本项目旨在在申请人原有学术成果基础上，提出两种新型的用于多通道信号关联分析的和谐系数，并系统地研究其统计特性、快速算法以及应用前景。理论方面：以多元高斯分布以及混合多元高斯分布为数学模型，以德尔塔方法为基本分析方法，以四元高斯分布正定限积分降维公式为辅助手段，推导所提出的和谐系数在给定相关系数矩阵下均值和方差的渐近表达式，并推导肯德尔和谐系数及平均肯德尔秩次相关系数在多元高斯模型下方差的精确表达式。算法方面：以肯德尔和谐系数为切入点，基于Daniel统一相关系数族以及申请人提出序统计量相关系数族，构建快速算法，将算法时间复杂度从与通道数成平方关系降低至与通道数成线性关系。应用方面：将新提出和谐系数应用于多通道心律失常信号、脑电信号及全基因组数据的关联分析，验证新方法的优越性。本项目是申请人在前期研究成果基础上的深化和拓展，是依托自身研究优势的立项，具有重要的理论价值与广阔的应用前景。

This project proposes two novel concordance coefficients for association analysis of multi-channel signals. Based on previous research achievements of the applicant, in this proposal we will systematically investigate the statistical characteristics, fast algorithms and application feasibility of the new developed concordance coefficients. In the aspect of theory, we will derive the asymptotic expressions of the expectation and variance of the two new coefficients under multivariate normal and contaminated normal models, with the assistance of Delta-method; we will also derive the exact formula of Kendall's concordance coefficient (KCC) and average Kendall's tau by Childs's reduction formula for the quadrivariate normal positive orthant probabilities. In the aspect of algorithm, we will develop fast algorithms for the two new methods by exploiting the fast algorithms of KCC along with the generalized correlation coefficient from Daniel and the generalized order statistics correlation coefficient proposed by the applicant. Our aim is to improve the original quadratic algorithms to linear ones in terms of channel numbers. In the aspect of application, we will apply the new proposed coefficients to the areas of multi-channel arrhythmia signal analysis, EEG signal analysis and genome wide association studies, in order to verify the advantages of the new methods compared with traditional ones. Rooted in our previous experience of correlation analysis, this project is an extended and deepened study which has important theoretical value and wide application foreground.