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Background: Protein is a kind of important organics in life. It is varied with its sequences, structures and functions. Protein evolutionary classification is one of the popular research topics in computational bioinformatics. Many studies have used protein sequence information to classify the evolutionary relationships of proteins. As the amount of protein sequence data increases, efficient computational tools are needed to make efficient protein evolutionary classifications with high accuracies in the big data paradigm. Methods: In this study, we propose a new simple and efficient computational approach based on the normalized mutual information rates to compute the relationship between protein sequences, we then use the “distances” defined on the relationships to perform the evolutionary classifications of proteins. The new method is computational efficient, model-free and unsupervised, which does not require training data when performing classifications. Result: Simulation studies on various examples demonstrate the efficiency of the new method. We use precision-recall curves to compare the efficiency of our new method with traditional methods, results show that the new method outperforms the traditional methods in most of the cases when performing evolutionary classifications. Conclusion: The new method is simple and proved to be efficient in protein evolutionary classifications, which is useful in future evolutionary analysis particularly in the big data paradigm.

This thesis describes a PhD project on time series causality analysis and applications. The project is motivated by two EEG measurements of music improvisation experiments, where we aim to use causality measures to construct neural networks to identify the neural differences between improvisation and non-improvisation. The research is based on mathematical backgrounds of time series analysis, information theory and network theory. We first studied a series of popular causality measures, namely, the Granger causality, partial directed coherence (PDC) and directed transfer function (DTF), transfer entropy (TE), conditional mutual information from mixed embedding (MIME) and partial MIME (PMIME), from which we proposed our new measures: the direct transfer entropy (DTE) and the wavelet-based extensions of MIME and PMIME. The new measures improved the properties and applications of their father measures, which were verified by simulations and examples. By comparing the measures we studied, MIME was found to be the most useful causality measure for our EEG analysis. Thus, we used MIME to construct both the intra-brain and cross-brain neural networks for musicians and listeners during the music performances. Neural differences were identified in terms of direction and distribution of neural information flows and activity of the large brain regions. Furthermore, we applied MIME on other EEG and financial data applications, where reasonable causality results were obtained. Open Access