[统计数据] 相干与相位同步：对的推广 多元时间序列与零滞后贡献的去除 [推广有奖]

摘要翻译：
对应于不同空间位置的时间序列之间的相干性和相位同步性通常被解释为位置之间连通性的标志。在神经生理学中，神经元电活动的时间序列是研究大脑互联性的关键。这些信号可以从深度电极侵入性地测量，或者通过sLORETA（标准化低分辨率脑电磁断层扫描）等断层扫描，从头皮电位差（EEG：Electronic Encephalogram）和磁场（MEG：magnetoencephalogram）的非常高时间分辨率、非侵入性、颅外记录中计算。这种情况下有两个问题。首先，在通常未知皮质几何结构的情况下，每个脑位置的估计信号是一个包含三个分量的向量（即电流密度向量），这意味着相干和相位同步必须推广到多变量时间序列对。其次，EEG/MEG层析成像固有的低空间分辨率引入了人为的高零滞后相干和相位同步。在本报告中，对这两个问题都提出了解决方案。简要地提到了两个附加的推广：（1）条件相干和相位同步；（2）非平稳时频分析。最后给出了连通性显著性检验的非参数随机化方法。本文提出的新的连通性度量可以应用于已发表文献中传统的单变量EEG/MEG信号对。然而，这些计算不能解释为连接性，因为通常将颅外电极或传感器与下层皮质联系起来是不正确的。
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英文标题：
《Coherence and phase synchronization: generalization to pairs of
  multivariate time series, and removal of zero-lag contributions》
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作者：
Roberto D. Pascual-Marqui
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最新提交年份：
2007
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Statistics        统计学
二级分类：Applications        应用程序
分类描述：Biology, Education, Epidemiology, Engineering, Environmental Sciences, Medical, Physical Sciences, Quality Control, Social Sciences
生物学，教育学，流行病学，工程学，环境科学，医学，物理科学，质量控制，社会科学
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英文摘要：
  Coherence and phase synchronization between time series corresponding to different spatial locations are usually interpreted as indicators of the connectivity between locations. In neurophysiology, time series of electric neuronal activity are essential for studying brain interconnectivity. Such signals can either be invasively measured from depth electrodes, or computed from very high time resolution, non-invasive, extracranial recordings of scalp electric potential differences (EEG: electroencephalogram) and magnetic fields (MEG: magnetoencephalogram) by means of a tomography such as sLORETA (standardized low resolution brain electromagnetic tomography). There are two problems in this case. First, in the usual situation of unknown cortical geometry, the estimated signal at each brain location is a vector with three components (i.e. a current density vector), which means that coherence and phase synchronization must be generalized to pairs of multivariate time series. Second, the inherent low spatial resolution of the EEG/MEG tomography introduces artificially high zero-lag coherence and phase synchronization. In this report, solutions to both problems are presented. Two additional generalizations are briefly mentioned: (1) conditional coherence and phase synchronization; and (2) non-stationary time-frequency analysis. Finally, a non-parametric randomization method for connectivity significance testing is outlined. The new connectivity measures proposed here can be applied to pairs of univariate EEG/MEG signals, as is traditional in the published literature. However, these calculations cannot be interpreted as connectivity, since it is in general incorrect to associate an extracranial electrode or sensor to the underlying cortex.
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PDF链接：
https://arxiv.org/pdf/706.1776