Mathematical models for biological networks and machine learning with applications

Systems biology studies complex systems which involve a large number of interacting entities such that their dynamics follow systematical regulations for transition. To develop computational models becomes an urgent need for studying and manipulating biologically relevant systems. The properties and behaviors of complex biological systems can be analyzed and studied by using computational biological network models. In this thesis, construction and computation methods are proposed for studying biological networks. Modeling Genetic Regulatory Networks (GRNs) is an important topic in genomic research. A number of promising formalisms have been developed in capturing the behavior of gene regulations in biological systems. Boolean Network (BN) has received sustainable attentions. Furthermore, it is possible to control one or more genes in a network so as to avoid the network entering into undesired states. Many works have been done on the control policy for a single randomly generated BN, little light has been shed on the analysis of attractor control problem for multiple BNs. An efficient algorithm was developed to study the attractor control problem for multiple BNs. However, one should note that a BN is a deterministic model, a stochastic model is more preferable in practice. Probabilistic Boolean Network (PBN), was proposed to better describe the behavior of genetic process. A PBN can be considered as a Markov chain process and the construction of a PBN is an inverse problem which is computationally challenging. Given a positive stationary distribution, the problem of constructing a sparse PBN was discussed. For the related inverse problems, an efficient algorithm was developed based on entropy approach to estimate the model parameters. The metabolite biomarker discovery problem is a hot topic in bioinformatics. Biomarker identification plays a vital role in the study of biochemical reactions and signalling networks. The lack of essential metabolites may result in triggering human diseases. An effective computational approach is proposed to identify metabolic biomarkers by integrating available biomedical data and disease-specific gene expression data. Pancreatic cancer prediction problem is another hot topic. Pancreatic cancer is known to be difficult to diagnose in the early stage, and early research mainly focused on predicting the survival rate of pancreatic cancer patients. The correct prediction of various disease states can greatly benefit patients and also assist in design of effective and personalized therapeutics. The issue of how to integrating the available laboratory data with classification techniques is an important and challenging issue. An effective approach was suggested to construct a feature space which serves as a significant predictor for classification. Furthermore, a novel method for identifying the outliers was proposed for improving the classification performance. Using our preoperative clinical laboratory data and histologically confirmed pancreatic cancer samples, computational experiments are conducted successfully with the use of Support Vector Machine (SVM) to predict the status of patients.published_or_final_versionMathematicsDoctoralDoctor of Philosoph