DNA microarray has become a powerful tool in genetics, molecular biology, and biomedical research. DNA microarray can be used for measuring the genotypes, structural changes, and gene expressions of human genomes. Detection and characterization of multilevel, high-throughput microarray genomic data pose new challenges to statistical pattern recognition and machine learning research. In this dissertation, we propose novel computational methods for analyzing DNA copy number changes and learning the trees of phenotypes using DNA microarray data. DNA copy number change is an important form of structural variations in human genomes. The copy number signals measured by high-density DNA microarrays usually have low signal-to-noise ratios and complex patterns due to inhomogeneous composition of tissue samples. We propose a robust detection method for extracting copy number changes in a single signal profile and consensus copy number changes in the signal profiles of a population. We adapt a solution-path algorithm to efficiently solve the optimization problems associated with the proposed method. We tested the proposed method on both simulation and real CGH and SNP microarray datasets, and observed competitively improved performance as compared to several widely-adopted copy number change detection methods. We also propose a chromosome instability measure to summarize the extracted copy number changes for assessing chromosomal instabilities of tumor genomes. The proposed measure demonstrates distinct patterns between different subtypes of ovarian serous carcinomas and normal samples. Among active research on complex human diseases using genomic data, little effort and progress have been made in discovering the relational structural information embedded in the molecular data. We propose two stability analysis based methods to learn stable and highly resolved trees of phenotypes using microarray gene expression data of heterogeneous diseases. In the first method, we use a hierarchical, divisive visualization approach to explore the tree of phenotypes and a leave-one-out cross validation to select stable tree structures. In the second method, we propose a node bandwidth constraint to construct stable trees that can balance the descriptive power and reproducibility of tree structures. Using a top-down merging procedure, we modify the binary tree structures learned by hierarchical group clustering methods to achieve a given node bandwidth. We use a bootstrap based stability analysis to select stable tree structures under different node bandwidth constraints. The experimental results on two microarray gene expression datasets of human diseases show that the proposed methods can discover stable trees of phenotypes that reveal the relationships between multiple diseases with biological plausibility. / Ph. D.

