Dai, Juan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 36-39). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Previous Work --- p.3 / Chapter 1.2 --- Proposed Framework --- p.5 / Chapter 1.3 --- Overview --- p.6 / Chapter 2 --- Placement of the Local Classifiers --- p.8 / Chapter 2.1 --- The Uncertainty Map --- p.9 / Chapter 2.2 --- Responsibility Mixture Model --- p.11 / Chapter 2.3 --- EM for Parameter Estimation --- p.12 / Chapter 2.3.1 --- E-Step --- p.14 / Chapter 2.3.2 --- M-Step --- p.15 / Chapter 2.3.3 --- Relationship with Gaussian Mixture Mod- els(GMM) --- p.16 / Chapter 3 --- Fusing of Locally Adaptive Classifiers --- p.18 / Chapter 3.1 --- Training --- p.18 / Chapter 3.2 --- Testing --- p.21 / Chapter 4 --- Algorithmic Characteristics --- p.23 / Chapter 4.1 --- Uncertainty Piloted Placement of Local Classifiers --- p.23 / Chapter 4.2 --- Uncertainty Piloted Fusing of Local Classifiers --- p.24 / Chapter 4.3 --- Related Work --- p.25 / Chapter 5 --- Experiments --- p.27 / Chapter 5.1 --- Dimensionality Reduction --- p.27 / Chapter 5.2 --- Two-Class Classification Problem: Gender Classification --- p.29 / Chapter 5.3 --- Multi-Class Classification: Face Recognition --- p.30 / Chapter 5.3.1 --- Varying the Lighting --- p.31 / Chapter 5.3.2 --- Varying the Pose --- p.32 / Chapter 5.3.3 --- Number of Features Extracted --- p.33 / Chapter 6 --- Conclusion --- p.34 / Bibliography --- p.36

Duan, Ben. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 61-67). / Abstracts in English and Chinese. / Acknowledgments --- p.2 / Abstract --- p.i / Introduction --- p.3 / Chapter 1 --- Stability of Shock Waves in Viscous Conservation Laws --- p.10 / Chapter 1.1 --- Cauchy Problem for Scalar Viscous Conservation Laws and Viscous Shock Profiles --- p.10 / Chapter 1.2 --- Stability of Shock Waves by Energy Method --- p.15 / Chapter 1.3 --- L1 Stability of Shock Waves in Scalar Viscous Con- servation Laws --- p.20 / Chapter 2 --- Slow Motion of a Viscous Shock --- p.29 / Chapter 2.1 --- Propagation of a Viscous Shock in Bounded Domain --- p.29 / Chapter 2.1.1 --- Steady Problem --- p.30 / Chapter 2.1.2 --- Time-Dependent Problem --- p.34 / Chapter 2.1.3 --- Super-Sensitivity of Boundary Conditions --- p.36 / Chapter 2.2 --- Propagation of a Stationary Shock in Half Space --- p.39 / Chapter 2.2.1 --- Asymptotic Analysis --- p.39 / Chapter 2.2.2 --- Pointwise Estimate --- p.40 / Chapter 3 --- Viscous Transonic Flow Through a Nozzle --- p.47 / Chapter 3.1 --- Nonlinear Stability and Instability of Shock Waves --- p.48 / Chapter 3.2 --- Asymptotic Stability and Instability --- p.49 / Chapter 3.3 --- Matched Asymptotic Analysis --- p.53 / Chapter 4 --- C --- p.60 / Bibliography --- p.61

