Recent medical studies have led cardiologists to revise theories regarding the cause of heart attacks. Rather than a gradual clogging of the arteries, eruption of a vulnerable plaque is thought to be the cause of approximately 75% of all heart attacks. As a result, traditional risk factors are no longer sufficient indicators of who is at risk for a heart attack. Therefore, this research investigates the willingness to pay (WTP) for a new, hypothetical detection (screening) and treatment method for vulnerable plaque. For this study, two survey instruments were developed that take advantage of the visual and interactive aspects of the Internet. Individuals report their perception of heart attack risk both prior to and after receiving new information on who cardiologists currently believe to be at risk for a heart attack. In addition, respondents are provided with information about the effectiveness and risks associated with screening and treatment. Using webbased surveys, which follow a contingent valuation format, an iterative bidding process is used to elicit the respondents WTP for either the screening or treatment method. Internet, on-line surveys are often prone to coverage bias; however, the survey valuing screening (a simple blood test) used a Knowledge Networks panel and resulted in a sample of 268 adults that is essentially representative of the general population. The survey valuing treatment (a more invasive heart catheterization procedure) was administered only to individuals with doctor-diagnosed heart problems, who are presumably more familiar with these types of medical decisions, and resulted in a sample of 295 adults. The mean for screening is $69 and the mean WTP for treatment that is 85% effective is $5,816. A two-part model is used to identify the factors that influence WTP, as well as the decision to receive the screening/treatment. The data suggests that these factors vary across genders. The data obtained for this study demonstrate construct validity; therefore, the results may provide useful information for policy analysis regarding the screening and treatment of heart attack.

An iterative control algorithm (ICA) which uses an approximate inverse-hysteresis model is implemented to compensate for hysteresis to precisely fabricate features on a soft polymer substrate using an atomic force microscope (AFM). The AFM is an important instrument in micro/nanotechnology because of its ability to interrogate, manipulate, and fabricate objects at the micro/nanoscale. The AFM uses a piezoelectric actuator to position an AFM-probe tip relative to the sample surface in three dimensions. In particular, precision lateral control of the AFM-probe tip relative to the sample surface is needed to ensure high-performance operation of the AFM. However, precision lateral positioning of the AFM-probe tip is challenging due to significant positioning error caused by hysteresis effect. An ICA which incorporates an approximate inverse of the hysteresis behavior is proposed to compensate for the hysteresis-caused positioning error. The approach is applied to fabricate a feature using the AFM on a polycarbonate surface, and it is demonstrated that the maximum tracking error can be reduced to 0.225% of the displacement range, underscoring the benefits of the control method.

The aim of this work is the study of infinite conformal iterated function systems. More specifically, we investigate some properties of a limit set J associated to such system, its Hausdorff and packing measure and Hausdorff dimension. We provide necessary and sufficient conditions for such systems to be bi-Lipschitz equivalent. We use the concept of scaling functions to obtain some result about 1-dimensional systems. We discuss particular examples of infinite iterated function systems derived from complex continued fraction expansions with restricted entries. Each system is obtained from an infinite number of contractions. We show that under certain conditions the limit sets of such systems possess zero Hausdorff measure and positive finite packing measure. We include an algorithm for an approximation of the Hausdorff dimension of limit sets. One numerical result is presented. In this thesis we also explore the concept of positively recurrent function. We use iterated function systems to construct a natural, wide class of such functions that have strong ergodic properties.

PT-symmetric Hamiltonians proposed by Bender and Boettcher can have real energy spectra. As an extension of the Hermitian Hamiltonian, PT-symmetric systems have attracted a great interest in recent years. Understanding the underlying mathematical structure of these theories sheds insight on outstanding problems of physics. These problems include the nature of Higgs particles, the properties of dark matter, the matter-antimatter asymmetry in the universe, and neutrino oscillations. Furthermore, PT-phase transition has been observed in lasers, optical waveguides, microwave cavities, superconducting wires and circuits. The objective of this thesis is to extend the iterative method of solving Schrodinger equation used for an harmonic oscillator systems to Hamiltonians with PT-symmetric potentials. An important aspect of this approach is the high accuracy of eigenvalues and the fast convergence. Our method is a combination of Hill determinant method [8] and the power series expansion. eigenvalues and the fast convergence. One can transform the Schrodinger equation into a secular equation by using a trial wave function. A recursion structure can be obtained using the secular equation, which leads to accurate eigenvalues. Energy values approach to exact ones when the number of iterations is increased. We obtained eigenvalues for a set of PT-symmetric Hamiltonians.

