使用时变持续同调的函数假设检验检测集体运动状态间的转变
Detecting transitions between collective motion regimes using functional hypothesis test of the time-varying persistence homology
AI总结：
本研究针对自驱粒子从非相干到相干态的集体运动转变时间问题，提出基于持续同调的函数假设检验方法定位转变时刻，在自驱粒子模型上验证后用于分析细胞运动的状态转变。
摘要：
在由大量相似自驱实体（如鸟群、鱼群、细胞和分子）组成的系统中，个体与邻近个体的相互作用可形成“相干态”，即通过速度和方向的局部调整形成视觉上显著的聚集模式。本研究探讨了集体模式研究中一个悬而未决的问题：当此类实体（本研究中视为粒子）从非相干（随机）状态开始趋向相干态时，转变的时间间隔是多少？模型参数又如何影响这一转变时间间隔？\n给定特定时间段内粒子迁移的观测结果（作为在离散时间点采样的点云数据），我们使用拓扑数据分析（具体为持续同调）来推断粒子发生状态转变的时间间隔。任意时刻粒子构型的拓扑结构由持续同调（具体为Persistence Landscapes（持续景观））捕获。我们通过对时间演化子集对应的持续同调输出执行统计显著性检验（即函数假设检验），在时间上定位这种转变发生的时刻。\n该过程在一个已知的自驱粒子集体行为模型上得到验证，其中状态转变由随时间改变模型参数触发。作为应用，所开发的技术最终被用于描述环境改变时细胞运动从无序状态到集体运动的转变。
英文摘要：
In a system of many similar self-propelled entities such as flocks of birds, fish school, cells and molecules, the interactions with neighbors can lead to a "coherent state", meaning the formation of visually compelling aggregation patterns due to the local adjustment of speed and direction. In this study, we explore one of the open questions that arise in studying collective patterns. When such entities, considered here as particles, tend to assume a coherent state beginning from an incoherent (random) state, what is the time interval for the transition? Also, how do model parameters affect this transition time interval? Given the observations of particle migration over a given time period as a point cloud data sampled at discrete time points, we use Topological Data Analysis, specifically persistent homology, to infer the transition time interval in which the particles undergo regime change. The topology of the particle configuration at any given time instance is captured by the persistent homology specifically Persistence Landscapes. We localize (in time) when such a transition happens by conducting the statistical significance tests namely functional hypothesis tests on persistent homology outputs corresponding to subsets of the time evolution. This process is validated on a known collective behavior model of the self-propelled particles with the regime transitions triggered by changing the model parameters in time. As an application, the developed technique was ultimately used to describe the transition in cellular movement from a disordered state to collective motion when the environment was altered.
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