AI 中文总结
本研究提出基于相位的空间序贯模式框架，定义空间置换熵，可表征振荡系统时空动力学，区分锁相状态与部分同步状态，在合成网络和人脑电数据上验证了方法有效性。
AI 中文摘要
从神经群体到工程网络，振荡系统中有序时空模式的出现是普遍存在的现象。识别这些模式并追踪其随时间的演变仍然具有挑战性，尤其是当系统表现出瞬态动力学时。本文引入了一种基于空间序贯模式的框架，用于表征振荡系统的时空动力学。该方法直接作用于相位而非振幅，同时引入额外的模式以处理接近相等的相位。这种符号表示编码了局部空间序关系，在单一框架内同时捕获相位梯度和同步集群。基于此构造，我们定义了空间置换熵，该熵可量化每个时间点时空模式的多样性，从而能够在瞬态动力学和状态转变发生时对其进行检测。我们表明，该方法可区分全局同步水平相同但空间组织不同的锁相状态，还可表征部分同步状态。我们在多个时空状态下的合成振荡器网络以及人类志愿者的静息态脑电图记录上验证了该方法，该方法可区分个体志愿者的不同状态。
英文摘要
The emergence of organized spatiotemporal patterns is ubiquitous in oscillatory systems, from neural populations to engineered networks. Identifying these patterns and tracking how they evolve over time remains challenging, particularly when systems exhibit transient dynamics. Here, we introduce a framework based on spatial ordinal patterns to characterize the spatiotemporal dynamics of oscillatory systems. Our approach acts directly on the phase rather than the amplitude, with additional patterns introduced to account for near-equal phases. This symbolic representation encodes local spatial ordering relations, capturing both phase gradients and synchronized clusters within a single framework. From this construction, we define a spatial permutation entropy that quantifies the diversity of spatiotemporal patterns at each point in time, enabling the detection of transient dynamics and regime transitions as they occur. We show that this approach distinguishes phase-locked states with identical levels of global synchronization but distinct spatial organization and also characterizes partially synchronized states. We demonstrate the method on synthetic oscillator networks across multiple spatiotemporal regimes, and on resting-state EEG recordings from human volunteers, where it distinguishes different conditions within individual volunteers.
