发表机构
Russian Clinical Research Center of Gerontology; Pirogov Russian National Research Medical University; Russian Academy of Sciences; Kabardino-Balkarian Scientific Center; Institute of Applied Mathematics and Automation（俄罗斯老年学临床研究中心; 皮罗戈夫俄罗斯国立研究医科大学; 俄罗斯科学院; 卡巴尔达-巴尔卡尔科学中心; 应用数学与自动化研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对异构数据集的对角多组学整合问题，分析生物异质性处理方法，研究复欧氏空间中同胚于Stiefel流形的集合上耦合拉普拉斯算子的极值迹问题，提出基于极值点差值范数的数据集异质性新特征。
AI 中文摘要
本文研究异构数据集的对角多组学整合方法，分析并开发多种生物异质性处理方法以更清晰地理解产生的差异；具体研究复欧氏空间中嵌入的同胚于Stiefel流形的集合上耦合拉普拉斯算子的极值迹问题，从经典泛函分析角度阐述该最大化问题的梯度上升方法，该方法本身具有重要意义；在此基础上，通过利用最大值点与最小值点差值的范数，引入一种新的数据集异质性特征。
英文摘要
In this paper, we consider methods for the diagonal multi-omics integration of heterogeneous datasets. Several approaches to the nature of biological heterogeneity are analyzed and developed to comprehend more clearly the generated differences. Specifically, the extremal trace problems for the coupled Laplacian on sets homeomorphic to the Stiefel manifold embedded in the complex Euclidean space are investigated. The gradient ascent method for the maximization problem is elaborated in the classical terms of functional analysis, which is of significant interest in itself. On this basis, we introduce a novel characteristic of dataset heterogeneity by employing the norm of the difference between the maximum and minimum points.
