论文标题
遗传比对的算术拓扑
The arithmetic topology of genetic alignments
论文作者
论文摘要
我们提出了一种新的数学范式，用于研究序列比对的遗传变异。该框架起源于扩展成对关系的概念，该框架基于当前的分析基于k-ary差异。这种差异自然会通过与边界运算符兼容的权重来赋予简单复合物的概括。我们介绍了K-Stances和Intiquility Complex的概念，前者封装了算术以及表达这些Kary关系的拓扑结构。我们研究了差异复合物的基本数学特性，并显示了这种方法如何在SARS-COV-2和H1N1流感基因组数据的背景下捕获全新的生物学相关病毒动力学层。
We propose a novel mathematical paradigm for the study of genetic variation in sequence alignments. This framework originates from extending the notion of pairwise relations, upon which current analysis is based on, to k-ary dissimilarity. This dissimilarity naturally leads to a generalization of simplicial complexes by endowing simplices with weights, compatible with the boundary operator. We introduce the notion of k-stances and dissimilarity complex, the former encapsulating arithmetic as well as topological structure expressing these k-ary relations. We study basic mathematical properties of dissimilarity complexes and show how this approach captures an entirely new layer of biologically relevant viral dynamics in the context of SARS-CoV-2 and H1N1 flu genomic data.
