标题： RNA速度的数学II：算法方面 显示英文标题

标题： On the Mathematics of RNA Velocity II: Algorithmic Aspects

摘要： 在先前的论文[CSIAM Trans. Appl. Math. 2 (2021), 1-55]中，作者提出了一个理论框架，用于分析RNA速度，这是一个在单细胞RNA测序数据中揭示细胞状态转换动态过程的有前景的概念。本文致力于RNA速度工作流程中一些关键组件的算法研究。本文解决了四个重要问题：(1) 我们构建了一种合理的时间尺度固定方法，可以确定细胞的全局基因共享潜在时间。(2) 我们提出了一种不确定性量化策略，用于通过EM算法推断得到的参数。(3) 我们建立了相对于下游分析中样本量的速度核带宽选择的最优准则，并讨论了其意义。(4) 我们提出了一种沿细胞发育路径的两个细胞簇之间的时序距离估计方法。还进行了一些示例数值测试以验证我们的分析。这些结果旨在为未来RNA速度类型方法的发展提供工具和见解。 显示英文摘要

摘要： In a previous paper [CSIAM Trans. Appl. Math. 2 (2021), 1-55], the authors proposed a theoretical framework for the analysis of RNA velocity, which is a promising concept in scRNA-seq data analysis to reveal the cell state-transition dynamical processes underlying snapshot data. The current paper is devoted to the algorithmic study of some key components in RNA velocity workflow. Four important points are addressed in this paper: (1) We construct a rational time-scale fixation method which can determine the global gene-shared latent time for cells. (2) We present an uncertainty quantification strategy for the inferred parameters obtained through the EM algorithm. (3) We establish the optimal criterion for the choice of velocity kernel bandwidth with respect to the sample size in the downstream analysis and discuss its implications. (4) We propose a temporal distance estimation approach between two cell clusters along the cellular development path. Some illustrative numerical tests are also carried out to verify our analysis. These results are intended to provide tools and insights in further development of RNA velocity type methods in the future.