The advent of various types of high-throughput genomic data has enabled researchers to investigate complex biological systems in a systemic way and started to shed light on the underlying molecular mechanisms in cancers. To analyze huge amounts of genomic data, effective statistical and machine learning tools are clearly needed; more importantly, integrative approaches are especially needed to combine different types of genomic data for a network or pathway view of biological systems. Motivated by such needs, we make efforts in this dissertation to develop integrative framework for pathway analysis. Specifically, we dissect the molecular pathway into two parts: protein-DNA interaction network and protein-protein interaction network. Several novel approaches are proposed to integrate gene expression data with various forms of biological knowledge, such as protein-DNA interaction and protein-protein interaction for reliable molecular network identification. The first part of this dissertation seeks to infer condition-specific transcriptional regulatory network by integrating gene expression data and protein-DNA binding information. Protein-DNA binding information provides initial relationships between transcription factors (TFs) and their target genes, and this information is essential to derive biologically meaningful integrative algorithms. Based on the availability of this information, we discuss the inference task based on two different situations: (a) if protein-DNA binding information of multiple TFs is available: based on the protein-DNA data of multiple TFs, which are derived from sequence analysis between DNA motifs and gene promoter regions, we can construct initial connection matrix and solve the network inference using a constraint least-squares approach named motif-guided network component analysis (mNCA). However, connection matrix usually contains a considerable amount of false positives and false negatives that make inference results questionable. To circumvent this problem, we propose a knowledge based stability analysis (kSA) approach to test the conditional relevance of individual TFs, by checking the discrepancy of multiple estimations of transcription factor activity with respect to different perturbations on the connections. The rationale behind stability analysis is that the consistency of observed gene expression and true network connection shall remain stable after small perturbations are applied to initial connection matrix. With condition-specific TFs prioritized by kSA, we further propose to use multivariate regression to highlight condition-specific target genes. Through simulation studies comparing with several competing methods, we show that the proposed schemes are more sensitive to detect relevant TFs and target genes for network inference purpose. Experimentally, we have applied stability analysis to yeast cell cycle experiment and further to a series of anti-estrogen breast cancer studies. In both experiments not only biologically relevant regulators are highlighted, the condition-specific transcriptional regulatory networks are also constructed, which could provide further insights into the corresponding cellular mechanisms. (b) if only single TF's protein-DNA information is available: this happens when protein-DNA binding relationship of individual TF is measured through experiments. Since original mNCA requires a complete connection matrix to perform estimation, an incomplete knowledge of single TF is not applicable for such approach. Moreover, binding information derived from experiments could still be inconsistent with gene expression levels. To overcome these limitations, we propose a linear extraction scheme called regulatory component analysis (RCA), which can infer underlying regulation relationships, even with partial biological knowledge. Numerical simulations show significant improvement of RCA over other traditional methods to identify target genes, not only in low signal-to-noise-ratio situations and but also when the given biological knowledge is incomplete and inconsistent to data. Furthermore, biological experiments on Escherichia coli regulatory network inferences are performed to fairly compare traditional methods, where the effectiveness and superior performance of RCA are confirmed. The second part of the dissertation moves from protein-DNA interaction network up to protein-protein interaction network, to identify dys-regulated protein sub-networks by integrating gene expression data and protein-protein interaction information. Specifically, we propose a statistically principled method, namely Metropolis random walk on graph (MRWOG), to highlight condition-specific PPI sub-networks in a probabilistic way. The method is based on the Markov chain Monte Carlo (MCMC) theory to generate a series of samples that will eventually converge to some desired equilibrium distribution, and each sample indicates the selection of one particular sub-network during the process of Metropolis random walk. The central idea of MRWOG is built upon that the essentiality of one gene to be included in a sub-network depends on not only its expression but also its topological importance. Contrasted to most existing methods constructing sub-networks in a deterministic way and therefore lacking relevance score for each protein, MRWOG is capable of assessing the importance of each individual protein node in a global way, not only reflecting its individual association with clinical outcome but also indicating its topological role (hub, bridge) to connect other important proteins. Moreover, each protein node is associated with a sampling frequency score, which enables the statistical justification of each individual node and flexible scaling of sub-network results. Based on MRWOG approach, we further propose two strategies: one is bootstrapping used for assessing statistical confidence of detected sub-networks; the other is graphic division to separate a large sub-network to several smaller sub-networks for facilitating interpretations. MRWOG is easy to use with only two parameters need to be adjusted, one is beta value for performing random walk and another is Quantile level for calculating truncated posteriori mean. Through extensive simulations, we show that the proposed scheme is not sensitive to these two parameters in a relatively wide range. We also compare MRWOG with deterministic approaches for identifying sub-network and prioritizing topologically important proteins, in both cases MRWG outperforms existing methods in terms of both precision and recall. By utilizing MRWOG generated node/edge sampling frequency, which is actually posteriori mean of corresponding protein node/interaction edge, we illustrate that condition-specific nodes/interactions can be better prioritized than the schemes based on scores of individual node/interaction. Experimentally, we have applied MRWOG to study yeast knockout experiment for galactose utilization pathways to reveal important components of corresponding biological functions; we also applied MRWSOG to study breast cancer patient prognostics problems, where the sub-network analysis could lead to an understanding of the molecular mechanisms of antiestrogen resistance in breast cancer. Finally, we conclude this dissertation with a summary of the original contributions, and the future work for deepening the theoretical justification of the proposed methods and broadening their potential biological applications such as cancer studies. / Ph. D.

