Center for Complex Systems and Brain Sciences, Florida Atlantic University, Boca Raton, FL, USA; Department of Psychiatry and Behavioral Sciences, Stanford University, Stanford, CA, USA.
Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL, USA.
J Neurosci Methods. 2020 Jun 1;339:108672. doi: 10.1016/j.jneumeth.2020.108672. Epub 2020 Mar 6.
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a challenge in both theoretical and empirical realms. The present work shows how integrating approaches from computational algebraic topology and dynamical systems may help us meet this challenge. In particular, we focus on the application of multiscale topological analysis to coordinated rhythmic processes. First, theoretical arguments are introduced as to why certain topological features and their scale-dependency are highly relevant to understanding complex collective dynamics. Second, we propose a method to capture such dynamically relevant topological information using persistent homology, which allows us to effectively construct a multiscale topological portrait of rhythmic coordination. Finally, the method is put to test in detecting transitions in real data from an experiment of rhythmic coordination in ensembles of interacting humans. The recurrence plots of topological portraits highlight collective transitions in coordination patterns that were elusive to more traditional methods. This sensitivity to collective transitions would be lost if the behavioral dynamics of individuals were treated as separate degrees of freedom instead of constituents of the topology that they collectively forge. Such multiscale topological portraits highlight collective aspects of coordination patterns that are irreducible to properties of individual parts. The present work demonstrates how the analysis of multiscale coordination dynamics can benefit from topological methods, thereby paving the way for further systematic quantification of complex, high-dimensional dynamics in living systems.
生命系统在多个时空尺度上表现出复杂而有序的行为。为了研究生命系统中多尺度协调的本质，我们需要有一种有意义且系统的方法来量化复杂的动力学，这在理论和经验领域都是一个挑战。本工作展示了如何整合计算代数拓扑和动力系统方法来帮助我们应对这一挑战。具体来说，我们专注于将多尺度拓扑分析应用于协调的节奏过程。首先，引入了理论论证，说明为什么某些拓扑特征及其尺度依赖性与理解复杂的集体动力学高度相关。其次，我们提出了一种使用持久同调捕捉这种动态相关拓扑信息的方法，该方法使我们能够有效地构建节奏协调的多尺度拓扑图像。最后，该方法被用于检测来自人类相互作用群体中节奏协调实验的真实数据中的转变。拓扑图像的递归图突出显示了协调模式中的集体转变，这些转变是传统方法难以发现的。如果将个体的行为动力学视为独立的自由度，而不是它们共同形成的拓扑的组成部分，那么这种对集体转变的敏感性就会丧失。这种多尺度拓扑图像突出了协调模式的集体方面，这些方面无法简化为个体部分的属性。本工作展示了多尺度协调动力学的分析如何受益于拓扑方法，从而为进一步系统地量化生命系统中的复杂、高维动力学铺平了道路。
