论文标题
连续性缩放：准确检测和量化因果关系的严格框架
Continuity scaling: A rigorous framework for detecting and quantifying causality accurately
论文作者
论文摘要
基于数据的检测和量化复杂的非线性动力学系统对科学，工程及其他地区至关重要。近年来，基于跨图的技术受到广泛使用的方法的启发，我们开发了一个通用框架，以迈向对动态因果机制的全面理解，这与因果关系的自然解释是一致的。特别是，我们没有通过常规实施的横图的平滑度来定义因果关系，以直接测量{\ it缩放定律}的连续性直接的连续性。未透明的缩放定律可以在一般复杂的动力学系统中对因果关系的准确，可靠和有效地检测其强度，从而胜过那些现有的代表性方法。使用模型复杂系统和现实世界中的数据集对基于连续性缩放的框架进行了严格建立和证明。
Data based detection and quantification of causation in complex, nonlinear dynamical systems is of paramount importance to science, engineering and beyond. Inspired by the widely used methodology in recent years, the cross-map-based techniques, we develop a general framework to advance towards a comprehensive understanding of dynamical causal mechanisms, which is consistent with the natural interpretation of causality. In particular, instead of measuring the smoothness of the cross map as conventionally implemented, we define causation through measuring the {\it scaling law} for the continuity of the investigated dynamical system directly. The uncovered scaling law enables accurate, reliable, and efficient detection of causation and assessment of its strength in general complex dynamical systems, outperforming those existing representative methods. The continuity scaling based framework is rigorously established and demonstrated using datasets from model complex systems and the real world.
