标题： 基因组的拓扑序列分析：类别方法 显示英文标题

标题： Topological Sequence Analysis of Genomes: Category Approaches

摘要： 序列数据，如DNA、RNA和蛋白质序列，表现出复杂的多尺度结构，这对传统分析方法构成了重大挑战，特别是那些依赖于比对或纯统计表示的方法。 在本工作中，我们引入了基于类别的基因组拓扑序列分析（CTSA）。 CTSA将序列建模为分辨率范畴，通过范畴构造捕捉其层次结构。 然后从这种范畴表示中推导出子结构复形，并计算其持续同调性以提取多尺度拓扑特征。 我们的模型通过融入基于序列拓扑的结构化数学形式，区别于传统的无比对方法。 所产生的拓扑签名在各种任务中提供了有信息量的表示，包括SARS-CoV-2变体的系统发育分析和蛋白质-核酸结合亲和力的预测。 与六种最先进的方法进行了比较研究。 实验结果表明，CTSA在这些任务中表现出色且一致，表明其具有广泛的适用性和鲁棒性。 除了序列分析外，所提出的框架为范畴理论和同调理论在生物序列分析中的整合开辟了新的方向。 显示英文摘要

摘要： Sequence data, such as DNA, RNA, and protein sequences, exhibit intricate, multi-scale structures that pose significant challenges for conventional analysis methods, particularly those relying on alignment or purely statistical representations. In this work, we introduce category-based topological sequence analysis (CTSA ) of genomes. CTSA models a sequence as a resolution category, capturing its hierarchical structure through a categorical construction. Substructure complexes are then derived from this categorical representation, and their persistent homology is computed to extract multi-scale topological features. Our models depart from traditional alignment-free approaches by incorporating structured mathematical formalisms rooted in sequence topology. The resulting topological signatures provide informative representations across a variety of tasks, including the phylogenetic analysis of SARS-CoV-2 variants and the prediction of protein-nucleic acid binding affinities. Comparative studies were carried out against six state-of-the-art methods. Experimental results demonstrate that CTSA achieves excellent and consistent performance in these tasks, suggesting its general applicability and robustness. Beyond sequence analysis, the proposed framework opens new directions for the integration of categorical and homological theories for biological sequence analysis.