ANOVA table for the first simulation study.

In clinical neuroscience, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks—in which edges indicate strong enough coupling between brain regions—are consistent with the notion of percolation, which is a phenomenon in complex networks corresponding to the sudden emergence of a giant connected component. Traditionally, work has concentrated on noise-free percolation with a monotonic process of network growth, but real-world networks are more complex. We develop a class of random graph hidden Markov models (RG-HMMs) for characterizing percolation regimes in noisy, dynamically evolving networks in the presence of edge birth and edge death. This class is used to understand the type of phase transitions undergone in a seizure, and in particular, distinguishing between different percolation regimes in epileptic seizures. We develop a hypothesis testing framework for inferring putative percolation mechanisms. As a necessary precursor, we present an EM algorithm for estimating parameters from a sequence of noisy networks only observed at a longitudinal subsampling of time points. Our results suggest that different types of percolation can occur in human seizures. The type inferred may suggest tailored treatment strategies and provide new insights into the fundamental science of epilepsy.在临床神经科学领域，癫痫发作与全脑范围内耦合活动的突然涌现密切相关。由此产生的功能网络——其边代表脑区间足够强的耦合作用——符合渗流（percolation）的概念：渗流是复杂网络中的一种现象，指巨型连通分量的突然涌现。传统上，相关研究多聚焦于网络增长呈单调过程的无噪渗流场景，但现实世界中的网络更为复杂。我们提出了一类随机图隐马尔可夫模型（random graph hidden Markov models, RG-HMMs），用于刻画存在边生成与边消亡过程的含噪动态演化网络中的渗流状态。该类模型可用于解析癫痫发作过程中经历的相变类型，尤其能够区分癫痫发作中的不同渗流状态。我们构建了一套假设检验框架，用于推断推定的渗流机制。作为必要的前置步骤，我们提出了一种EM算法，用于从仅在时间点纵向子采样下观测到的含噪网络序列中估计模型参数。我们的研究结果表明，人类癫痫发作中可出现不同类型的渗流现象。所推断的渗流类型可为定制化治疗策略提供参考，并为癫痫的基础科学研究提供全新视角。