Dory：克服计算持久同源性的障碍
Dory: Overcoming Barriers to Computing Persistent Homology
摘要：
持久同调（PH）是一种拓扑数据分析（TDA）方法，它计算高维数据的多尺度拓扑不变特性，这些特性对噪声具有鲁棒性。虽然PH在各种应用中揭示了有用的模式，但计算要求将应用限制在几千个点的小数据集上。我们提出了多莉，一个有效的和可扩展的算法，可以计算持久的同源性的大型数据集。Dory使用的内存比已发布的算法少得多，并且与大多数算法相比，计算时间也大大减少。它可以扩展到处理数百万个点的数据集。作为一个应用程序，我们计算的PH值的人类基因组在高分辨率所揭示的全基因组Hi-C数据集。结果显示，人类基因组的拓扑结构在用生长素（一种降解粘附素的分子）处理后发生了显着变化，证实了粘附素在DNA环形成中起关键作用的假设。
英文摘要：
Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patterns across various applications, computational requirements have limited applications to small data sets of a few thousand points. We present Dory, an efficient and scalable algorithm that can compute the persistent homology of large data sets. Dory uses significantly less memory than published algorithms and also provides significant reductions in the computation time compared to most algorithms. It scales to process data sets with millions of points. As an application, we compute the PH of the human genome at high resolution as revealed by a genome-wide Hi-C data set. Results show that the topology of the human genome changes significantly upon treatment with auxin, a molecule that degrades cohesin, corroborating the hypothesis that cohesin plays a crucial role in loop formation in DNA.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