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in ful lment of the requirements for the degree of Doctor of Philosophy. Johannesburg, August 2015. / We construct, using rst principles, a number of non-trivial conservation laws of some partial di erence equations, viz, the discrete Liouville equation and the discrete Sine-Gordon equation. Symmetries and the more recent ideas and notions of characteristics (multipliers) for di erence equations are also discussed. We then determine the symmetry generators of some ordinary di erence equations and proceed to nd the rst integral and reduce the order of the di erence equations. We show that, in some cases, the symmetry generator and rst integral are associated via the `invariance condition'. That is, the rst integral may be invariant under the symmetry of the original di erence equation. We proceed to carry out double reduction of the di erence equation in these cases. We then consider discrete versions of the Painlev e equations. We assume that the characteristics depend on n and un only and we obtain a number of symmetries. These symmetries are used to construct exact solutions in some cases. Finally, we discuss symmetries of linear iterative equations and their transformation properties. We characterize coe cients of linear iterative equations for order less than or equal to ten, although our approach of characterization is valid for any order. Furthermore, a list of coe cients of linear iterative equations of order up to 10, in normal reduced form is given.

Fung Yiu-fai Phineas. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 142-148). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Model-based Pose Estimation --- p.3 / Chapter 1.1.1 --- Application - 3D Motion Tracking --- p.4 / Chapter 1.2 --- Image-based View Synthesis --- p.4 / Chapter 1.3 --- Thesis Contribution --- p.7 / Chapter 1.4 --- Thesis Outline --- p.8 / Chapter 2 --- General Background --- p.9 / Chapter 2.1 --- Notations --- p.9 / Chapter 2.2 --- Camera Models --- p.10 / Chapter 2.2.1 --- Generic Camera Model --- p.10 / Chapter 2.2.2 --- Full-perspective Camera Model --- p.11 / Chapter 2.2.3 --- Affine Camera Model --- p.12 / Chapter 2.2.4 --- Weak-perspective Camera Model --- p.13 / Chapter 2.2.5 --- Paraperspective Camera Model --- p.14 / Chapter 2.3 --- Model-based Motion Analysis --- p.15 / Chapter 2.3.1 --- Point Correspondences --- p.16 / Chapter 2.3.2 --- Line Correspondences --- p.18 / Chapter 2.3.3 --- Angle Correspondences --- p.19 / Chapter 2.4 --- Panoramic Representation --- p.20 / Chapter 2.4.1 --- Static Mosaic --- p.21 / Chapter 2.4.2 --- Dynamic Mosaic --- p.22 / Chapter 2.4.3 --- Temporal Pyramid --- p.23 / Chapter 2.4.4 --- Spatial Pyramid --- p.23 / Chapter 2.5 --- Image Pre-processing --- p.24 / Chapter 2.5.1 --- Feature Extraction --- p.24 / Chapter 2.5.2 --- Spatial Filtering --- p.27 / Chapter 2.5.3 --- Local Enhancement --- p.31 / Chapter 2.5.4 --- Dynamic Range Stretching or Compression --- p.32 / Chapter 2.5.5 --- YIQ Color Model --- p.33 / Chapter 3 --- Model-based Pose Estimation --- p.35 / Chapter 3.1 --- Previous Work --- p.35 / Chapter 3.1.1 --- Estimation from Established Correspondences --- p.36 / Chapter 3.1.2 --- Direct Estimation from Image Intensities --- p.49 / Chapter 3.1.3 --- Perspective-3-Point Problem --- p.51 / Chapter 3.2 --- Our Iterative P3P Algorithm --- p.58 / Chapter 3.2.1 --- Gauss-Newton Method --- p.60 / Chapter 3.2.2 --- Dealing with Ambiguity --- p.61 / Chapter 3.2.3 --- 3D-to-3D Motion Estimation --- p.66 / Chapter 3.3 --- Experimental Results --- p.68 / Chapter 3.3.1 --- Synthetic Data --- p.68 / Chapter 3.3.2 --- Real Images --- p.72 / Chapter 3.4 --- Discussions --- p.73 / Chapter 4 --- Panoramic View Analysis --- p.76 / Chapter 4.1 --- Advanced Mosaic Representation --- p.76 / Chapter 4.1.1 --- Frame Alignment Policy --- p.77 / Chapter 4.1.2 --- Multi-resolution Representation --- p.77 / Chapter 4.1.3 --- Parallax-based Representation --- p.78 / Chapter 4.1.4 --- Multiple Moving Objects --- p.79 / Chapter 4.1.5 --- Layers and Tiles --- p.79 / Chapter 4.2 --- Panorama Construction --- p.79 / Chapter 4.2.1 --- Image Acquisition --- p.80 / Chapter 4.2.2 --- Image Alignment --- p.82 / Chapter 4.2.3 --- Image Integration --- p.88 / Chapter 4.2.4 --- Significant Residual Estimation --- p.89 / Chapter 4.3 --- Advanced Alignment Algorithms --- p.90 / Chapter 4.3.1 --- Patch-based Alignment --- p.91 / Chapter 4.3.2 --- Global Alignment (Block Adjustment) --- p.92 / Chapter 4.3.3 --- Local Alignment (Deghosting) --- p.93 / Chapter 4.4 --- Mosaic Application --- p.94 / Chapter 4.4.1 --- Visualization Tool --- p.94 / Chapter 4.4.2 --- Video Manipulation --- p.95 / Chapter 4.5 --- Experimental Results --- p.96 / Chapter 5 --- Panoramic Walkthrough --- p.99 / Chapter 5.1 --- Problem Statement and Notations --- p.100 / Chapter 5.2 --- Previous Work --- p.101 / Chapter 5.2.1 --- 3D Modeling and Rendering --- p.102 / Chapter 5.2.2 --- Branching Movies --- p.103 / Chapter 5.2.3 --- Texture Window Scaling --- p.104 / Chapter 5.2.4 --- Problems with Simple Texture Window Scaling --- p.105 / Chapter 5.3 --- Our Walkthrough Approach --- p.106 / Chapter 5.3.1 --- Cylindrical Projection onto Image Plane --- p.106 / Chapter 5.3.2 --- Generating Intermediate Frames --- p.108 / Chapter 5.3.3 --- Occlusion Handling --- p.114 / Chapter 5.4 --- Experimental Results --- p.116 / Chapter 5.5 --- Discussions --- p.116 / Chapter 6 --- Conclusion --- p.121 / Chapter A --- Formulation of Fischler and Bolles' Method for P3P Problems --- p.123 / Chapter B --- Derivation of z1 and z3 in terms of z2 --- p.127 / Chapter C --- Derivation of e1 and e2 --- p.129 / Chapter D --- Derivation of the Update Rule for Gauss-Newton Method --- p.130 / Chapter E --- Proof of (λ1λ2-λ 4）>〉0 --- p.132 / Chapter F --- Derivation of φ and hi --- p.133 / Chapter G --- Derivation of w1j to w4j --- p.134 / Chapter H --- More Experimental Results on Panoramic Stitching Algorithms --- p.138 / Bibliography --- p.148

