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Phase synchrony information plays a crucial role in analyzing functional brain connectivity and identifying brain activities. A widely adopted feature extraction pipeline, composed of preprocessing, selection of EEG acquisition channels, and phase locking value (PLV) calculation, has achieved success in motor imagery classification (MI). However, this pipeline is manual and reliant on expert knowledge, limiting its convenience and adaptability to different application scenarios. Moreover, most studies have employed mediocre data-independent spatial filters to suppress noise, impeding the exploration of more significant phase synchronization phenomena. To address the issues, we propose the concept of phase synchrony component self-organization, which enables the adaptive learning of data-dependent spatial filters for automating both the preprocessing and channel selection procedures. Based on this concept, the first deep learning end-to-end network is developed, which directly extracts phase synchrony-based features from raw EEG signals and perform classification. The network learns optimal filters during training, which are obtained when the network achieves peak classification results. Extensive experiments have demonstrated that our network outperforms state-of-the-art methods. Remarkably, through the learned optimal filters, significant phase synchronization phenomena can be observed. Specifically, by calculating the PLV between a pair of signals extracted from each sample using two of the learned spatial filters, we have obtained an average PLV exceeding 0.87 across all tongue MI samples. This high PLV indicates a groundbreaking discovery in the synchrony pattern of tongue MI.

There are various metrics for financial risk, such as value at risk (VaR), expected shortfall, expected/unexpected loss, etc. When estimating these metrics, it was very common to assume Gaussian distribution for the asset returns, which may underestimate the real risk of the market, especially during the financial crisis. In this paper, we propose a series of time-varying mixture models for risk analysis and management. These mixture models contain two components: one component with Gaussian distribution, and the other one with a fat-tailed Cauchy distribution. We allow the distribution parameters and component weights to change over time to increase the flexibility of the models. Monte Carlo Expectation-Maximization algorithm is utilized to estimate the parameters. To verify the good performance of our models, we conduct some simulation studies, and implement our models to the real stock market. Based on these studies, our models are appropriate under different economic conditions, and the component weights can capture the correct pattern of the market volatility.