The widespread integration of power converters in applications such as microgrids and data centers has introduced significant stability challenges. This dissertation presents a novel approach to modeling and comprehensive stability analysis for both single-phase and three-phase converters, addressing vital gaps in the existing literature. The first part of the dissertation (Chapters 2 to 4) focuses on single-phase power supply units, proposing an impedance model and a loop gain model based on dq-frame analysis. These models have been validated through extensive experimental testing, demonstrating their effectiveness in stability analysis across a range of system configurations, including single-phase, three-phase three-wire, and three-phase four-wire systems. The second part (Chapters 5 and 6) examines three-phase converters used for integrating renewable energy into microgrids. It introduces a grid-forming control, followed by a detailed investigation into its impedance modeling and stability assessment. This part specifically tackles the challenges posed by the appearance of right-half-plane poles in stability analysis, proposing a new stability margin index to address these issues. The efficacy of these research findings is further substantiated by the development and implementation of a Power-Hardware-in-the-Loop testbed, providing practical validation. Overall, this dissertation has enhanced the modeling, understanding, and management of stability issues in power electronics systems, offering valuable insights and methodologies that are likely to influence future research and development in the field. / Doctor of Philosophy / Power electronics play a crucial role in many of today's advanced technologies, including Renewable Energy (like wind and solar power), Electric Vehicles, Cloud Computing, and Artificial Intelligence. In renewable energy, power electronics are key for converting energy sources for efficient grid integration. Electric vehicles rely on power converter systems for charging their batteries and driving their motors. Similarly, in Cloud Computing and Artificial Intelligence, power electronics ensure that the computers and servers in data centers have a steady and reliable power supply for operation. However, using these advanced power electronics on a large scale, like in wind farms or data centers, can lead to challenges, including many reported system instability issues. These issues highlight the importance of a thorough analysis and understanding of the behavior and interaction of power electronics systems. In addressing these challenges, power electronics converters, conceptualized as a blend of circuits and control systems, demand comprehensive modeling from the ground up. Such modeling is essential to understanding their behavior, ranging from individual components to the entire system. This is key to establishing a clear connection between intricate design details and overall system performance. With power electronics systems becoming more complex and the continual emergence of new technologies, there remains a significant array of unanswered questions, especially in the domain of stability analysis for AC power electronics systems. This dissertation delves into two prominent modeling methods for stability analysis: impedance modeling and loop gain modeling. By exploring and addressing specific gaps identified in prior research, this work aims to contribute to a more profound understanding and enhanced application of these critical methods. The research presented in this dissertation is methodically divided into two main sections. The first section, including Chapter 2 to Chapter 4 is dedicated to exploring single-phase converter power supply units (PSUs) systems. This section introduces innovative models for analyzing their stability, applicable to single-phase PSUs in various system configurations, including both single-phase and three-phase setups. This modeling approach is a significant step forward in understanding and enhancing the stability of single-phase PSU loads. The second section, including Chapter 5 and Chapter 6, delves into the analysis of three-phase converters used in integrating renewable energy sources into microgrids. A notable feature of these converters is their grid-forming control mechanism, which includes a new frequency and power droop control loop. This part also explores modeling the impact of these converters on microgrid stability. Moreover, the issue of right-half-plane (RHP) poles in impedance analysis- a complex problem that can affect stability analysis is addressed. It proposes innovative methods for measuring stability in such conditions. In conclusion, this research made advancements in the modeling for stability analysis of power converter systems. For single-phase converters, the developed impedance model and loop gain model, based on dq-frame analysis, have been proven to be accurate. These models are versatile for stability analysis in various AC systems with single-phase PSU loads. In the study of three-phase converters, the grid-forming converter was successfully designed to support the grid as a distributed energy resource interface. This design contributes positively to microgrid stability. Furthermore, to address the presence of RHP poles in stability analysis, a new stability margin index was defined to better understand and manage these challenges. These findings represent important steps forward in the field of power electronics and contribute valuable insights for future research and development.

L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques / The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters

Philosophiae Doctor - PhD / Fitted Numerical Methods for Delay Di erential Equations Arising in Biology E.B.M. Bashier PhD thesis, Department of Mathematics and Applied Mathematics,Faculty of Natural Sciences, University of the Western Cape. This thesis deals with the design and analysis of tted numerical methods for some delay di erential models that arise in biology. Very often such di erential equations are very complex in nature and hence the well-known standard numerical methods seldom produce reliable numerical solutions to these problems. Ine ciencies of these methods are mostly accumulated due to their dependence on crude step sizes and unrealistic stability conditions.This usually happens because standard numerical methods are initially designed to solve a class of general problems without considering the structure of any individual problems. In this thesis, issues like these are resolved for a set of delay di erential equations. Though the developed approaches are very simplistic in nature, they could solve very complex problems as is shown in di erent chapters.The underlying idea behind the construction of most of the numerical methods in this thesis is to incorporate some of the qualitative features of the solution of the problems into the discrete models. Resulting methods are termed as tted numerical methods. These methods have high stability properties, acceptable (better in many cases) orders of convergence, less computational complexities and they provide reliable solutions with less CPU times as compared to most of the other conventional solvers. The results obtained by these methods are comparable to those found in the literature. The other salient feature of the proposed tted methods is that they are unconditionally stable for most of the problems under consideration.We have compared the performances of our tted numerical methods with well-known software packages, for example, the classical fourth-order Runge-Kutta method, standard nite di erence methods, dde23 (a MATLAB routine) and found that our methods perform much better. Finally, wherever appropriate, we have indicated possible extensions of our approaches to cater for other classes of problems. May 2009.

This diploma thesis describes the design and assessment of steel structural design of the steel aggregate bins including roofing. The construction has a ground plan of about 33 x 9 m and it is divided into 8 cells bins. Main material is steel, grade S355 and S235. There is developed a static analysis of the main load-bearing parts of the structure, including joints and selected details.

