The first-order temporal structure functions (SFs), i.e., the first-order statistical moment of absolute increments of scaled multichannel resting state EEG signals in healthy children and teenagers over a wide range of temporal separation (time lags) are computed. Our research shows that the sill level (asymptote) of the SF is mainly defined by a determinant of EEG correlation matrix reflecting the EEG spatial structure. The temporal structure of EEG is found to be characterized by power-law scaling or statistical-scale invariance over time scales less than 0.028 s and at least by two dominant frequencies differing by less than 0.3 Hz. These frequencies define the oscillation behavior of the SF and are mainly distributed within the range of 7.5-12.0 Hz. In this paper, we propose the combined Bessel and exponential model that fits well the empirical SF. It provides a good fit with the mean relative error fitting of 2.8 % over the time lag range of 1 s, using a sampling interval of 4 ms, for all cases under analysis. We also show that the hyper gamma distribution (HGD) fits to the empirical probability density functions (PDFs) of absolute increments of scaled multichannel resting state EEG signals at any given time lag. It means that only two parameters (sample mean of absolute increments and relevant coefficient of variation) may approximately define the empirical PDFs for a given number of channels. A three-dimensional feature vector constructed from the shape and scale parameters of the HGD and the sill level may be used to estimate the closeness of the real EEG to the "random" EEG characterized by the absence of temporal and spatial correlation.

中文翻译：

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该结构作为多通道脑电图的时空特性的新整体度量。

计算一阶时间结构函数（SFs），即，在健康的儿童和青少年中，在较大的时间间隔范围内（时间滞后），缩放后的多通道静止状态EEG信号的绝对增量的一阶统计矩。我们的研究表明，SF的门槛水平（渐近线）主要由反映脑电空间结构的脑电相关矩阵的行列式定义。发现EEG的时间结构的特征是在小于0.028 s的时间范围内具有幂律定律或统计尺度不变性，并且至少具有两个相差小于0.3 Hz的主频。这些频率定义了SF的振荡行为，并且主要分布在7.5-12.0 Hz的范围内。在本文中，我们提出了非常适合经验SF的贝塞尔和指数组合模型。对于所有正在分析的情况，它在1 s的时滞范围内使用2.8 ms的平均相对误差拟合提供了良好的拟合，采样间隔为4 ms。我们还显示，在任何给定的时间滞后，超伽玛分布（HGD）都适合于按比例缩放的多通道静止状态EEG信号的绝对增量的经验概率密度函数（PDF）。这意味着对于给定数量的通道，只有两个参数（绝对增量的样本均值和相关的变化系数）可以近似定义经验PDF。由HGD的形状和比例参数以及门槛水平构成的三维特征向量可用于估计实际EEG与“随机”的接近度