Indiana University-Purdue University Indianapolis (IUPUI) / Traditional treatment strategy development for diseases involves the identification of target proteins related to disease states, and the interference of these proteins with drug molecules. Computational drug discovery and virtual screening from thousands of chemical compounds have accelerated this process. The thesis presents a comprehensive framework of computational drug discovery using system biology approaches. The thesis mainly consists of two parts: disease biomarker identification and disease treatment discoveries. The first part of the thesis focuses on the research in biomarker identification for human diseases in the post-genomic era with an emphasis in system biology approaches such as using the protein interaction networks. There are two major types of biomarkers: Diagnostic Biomarker is expected to detect a given type of disease in an individual with both high sensitivity and specificity; Predictive Biomarker serves to predict drug response before treatment is started. Both are essential before we even start seeking any treatment for the patients. In this part, we first studied how the coverage of the disease genes, the protein interaction quality, and gene ranking strategies can affect the identification of disease genes. Second, we addressed the challenge of constructing a central database to collect the system level data such as protein interaction, pathway, etc. Finally, we built case studies for biomarker identification for using dabetes as a case study. The second part of the thesis mainly addresses how to find treatments after disease identification. It specifically focuses on computational drug repositioning due to its low lost, few translational issues and other benefits. First, we described how to implement literature mining approaches to build the disease-protein-drug connectivity map and demonstrated its superior performances compared to other existing applications. Second, we presented a valuable drug-protein directionality database which filled the research gap of lacking alternatives for the experimental CMAP in computational drug discovery field. We also extended the correlation based ranking algorithms by including the underlying topology among proteins. Finally, we demonstrated how to study drug repositioning beyond genomic level and from one dimension to two dimensions with clinical side effect as prediction features.

Indiana University-Purdue University Indianapolis (IUPUI) / Some problems of complex systems are internal to the system whereas other problems exist peripherally; two such problems will be explored in this thesis. First, is the issue of excessive jerk from instantaneous velocity demand changes produced by an adaptive cruise control system. Calculations will be demonstrated and an example control solution will be proposed in Chapter 3. Second, is the issue of a non-perfect plant, called an uncertain or corrupted plant. In initial control analysis, the adaptive cruise control systems are assumed to have a perfect plant; that is to say, the plant always behaves as commanded. In reality, this is seldom the case. Plant corruption may come from a variation in performance through use or misuse, or from noise or imperfections in the sensor signal data. A model for plant corruption is introduced and methods for analysis and compensation are explored in Chapter 4. To facilitate analysis, Chapter 2 discusses the concept of system identification, an order reduction tool which is employed herein. Adaptive cruise control systems are also discussed with special emphasis on the situations most likely to employ jerk limitation.

This thesis details the development, verification and validation of an unsteady unstructured high order (≥ 3) h/p Discontinuous Galerkin - Fourier solver for the incompressible Navier-Stokes equations on static and rotating meshes in two and three dimensions. This general purpose solver is used to provide insight into cross-flow (wind or tidal) turbine physical phenomena. Simulation of this type of turbine for renewable energy generation needs to account for the rotational motion of the blades with respect to the fixed environment. This rotational motion implies azimuthal changes in blade aero/hydro-dynamics that result in complex flow phenomena such as stalled flows, vortex shedding and blade-vortex interactions. Simulation of these flow features necessitates the use of a high order code exhibiting low numerical errors. This thesis presents the development of such a high order solver, which has been conceived and implemented from scratch by the author during his doctoral work. To account for the relative mesh motion, the incompressible Navier-Stokes equations are written in arbitrary Lagrangian-Eulerian form and a non-conformal Discontinuous Galerkin (DG) formulation (i.e. Symmetric Interior Penalty Galerkin) is used for spatial discretisation. The DG method, together with a novel sliding mesh technique, allows direct linking of rotating and static meshes through the numerical fluxes. This technique shows spectral accuracy and no degradation of temporal convergence rates if rotational motion is applied to a region of the mesh. In addition, analytical mappings are introduced to account for curved external boundaries representing circular shapes and NACA foils. To simulate 3D flows, the 2D DG solver is parallelised and extended using Fourier series. This extension allows for laminar and turbulent regimes to be simulated through Direct Numerical Simulation and Large Eddy Simulation (LES) type approaches. Two LES methodologies are proposed. Various 2D and 3D cases are presented for laminar and turbulent regimes. Among others, solutions for: Stokes flows, the Taylor vortex problem, flows around square and circular cylinders, flows around static and rotating NACA foils and flows through rotating cross-flow turbines, are presented.

Indiana University-Purdue University Indianapolis (IUPUI) / In medical research, data analysis often requires complex statistical methods where no closed-form solutions are available. Under such circumstances, Monte Carlo (MC) methods have found many applications. In this dissertation, we proposed several novel statistical models where MC methods are utilized. For the first part, we focused on semicompeting risks data in which a non-terminal event was subject to dependent censoring by a terminal event. Based on an illness-death multistate survival model, we proposed flexible random effects models. Further, we extended our model to the setting of joint modeling where both semicompeting risks data and repeated marker data are simultaneously analyzed. Since the proposed methods involve high-dimensional integrations, Bayesian Monte Carlo Markov Chain (MCMC) methods were utilized for estimation. The use of Bayesian methods also facilitates the prediction of individual patient outcomes. The proposed methods were demonstrated in both simulation and case studies. For the second part, we focused on re-randomization test, which is a nonparametric method that makes inferences solely based on the randomization procedure used in clinical trials. With this type of inference, Monte Carlo method is often used for generating null distributions on the treatment difference. However, an issue was recently discovered when subjects in a clinical trial were randomized with unbalanced treatment allocation to two treatments according to the minimization algorithm, a randomization procedure frequently used in practice. The null distribution of the re-randomization test statistics was found not to be centered at zero, which comprised power of the test. In this dissertation, we investigated the property of the re-randomization test and proposed a weighted re-randomization method to overcome this issue. The proposed method was demonstrated through extensive simulation studies.