Law, Tak Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 38-39). / Abstracts in English and Chinese. / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Literature Review --- p.4 / Chapter 2.1 --- Brief Overview --- p.4 / Chapter 2.2 --- Determinants of the Target Debt Ratio --- p.7 / Chapter 2.3 --- Adjustments Toward the Target Ratio --- p.9 / Chapter Chapter 3. --- Methodology --- p.12 / Chapter 3.1 --- Estimation of the Target Leverage Ratio --- p.12 / Chapter 3.2 --- Factors affecting the Long-term Adjustment --- p.16 / Chapter 3.3 --- Persistence and Reversal of Effects --- p.19 / Chapter Chapter 4. --- Expected Signs of Variables --- p.22 / Chapter 4.1 --- Estimation of the Target Ratio --- p.22 / Chapter 4.2 --- Effects of Firm Histories --- p.24 / Chapter 4.2.1 --- Pecking order theory --- p.24 / Chapter 4.2.2 --- Tradeoff theory --- p.25 / Chapter 4.2.3 --- Market Timing Theory --- p.25 / Chapter Chapter 5. --- Data --- p.27 / Chapter Chapter 6. --- Empirical Findings --- p.29 / Chapter 6.1 --- Estimation of the Target Ratio --- p.29 / Chapter 6.2 --- Factors Affecting the Long-term Adjustment --- p.31 / Chapter 6.3 --- Persistence of the Effects --- p.33 / Chapter 6.4 --- Reversal of the Effects --- p.35 / Chapter Chapter 7. --- Concluding Remarks --- p.37 / References --- p.38 / Tables --- p.40

Zhao, Jin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 79-83). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Synchronization of Master-slave Systems --- p.1 / Chapter 1.2 --- Output Regulation --- p.2 / Chapter 1.3 --- Typical Nonlinear Systems --- p.4 / Chapter 1.4 --- Organization --- p.4 / Chapter 2 --- Synchronization of Chua's Circuit and Van der Pol Oscillator via Inter- nal Model Approach --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Problem Formulation --- p.8 / Chapter 2.3 --- Preliminaries --- p.10 / Chapter 2.4 --- Solvability of the Problem --- p.13 / Chapter 2.4.1 --- The solution of the regulator equations --- p.14 / Chapter 2.4.2 --- Steady-state generator --- p.15 / Chapter 2.4.3 --- Internal model --- p.19 / Chapter 2.4.4 --- Stabilization --- p.20 / Chapter 2.4.5 --- Simulation --- p.22 / Chapter 2.5 --- Conclusions --- p.27 / Chapter 3 --- Robust Output Regulation of Output Feedback Systems with Nonlinear Exosystems --- p.28 / Chapter 3.1 --- Introduction --- p.28 / Chapter 3.2 --- Assumptions and Preliminaries --- p.29 / Chapter 3.3 --- Solvability of the Synchronization Problem --- p.33 / Chapter 3.4 --- Comparing Two Approaches for Output Regulation --- p.42 / Chapter 3.4.1 --- Differences between the two approaches for the output regulation problem --- p.42 / Chapter 3.4.2 --- Solvability of the regulator equations --- p.43 / Chapter 3.4.3 --- Solvability of stabilization --- p.47 / Chapter 3.5 --- Conclusions --- p.49 / Chapter 4 --- Applications of Robust Regional Synchronization via Output Regulation Techniques --- p.50 / Chapter 4.1 --- Problem Formulation --- p.50 / Chapter 4.2 --- Duffing Oscillator Synchronizes with Chua's Circuit --- p.51 / Chapter 4.2.1 --- Transfer the synchronization problem into the stabilization problem --- p.53 / Chapter 4.2.2 --- Boundedness of Chua's circuit --- p.57 / Chapter 4.2.3 --- Stabilization --- p.59 / Chapter 4.2.4 --- Simulation Results --- p.64 / Chapter 4.3 --- The Chaotic SMIB Power System Synchronizes with Van der Pol Oscillator --- p.64 / Chapter 4.3.1 --- Transfer the synchronization problem into the stabilization problem --- p.68 / Chapter 4.3.2 --- Stabilization --- p.71 / Chapter 4.3.3 --- Simulation Results --- p.74 / Chapter 4.4 --- Conclusions --- p.76 / Chapter 5 --- Conclusions --- p.77 / Bibliography --- p.79