In this study, the initial hydrostatic stability, the hydrostatic stability and the structure realibility of three different barge-shaped vessels is simulated and evaluated in order to see which of the vessels would be the most optimal to use for deployment of wave energy converters, WECs. The vessels differ in their hull type: Bulbous-bow hull vessel, Barge hull vessel and Modified-barge hull vessel. In order to do the evaluation, the hull of each vessel is designed in DELFTship and further design is proceeded in SolidWorks 2014. Structural strength analysis is performed in SolidWorks 2014 and hydrostatic properties are simualted in Ansys Aqwa 16.0. The collected results are pointing at that the Modified-barge hull vessel is slightly superior to the others in terms of hydrostatic stability, while the structure stability is equal. The results of this study will provide a foundation for further evaluation of vessels capable of deploying wave energy converters.

Thesis (PhD (Electrical and Electronic Engineering))--University of Stellenbosch, 2011. / AFRIKAANSE OPSOMMING: Hierdie proefskrif handel oor die natuurlike balanserings meganismes van veelvlakkige en modulêre omsetters wat fase-skuif dragolf puls wydte modulasie gebruik. Die meganismes kan in twee hoof groepe verdeel word: ‘n swak balanserings meganisme wat afhanklik is van die oorvleuling van die skakelfunksies en ‘n sterk meganisme wat voorkom ongeag of die skakelfunksies oorvleul al dan nie. Die sterk meganisme verdeel verder in twee subgroepe, ‘n direkte oordrag van onbalans energie en ‘n meganisme wat afhang van die verliese in die stelsel. Elkeen van die meganismes word aan die hand van ‘n omsetter topologie waarin die spesifieke meganisme oorheers beskryf en ontleed. In die ondersoek word klem geplaas op die daarstelling van uitdrukkings om die tydskonstantes van herbalansering na ’n afwyking vir elk van die omsetter toplologieë te beskryf. / ENGLISH ABSTRACT: This thesis investigates the natural balancing mechanisms in multilevel and modular converters using phase shifted carrier pulse width modulation. Two groups of mechanisms are identified; a weak balancing mechanism that is only present when the switching functions are interleaved and a strong mechanism that occurs irrespective of the interleaving of the switching functions. It is further shown that the strong balancing mechanism can be divided into a balancing mechanism that depends on the direct exchange of unbalance energy and a loss based balancing mechanism. Each of the mechanisms is discussed and analysed using a converter where the specific mechanism dominates as example. Emphasis is placed on the calculation of the rebalancing time constant following a perturbation. Closed form expressions for the rebalancing time constants for each of the analysed converters are presented.

This work is concerned with stability and receptivity analysis as well as studies on control of the laminar-turbulent transition in boundary-layer flows through direct numerical simulations. Various flow configurations are considered to address flow around straight and swept wings. The aim of this study is to contribute to a better understanding of stability characteristics and different means of transition control of such flows which are of great interest in aeronautical applications. Acoustic receptivity of flow over a finite-thickness flat plate with elliptic leading edge is considered. The objective is to compute receptivity coefficient defined as the relative amplitude of acoustic disturbances and TS wave. The existing results in the literature for this flow case plot a scattered image and are inconclusive. We have approached this problem in both compressible and incompressible frameworks and used high-order numerical methods. Our results have shown that the generally-accepted level of acoustic receptivity coefficient for this flow case is one order of magnitude too high. The continuous increase of computational power has enabled us to perform global stability analysis of three-dimensional boundary layers. A swept flat plate of FSC type boundary layer with surface roughness is considered. The aim is to determine the critical roughness height for which the flow becomes turbulent. Global stability characteristics of this flow have been addressed and sensitivity of such analysis to domain size and numerical parameters have been discussed. The last flow configuration studied here is infinite swept-wing flow. Two numerical set ups are considered which conform to wind-tunnel experiments where passive control of crossflow instabilities is investigated. Robustness of distributed roughness elements in the presence of acoustic waves have been studied. Moreover, ring-type plasma actuators are employed as virtual roughness elements to delay laminar-turbulent transition. / <p>QC 20161124</p>

It is specifically important to focus on voltage stability analysis of the power system to avoid worst case scenarios such as voltage collapse. The purpose of this thesis is to identify methods for enhancing the steady-state voltage stability using FACTS devices and determining their impact on real and reactive power losses, improvement of bus voltage magnitude, and transmission line loadability. To achieve this, FACTS devices such as Static VAR Compensator (SVC), Static Synchronous Compensator (STATCOM), and Thyristor Controlled Series Capacitor (TCSC) are used in the test system as three separate test cases. The results obtained assist in drawing conclusions on the effectiveness of each FACTS devices at generator, load and swing buses, on lines between two load buses, and between a load bus and a generator bus, in terms of metrics such as voltage magnitude profile, PV curves, and active and reactive power losses.