by Cheng Sze Wan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves 72-[76]). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Traffic Scheduling in Input-buffered Switches .。 --- p.3 / Chapter 1.3 --- Organization of Thesis --- p.7 / Chapter 2 --- Principle of Enchanced PIM Algorithm --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.1.1 --- Switch Model --- p.9 / Chapter 2.2 --- Enhanced Parallel Iterative Matching Algorithm (EPIM) --- p.10 / Chapter 2.2.1 --- Motivation --- p.10 / Chapter 2.2.2 --- Algorithm --- p.12 / Chapter 2.3 --- Performance Evaluation --- p.16 / Chapter 2.3.1 --- Simulation --- p.16 / Chapter 2.3.2 --- Delay Analysis --- p.18 / Chapter 3 --- Providing Bandwidth Guarantee in Input-Buffered Switches --- p.25 / Chapter 3.1 --- Introduction --- p.25 / Chapter 3.2 --- Bandwidth Reservation in Static Scheduling Algorithm --- p.26 / Chapter 3.3 --- Incorporation of Dynamic and Static Scheduling Algorithms .。 --- p.32 / Chapter 3.4 --- Simulation --- p.34 / Chapter 3.4.1 --- Switch Model --- p.35 / Chapter 3.4.2 --- Simulation Results --- p.36 / Chapter 3.5 --- Comparison with Existing Schemes --- p.42 / Chapter 3.5.1 --- Statistical Matching --- p.42 / Chapter 3.5.2 --- Weighted Probabilistic Iterative Matching --- p.45 / Chapter 4 --- EPIM and Cross-Path Switch --- p.50 / Chapter 4.1 --- Introduction --- p.50 / Chapter 4.2 --- Concept of Cross-Path Switching --- p.51 / Chapter 4.2.1 --- Principle --- p.51 / Chapter 4.2.2 --- Supporting Performance Guarantee in Cross-Path Switch --- p.52 / Chapter 4.3 --- Implication of EPIM on Cross-Path switch --- p.55 / Chapter 4.3.1 --- Problem Re-definition --- p.55 / Chapter 4.3.2 --- Scheduling in Input Modules with EPIM --- p.58 / Chapter 4.4 --- Simulation --- p.63 / Chapter 5 --- Conclusion --- p.70 / Bibliography --- p.72

