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

该项目的目标是建立新的随机模型的EEG数据使用随机过程，即重尾扩散。脑电图（EEG）是大脑中大量皮层神经元产生的电活动的记录。监管人员拥有受脑型疟疾影响的非洲儿童的真实脑电图数据，以及这些儿童随后的神经发育和认知结果的数据。该项目的主要目标是利用随机过程，即重尾扩散和分数阶扩散，为脑电数据建立新的随机模型。所提出的新的数学方法将导致EEG参数的估计，这可以预测哪些儿童在脑型疟疾幸存后会有神经认知缺陷。对现有EEG数据的初步分析表明，某些通道的EEG记录增量具有正态分布或Student分布。Student分布是一个重尾分布，因此它更适合于对大脑活动中极端跳跃更为常见的记录分布进行建模。更有趣的是直方图是对称的两个甚至三个峰，这表明EEG记录的增量分布应该用一种新的对称多峰分布来建模

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