非平稳序列间的偏交叉相关性与偏信息转移及其应用

Identifying and quantifying dynamical networks of diverse systems with different types of interactions and mutual effects remains a bottleneck and challenge in investigating complex system. Based on multivariate statistics, nonlinear time series analysis and data analysis technique, this project aims to uncover the inner mechanism of partial cross-correlations and partial information transfer between nonstationary signals, track effect of time delay on partial cross-correlations and partial information transfer, construct dynamical models as well as optimal algorithms for calculating the partial cross-correlation coefficients and information transfer directions and strength, and strive to provide new insights on both methodology and application. Moreover, we introduce the methodology to urban traffic system to probe the partial cross-correlations and partial information transfer across various ring, detector and time delay. The presented framework has important theoretical value and practical significance to improve traffic management and solve worsening traffic problems. Finally, we try to investigate the network of interactions between physiological systems. We focus on the characteristic time delay partial cross-correlations and partial information transfer regulation of brain rhythms and cardiac dynamics and their relevance to physiological state, age and disease, which is essential for understanding the basic neural regulation of brain and cardiac dynamics with potential for broad clinical application.

确定和量化各系统间不同类型的交互作用是研究复杂系统的瓶颈与难点。本项目基于多元统计分析、非线性时间序列分析、数据分析理论，旨在揭示非平稳序列间的偏交叉相关性及偏信息转移的内在机理，探讨时间延迟对信号间的偏交叉相关性及偏信息转移的影响，建立系统化的模型和优化算法以计算偏交叉相关系数及偏信息转移方向与强度，力求在理论和应用上有新的突破。并且，尝试在城市交通系统分析中加以应用，探讨不同环线、检测器、时间延迟的偏交叉相关性及偏信息转移规律，对提高交通管理水平以及解决日益恶化的交通问题具有重要的学术价值和现实意义。最后，尝试将其应用到生理网络研究中，探讨不同生理状态下，脑电波各节律与心率波动间的时滞偏交叉相关性及偏信息转移，并分析年龄与疾病的影响，对于深入了解心脑系统交互的神经调节机理，并辅助进行医学诊断和临床治疗有重要意义。

本项目依照研究计划，旨在揭示复杂系统各子系统间的交互性及偏交互性机理。基于多元统计分析、非线性时间序列分析及数据分析等理论，本项目建立了系统化的模型与算法以度量信号的相关性、信号间的交叉相关性及信息转移，偏交叉相关性及偏信息转移，并应用于金融、交通和生理等领域，具有重要的理论意义及现实意义。本项目的研究达到了主要的预期目标，主要研究成果包括以下几个方面：（1）信号间的交叉相关性及偏交叉相关性问题。（2）信号间信息转移及偏信息转移问题。（3）复杂系统的相关性、确定性及复杂性分析。（4）相关性、复杂性与交互性等在金融、交通及生理中的应用。