Title: Quantifying topological features and irregularities in zebrafish patterns using the sweeping-plane filtration Show Chinese title

Title: 使用扫平面过滤方法量化斑马鱼图案中的拓扑特征和不规则性

Abstract: Complex patterns emerge across a wide range of biological systems. While such patterns often exhibit remarkable robustness, variation and irregularity exist at multiple scales and can carry important information about the underlying agent interactions driving collective dynamics. Many methods for quantifying biological patterns focus on large-scale, characteristic features (such as stripe width or spot number), but questions remain on how to characterize messy patterns. In the case of cellular patterns that emerge during development or regeneration, understanding where patterns are most susceptible to variability may help shed light on cell behavior and the tissue environment. Motivated by these challenges, we introduce methods based on topological data analysis to classify and quantify messy patterns arising from agent-based interactions, by extracting meaningful biological interpretations from persistence barcode summaries. To compute persistent homology, our methods rely on a sweeping-plane filtration which, in comparison to the Vietoris--Rips filtration, is more rarely applied to biological systems. We demonstrate how results from the sweeping-plane filtration can be interpreted to quantify stripe patterns (with and without interruptions) by analyzing in silico zebrafish skin patterns, and we generate new quantitative predictions about which pattern features may be most robust or variable. Our work provides an automated framework for quantifying features and irregularities in spot and stripe patterns and highlights how different approaches to persistent homology can provide complementary insight into biological systems. Show Chinese abstract

Abstract: 在广泛的生物系统中会出现复杂的模式。 尽管这些模式通常表现出显著的鲁棒性，但在多个尺度上仍存在变异和不规则性，并可能包含有关驱动集体动态的底层代理相互作用的重要信息。 许多用于量化生物模式的方法关注于大尺度、特征性特征（如条纹宽度或斑点数量），但对于如何描述杂乱的模式仍存在疑问。 在发育或再生过程中出现的细胞模式的情况下，了解模式在何处最容易受到变异影响，可能有助于揭示细胞行为和组织环境。 受这些挑战的启发，我们引入了基于拓扑数据分析的方法，通过从持久性条形码摘要中提取有意义的生物学解释，对由代理交互产生的杂乱模式进行分类和量化。 为了计算持久同调性，我们的方法依赖于一种扫平面过滤器，与 Vietoris--Rips 过滤器相比，这种过滤器在生物系统中较少被应用。 我们展示了如何解释扫平面过滤器的结果，以量化条纹模式（有或没有中断），通过对计算机模拟的斑马鱼皮肤模式进行分析，并生成关于哪些模式特征可能最稳健或最易变的新定量预测。 我们的工作提供了一个自动化的框架，用于量化斑点和条纹模式中的特征和不规则性，并突显了不同的持久同调性方法如何为生物系统提供互补的见解。