论文标题
使用拓扑数据分析量化不同的建模框架：具有斑马鱼模式的案例研究
Quantifying different modeling frameworks using topological data analysis: a case study with zebrafish patterns
论文作者
论文摘要
数学模型在生物学应用中有多种形式。在复杂，空间动力学和模式形成的情况下，随机模型也面临两个主要挑战：模式数据在很大程度上是定性的，模型实现可能会有很大的变化。这些问题共同使模型和经验数据（甚至模型）很难限制如何将不同的方法组合在一起以提供对生物学的新见解。这些挑战还引发了有关模型如何相关的数学问题，因为解决了相同问题的替代方法 - 例如蜂窝potts模型；基于代理的模型非现场模型；现场，细胞自动机模型；和连续性方法 - 以不同的方式处理不确定性并实施细胞行为。为了帮助在此类问题上打开未来工作的大门，在这里，我们将方法从拓扑数据分析和计算几何形状中调整为定量以公平的，可比的方式定量相同的同一生物过程模型。为了集中工作并说明具体挑战，我们关注斑马鱼皮模式形成的示例，并将基于代理和蜂窝自动机模型引起的模式相关联。
Mathematical models come in many forms across biological applications. In the case of complex, spatial dynamics and pattern formation, stochastic models also face two main challenges: pattern data is largely qualitative, and model realizations may vary significantly. Together these issues make it difficult to relate models and empirical data -- or even models and models -- limiting how different approaches can be combined to offer new insights into biology. These challenges also raise mathematical questions about how models are related, since alternative approaches to the same problem -- e.g., cellular Potts models; off-lattice, agent-based models; on-lattice, cellular automaton models; and continuum approaches -- treat uncertainty and implement cell behavior in different ways. To help open the door to future work on questions like these, here we adapt methods from topological data analysis and computational geometry to quantitatively relate two different models of the same biological process in a fair, comparable way. To center our work and illustrate concrete challenges, we focus on the example of zebrafish-skin pattern formation, and we relate patterns that arise from agent-based and cellular automaton models.
