无标度大脑活动,与学习有关,不同时间尺度的积分,和心理模型的形成,与亚稳态的认知基础相关。光谱斜率,无标度动力学的一个关键方面,被提议作为区分不同睡眠阶段的潜在指标。研究表明,大脑网络在清醒状态下保持一致的无标度结构,麻醉,和恢复。尽管性别之间的麻醉敏感性差异得到了认可,这些变化在皮质的临床脑电图记录中并不明显。最近,发现神经活动的幂律指数的斜率变化与Rényi熵的变化相关,香农信息熵的扩展概念。这些发现将量词确立为研究大脑无标度动力学的有前途的工具。我们的研究提出了一种新颖的视觉表示,称为Rényi熵-复杂性因果关系空间,它封装了复杂性,排列熵,和Rényi参数q。这项研究的主要目标是在理论范围内为经典动力系统定义这个空间。此外,该研究旨在调查模拟无标度活动的不同时间序列在多大程度上可以被区分。最后,该工具用于检测颅内脑电图(iEEG)信号的动态特征。为了实现这些目标,本研究实施了序数模式的Bandt和Pompe方法。在这个过程中,每个信号都与概率分布相关联,基于参数q计算Rényi熵和复杂度的因果度量。该方法是分析模拟时间序列的有价值的工具。它有效地区分了相关噪声的元素,并提供了一种直接的方法来检查行为差异,特点,和分类。对于iEEG实验数据,REM状态显示出更多的显著性别差异,而上回区在不同模式和分析中表现出最大的变化。用这个框架探索无标度大脑活动可以为认知和神经系统疾病提供有价值的见解。该结果可能对理解两性之间的大脑功能差异及其与神经系统疾病的可能相关性具有意义。
Scale-free brain activity, linked with learning, the integration of different time scales, and the formation of mental models, is correlated with a metastable cognitive basis. The spectral slope, a key aspect of scale-free dynamics, was proposed as a potential indicator to distinguish between different sleep stages. Studies suggest that brain networks maintain a consistent scale-free structure across wakefulness, anesthesia, and recovery. Although differences in anesthetic sensitivity between the sexes are recognized, these variations are not evident in clinical electroencephalographic recordings of the cortex. Recently, changes in the slope of the power law exponent of neural activity were found to correlate with changes in Rényi entropy, an extended concept of Shannon\'s information entropy. These findings establish quantifiers as a promising tool for the study of scale-free dynamics in the brain. Our study presents a novel visual representation called the Rényi entropy-complexity causality space, which encapsulates complexity, permutation entropy, and the Rényi parameter q. The main goal of this study is to define this space for classical dynamical systems within theoretical bounds. In addition, the study aims to investigate how well different time series mimicking scale-free activity can be discriminated. Finally, this tool is used to detect dynamic features in intracranial electroencephalography (iEEG) signals. To achieve these goals, the study implementse the Bandt and Pompe method for ordinal patterns. In this process, each signal is associated with a probability distribution, and the causal measures of Rényi entropy and complexity are computed based on the parameter q. This method is a valuable tool for analyzing simulated time series. It effectively distinguishes elements of correlated noise and provides a straightforward means of examining differences in behaviors, characteristics, and classifications. For the iEEG experimental data, the REM state showed a greater number of significant sex-based differences, while the supramarginal gyrus region showed the most variation across different modes and analyzes. Exploring scale-free brain activity with this framework could provide valuable insights into cognition and neurological disorders. The results may have implications for understanding differences in brain function between the sexes and their possible relevance to neurological disorders.