Stochastic models for increments of EEG recordings using heavy-tailed and fractional diffusions

本课题的目标是利用随机过程，即重尾扩散，为脑电信号建立新的随机模型。脑电(EEG)是大脑中大量皮质神经元产生的电活动的记录。这些监督者拥有受脑型疟疾影响的非洲儿童的真实脑电数据，以及这些儿童随后的神经发育和认知结果的数据。该项目的总体目标是使用随机过程，即重尾扩散和分数扩散，为脑电数据建立新的随机模型。拟议的新数学方法将导致对脑电参数的估计，这可以预测哪些儿童在脑型疟疾存活后会出现神经认知缺陷。对现有脑电数据的初步分析表明，某些通道的脑电记录增量服从正态分布或学生分布。学生分布是一种重尾分布，因此它是对大脑活动极端跳跃更常见的记录的分布进行建模的首选。更有趣的是，直方图是对称的，有两个甚至三个峰值，这表明脑电记录增量的分布应该用新的对称多峰分布建模

The goal of this project is to build new stochastic models for the EEG data using stochastic processes, namely heavy-tailed diffusion. Electroencephalogram (EEG) is a record of electrical activity generated by a large number of cortical neurons in the brain. The supervisors have real-world EEG data from African children affected by cerebral malaria, as well as data on subsequent neurodevelopmental and cognitive outcomes of these children. The over-arching goal of the project is to build new stochastic models for the EEG data using stochastic processes, namely heavy-tailed diffusion and fractional diffusion. The proposed new mathematical methods will result in estimation of the EEG parameters, which could predict which children would have neurocognitive deficits after surviving cerebral malaria. Preliminary analyses of the available EEG data indicate that the increments of EEG recordings for some channels have a normal distribution or Student distribution. Student distribution is a heavy-tailed distribution, so it is preferred for modeling the distribution of recordings in which extreme jumps in brain activity are much more common. Much more interesting histograms are symmetric with two or even three peaks, indicating that the distribution of increments of EEG recordings should be modeled with a new symmetric multimodal distribution