A complex system is often associated with emergence of new phenomena from the interactions between the system's components. General anesthesia reduces brain complexity and so inhibits the emergence of consciousness. An understanding of complexity is necessary for the interpretation of brain monitoring algorithms. Complexity indices capture the "difficulty" of understanding brain activity over time and/or space. Complexity-entropy plots reveal the types of complexity indices and their balance of randomness and structure. Lempel-Ziv complexity is a common index of temporal complexity for single-channel electroencephalogram containing both power spectral and nonlinear effects, revealed by phase-randomized surrogate data. Computing spatial complexities involves forming a connectivity matrix and calculating the complexity of connectivity patterns. Spatiotemporal complexity can be estimated in multiple ways including temporal or spatial concatenation, estimation of state switching, or integrated information. This article illustrates the concept and application of various complexities by providing working examples; a website with interactive demonstrations has also been created.

中文翻译：

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大脑复杂性和麻醉：它们的意义和测量。

一个复杂的系统通常与系统组件之间相互作用的新现象的出现有关。全身麻醉降低了大脑的复杂性，因此抑制了意识的出现。理解复杂性对于解释大脑监测算法是必要的。复杂性指数反映了随着时间和/或空间理解大脑活动的“难度”。复杂性熵图揭示了复杂性指数的类型及其随机性和结构的平衡。Lempel-Ziv 复杂度是包含功率谱和非线性效应的单通道脑电图时间复杂度的常用指标，由相位随机替代数据揭示。计算空间复杂度包括形成连接矩阵和计算连接模式的复杂度。时空复杂性可以通过多种方式进行估计，包括时间或空间连接、状态切换估计或集成信息。本文通过提供工作示例来说明各种复杂性的概念和应用；还创建了一个提供交​​互式演示的网站。