. The "position paradigm", in which genomes are represented as permutations signifying the position (and orientation) of each region, enables a refined model-based approach, where one can select biologically plausible rearrangements and assign to them relative probabilities/costs. Here, one must further incorporate any underlying structural symmetry of the genomes into the calculations and ensure that this symmetry is reflected in the model. In our recently-introduced framework of {\em genome algebras}, each genome corresponds to an element that simultaneously incorporates all of its inherent physical symmetries. The representation theory of these algebras then provides a natural model of evolution via rearrangement as a Markov chain. Whilst the implementation of this framework to calculate distances for genomes with `practical' numbers of regions is currently computationally infeasible, we consider it to be a significant theoretical advance: one can incorporate different genomic modelling assumptions, calculate various genomic distances, and compare the results under different rearrangement models. The aim of this paper is to demonstrate some of these features. Show Chinese abstract

Abstract: 在许多通过基因组重排模型计算进化距离的现代方法中，大多数都与特定的基因组建模假设相关，并且仅限于一类允许的重排。 "位置范式"中，基因组被表示为排列，表明每个区域的位置（和方向），这使得可以采用一种更精细的基于模型的方法，其中可以选择生物学上合理的重排并为其分配相对概率/成本。 在这里，必须进一步将基因组的任何潜在结构对称性纳入计算，并确保这种对称性反映在模型中。 在我们最近引入的{\em 基因组代数}框架中，每个基因组对应一个同时包含其所有固有物理对称性的元素。 这些代数的表示理论然后提供了一种通过重排进行进化的自然模型，即马尔可夫链。 尽管目前将此框架应用于具有“实际”区域数的基因组计算距离在计算上不可行，但我们认为这是一个重要的理论进展：可以纳入不同的基因组建模假设，计算各种基因组距离，并在不同的重排模型下比较结果。 本文的目的是展示其中的一些特性。