Wai-shing Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 114). / Abstracts in English and Chinese. / Contents --- p.i / List of Figures --- p.iv / List of Tables --- p.v / Abstract --- p.vi / Acknowledgement --- p.vii / Chapter Chapter 1. --- Layout of the thesis --- p.1 / Chapter Chapter 2. --- Introduction --- p.3 / Chapter 2.1 --- What is the reasoning problem? --- p.3 / Chapter 2.2 --- Fundamental nature of Knowledge --- p.4 / Chapter 2.3 --- Fundamental methodology of Reasoning --- p.7 / Chapter 2.4 --- Our intended approach --- p.9 / Chapter Chapter 3. --- Probabilistic reasoning networks --- p.11 / Chapter 3.1 --- Overview --- p.11 / Chapter 3.2 --- Causality and influence diagrams --- p.11 / Chapter 3.3 --- Bayesian networks - influence diagrams endowed with a probability interpretation --- p.13 / Chapter 3.3.1 --- A detour to the interpretations of probability --- p.13 / Chapter 3.3.2 --- Bayesian networks --- p.15 / Chapter 3.3.3 --- Acyclicity and global probability --- p.17 / Chapter 3.4 --- Reasoning on probabilistic reasoning networks I - local updating formulae --- p.17 / Chapter 3.4.1 --- Rationale of the intended reasoning strategy --- p.18 / Chapter 3.4.2 --- Construction of the local updating formula --- p.19 / Chapter 3.5 --- Cluster graphs - another perspective to reasoning problems --- p.23 / Chapter 3.6 --- Semi-lattices - another representation of Cluster graphs --- p.26 / Chapter 3.6.1 --- Construction of semi-lattices --- p.26 / Chapter 3.7 --- Bayesian networks and semi-lattices --- p.28 / Chapter 3.7.1 --- Bayesian networks to acyclic semi-lattices --- p.29 / Chapter 3.8 --- Reasoning on (acyclic) probabilistic reasoning networks II - global updating schedules --- p.29 / Chapter 3.9 --- Conclusion --- p.30 / Chapter Chapter 4. --- Cyclic reasoning networks - a possibility? --- p.32 / Chapter 4.1 --- Overview --- p.32 / Chapter 4.2 --- A meaningful cyclic structure - derivation of the ideal gas law --- p.32 / Chapter 4.3 --- "What's ""wrong"" to be in a cyclic world" --- p.35 / Chapter 4.4 --- Communication - Dynamics - Complexity --- p.39 / Chapter 4.4.1 --- Communication as dynamics; dynamics to complexity --- p.42 / Chapter 4.5 --- Conclusion --- p.42 / Chapter Chapter 5. --- Cyclic reasoning networks ´ؤ error-control application --- p.43 / Chapter 5.1 --- Overview --- p.43 / Chapter 5.2 --- Communication schemes on cyclic reasoning networks directed to error-control applications --- p.43 / Chapter 5.2.1 --- Part I ´ؤ Local updating formulae --- p.44 / Chapter 5.2.2 --- Part II - Global updating schedules across the network --- p.46 / Chapter 5.3 --- Probabilistic reasoning based error-control schemes --- p.47 / Chapter 5.3.1 --- Local sub-universes and global universe underlying the error- control structure --- p.47 / Chapter 5.4 --- Error-control structure I --- p.48 / Chapter 5.4.1 --- Decoding algorithm - Communication between local sub- universes in compliance with the global topology --- p.51 / Chapter 5.4.2 --- Decoding rationales --- p.55 / Chapter 5.4.3 --- Computational results --- p.55 / Chapter 5.5 --- Error-control structure II --- p.57 / Chapter 5.5.1 --- Structure of the code and the corresponding decoding algorithm --- p.57 / Chapter 5.5.2 --- Computational results --- p.63 / Chapter 5.6 --- Error-control structure III --- p.66 / Chapter 5.6.1 --- Computational results --- p.70 / Chapter 5.7 --- Error-control structure IV --- p.71 / Chapter 5.7.1 --- Computational results --- p.73 / Chapter 5.8 --- Conclusion --- p.74 / Chapter Chapter 6. --- Dynamics on cyclic probabilistic reasoning networks --- p.75 / Chapter 6.1 --- Overview --- p.75 / Chapter 6.2 --- Decoding rationales --- p.76 / Chapter 6.3 --- Error-control structure I - exact solutions --- p.77 / Chapter 6.3.1 --- Dynamical invariant - a key to tackle many dynamical problems --- p.77 / Chapter 6.3.2 --- Dynamical invariant for error-control structure I --- p.78 / Chapter 6.3.3 --- Iteration dynamics --- p.79 / Chapter 6.3.4 --- Structure preserving property and the maximum a posteriori solutions --- p.86 / Chapter 6.4 --- Error-control structures III & IV - exact solutions --- p.92 / Chapter 6.4.1 --- Error-control structure III --- p.92 / Chapter 6.4.1.1 --- Dynamical invariants for error-control structure III --- p.92 / Chapter 6.4.1.2 --- Iteration dynamics --- p.93 / Chapter 6.4.2 --- Error-control structure IV --- p.96 / Chapter 6.4.3 --- Structure preserving property and the maximum a posteriori solutions --- p.98 / Chapter 6.5 --- Error-control structure II - exact solutions --- p.101 / Chapter 6.5.1 --- Iteration dynamics --- p.102 / Chapter 6.5.2 --- Structure preserving property and the maximum a posteriori solutions --- p.105 / Chapter 6.6 --- A comparison on the four error-control structures --- p.106 / Chapter 6.7 --- Conclusion --- p.108 / Chapter Chapter 7. --- Conclusion --- p.109 / Chapter 7.1 --- Our thesis --- p.109 / Chapter 7.2 --- Hind-sights and foresights --- p.110 / Chapter 7.3 --- Concluding remark --- p.111 / Appendix A. An alternative derivation of the local updating formula --- p.112 / Bibliography --- p.114

The Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Ensemble Kalman Filter (EnKF) are commonly implemented practical solutions for solving nonlinear state space estimation problems; all based on the linear state space estimator, the Kalman Filter. Often, the UKF and EnKF are cited as a superior methods to the EKF with respect to error-based performance criteria. The UKF in turn has the advantage over the EnKF of smaller computational complexity. In practice however the UKF often fails to live up to this expectation, with performance which does not surpass the EKF and estimates which are not as robust as the EnKF. This work explores the geometry of alternative sigma point sets, which form the basis of the UKF, contributing several new sets along with novel methods used to generate them. In particular, completely novel systems of sigma points that preserve higher order statistical moments are found and evaluated. Additionally a new method for scaling and problem specific tuning of sigma point sets is introduced as well as a discussion of why this is necessary, and a new way of thinking about UKF systems in relation to the other two Kalman Filter methods. An Iterated UKF method is also introduced, similar to the smoothing iterates developed previously for the EKF. The performance of all of these methods is demonstrated using problem exemplars with the improvement of the contributed methods highlighted.

by Ye Yuanling. / "August 2000." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (p. 82-85). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.