Digitized by Kansas Correctional Industries

The purpose of this thesis is to develop various advanced linear algebra techniques that apply to image processing. With the increasing use of computers and digital photography, being able to manipulate digital images efficiently and with greater freedom is extremely important. By applying the tools of linear algebra, we hope to improve the ability to process such images. We are especially interested in developing techniques that allow computers to manipulate images with the least amount of human guidance. In Chapter 2 and Chapter 3, we develop the basic definitions and linear algebra concepts that lay the foundation for later chapters. Then, in Chapter 4, we demonstrate techniques that allow a computer to rotate an image to the correct orientation automatically, and similarly, for the computer to correct a certain class of color distortion automatically. In both cases, we use certain properties of the eigenvalues and eigenvectors of covariance matrices. We then model color clashing and color variation in Chapter 5 using a powerful tool from linear algebra known as the Perron-Frobenius theorem. Finally, we explore ways to determine whether an image is a blur of another image using invariant functions. The inspiration behind these functions are recent applications of Lie Groups and Lie algebra to image processing.

Economic systems are distributed in the sense that economic agents make decisions without any central control. Prices, quantities, wealth, and market structure emerge from the interaction of agents acting in their own self interest. The concepts and language of systems science are used to define economic systems in a manner that captures and articulates the distributed nature of economic systems. Further, the systems definition permits multiple views of the economic system, and in addition, allows the agents to "step outside" the system in order to study it. Economic systems are defined in such a way that it is feasible to construct artificial economic systems, and in particular, ones that are composed of self-interested agents that operate according to principles that are prescribed by the researcher. An artificial economic system was actually constructed and tested in a computer environment. The model was verified with reference to several theoretical models such as static and adaptive expectations. The system constructed allows up to 1000 agents to interact without any central control. A computer "blackboard system" is used as the architecture for providing common information to the agents in the artificial economic system. The blackboard design successfully allows complex agents to compete and trade in an artificial economic system created by the researcher. Prices, quantities, wealth, and market structure emerge naturally in the artificial economy that depend on the characteristics and prescribed strategies of the agents in the system. After a transition period, the trading frequently produces price and quantity time series that have the characteristics of a random walk, a condition that is well known in real world markets. Three classes of producer agents were used in these artificial economic systems: optimizing agents that incorporate neural networks, satisficing agents that incorporate very simple rule-based approaches, and Stackelberg agents that have knowledge about the consumers in the system, but do not have knowledge about their competitor's strategies or intentions. Neural networks are used to model the behavior and strategies of economic agents that can be said to learn, i.e., those agents that develop general principles for adapting to changing market conditions that transfer across markets. The focus of this research was on the producers in the system. The consumption side of the economic system was represented by a set of simple consumers. An important result emerging from this research is that at least one agent out of four in these experiments with accurate knowledge about market demand increases the wealth of the system as a whole. Markets containing a single Stackelberg or neural agent produced far more wealth than markets composed only of satisficing agents. However, the agents with knowledge do not necessarily capture the highest share of the wealth. The success of individual agents depends on the agent's trading strategy, as expected, and in addition depends on the combination of agents in the system. Certain strategies appeared to be flexible while others were brittle, and were easily foiled by changing the agents in the market, or by changing the market conditions. Earlier studies attempted to use neural networks to simulate an entire economic system, but were rejected because the organizing principles of the two systems are not analogous. Additionally, neural networks were successfully tested for solving various economics problems that were not related to the simulation of economic systems. Neural networks were found to effectively solve problems with missing and redundant data that are not directly solvable with well known methods such as least squares.

A modified Witten-Sander algorithm was devised for the diffusion-limited aggregation process. The simulation and analysis were performed on a personal computer. The fractal dimension was determined by using various forms of a two-point density correlation function and by the radius of gyration. The results of computing the correlation function with square and circular windows were analyzed. The correlation function was further modified to include the edge from analysis and those results were compared to the fractal dimensions obtained from the whole aggregate. The fractal dimensions of 1.67 ± .01 and 1.75 ± .08 agree with the accepted values. Animation of the aggregation process elucidated the limited penetration into the interior and the zone of most active deposition at the exterior of the aggregate.

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Bibliography: p. 145-148 Electronic publication; full text available in PDF format; abstract in HTML format. This thesis deals with the squat of a moving ship, that is, the downward displacement and angle of trim caused by its forward motion. The aim is to be able to predict accurately the squat of any ship at any given speed and water depth. (introduction) Electronic reproduction.[Australia] :Australian Digital Theses Program,2001.