Thesis (M.S.)--West Virginia University, 2005. / Title from document title page. Document formatted into pages; contains iii, 33 p. Includes abstract. Includes bibliographical references (p. 33).

The concept of a tree has been used in various areas of mathematics for over a century. In particular, trees appear to be one of the most fundamental notions in computer science. Sequential algorithms for trees are generally well studied. Unfortunately many of these sequential algorithms use methods which seem to be inherently sequential. One of the contributions of this thesis is the introduction of several parallel techniques for the construction of various types of trees and the presentation of new parallel tree construction algorithms using these methods. Along with the parallel tree construction techniques presented here, we develop techniques which have broader applications. We use the Parallel Random Access Machine as our model of computation. We consider two basic methods of constructing trees:tree expansion and tree synthesis. In the tree expansion method, we start with a single vertex and construct a tree by adding nodes of degree one and/or by subdividing edges. We use the parallel tree expansion technique to construct the tree representation for graphs in the family of graphs known as cographs. In the tree synthesis method, we start with a forest of single node subtrees and construct a tree by adding edges or (for rooted trees) by creating parent nodes for some roots of the trees in the forest. We present a family of parallel and sequential algorithms to construct various approximations to the Huffman tree. All these algorithms apply the tree synthesis method by constructing a tree in a level-by-level fashion. To support one of the algorithms in the family we develop a technique which we call the cascading sampling technique. One might suspect that the parallel tree synthesis method can be applied only to trees of polylogarithmic height, but this is not the case.We present a technique which we call the valley filling technique and develop its accelerated version called the accelerated valley filling technique. We present an application of this technique to an optimal parallel algorithm for construction of minimax trees. / Science, Faculty of / Computer Science, Department of / Graduate

M.Sc. (Mathematics) / Please refer to full text to view abstract

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Piaget and Freudenthal advocated thinking levels. In the 1950's the van Hieles developed a five level model of geometric thought. Judith Land adapted the model in 1990, utilising four levels to teach the concept of functions. These four levels have been considered here in the formation of concepts of sequences and series. The origin and relevance of sequences and series have been studied and the importance of visualisation, patterning and generalisation in the instructional process investigated. A series of lessons on these topics was taught to a group of six higher grade matriculation students of mixed ability and gender. Questionnaires related to student progress through the various levels were answered, categorised, graphed and analysed. Despite the small number of students, results seem to indicate that emphasising visualisation, exploring patterns and generalisation and teaching the topics as a reinvention had made a positive contribution towards progress through the various thought levels. / Mathematics Education / M.A. (Mathematics Education)

by Mow Wai Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1991. / Bibliographies: leaves 98-104. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Channel Model and Other Basic Assumptions --- p.5 / Chapter 1.2 --- Complexity Measure --- p.8 / Chapter 1.3 --- Maximum Likelihood Sequence Estimator --- p.9 / Chapter 1.4 --- The Viterbi Algorithm ´ؤ An Implementation of MLSE --- p.11 / Chapter 1.5 --- Error Performance of the Viterbi Algorithm --- p.14 / Chapter 1.6 --- Suboptimal Viterbi-like Algorithms --- p.17 / Chapter 1.7 --- Trends of Digital Transmission and MLSE --- p.19 / Chapter 2 --- New Formulation of MLSE --- p.21 / Chapter 2.1 --- The Truncated Viterbi Algorithm --- p.21 / Chapter 2.2 --- Choice of Truncation Depth --- p.23 / Chapter 2.3 --- Decomposition of MLSE --- p.26 / Chapter 2.4 --- Lattice Interpretation of MLSE --- p.29 / Chapter 3 --- The Closest Vector Problem --- p.34 / Chapter 3.1 --- Basic Definitions and Facts About Lattices --- p.37 / Chapter 3.2 --- Lattice Basis Reduction --- p.40 / Chapter 3.2.1 --- Weakly Reduced Bases --- p.41 / Chapter 3.2.2 --- Derivation of the LLL-reduction Algorithm --- p.43 / Chapter 3.2.3 --- Improved Algorithm for LLL-reduced Bases --- p.52 / Chapter 3.3 --- Enumeration Algorithm --- p.57 / Chapter 3.3.1 --- Lattice and Isometric Mapping --- p.58 / Chapter 3.3.2 --- Enumerating Points in a Parallelepiped --- p.59 / Chapter 3.3.3 --- Enumerating Points in a Cube --- p.63 / Chapter 3.3.4 --- Enumerating Points in a Sphere --- p.64 / Chapter 3.3.5 --- Comparisons of Three Enumeration Algorithms --- p.66 / Chapter 3.3.6 --- Improved Enumeration Algorithm for the CVP and the SVP --- p.67 / Chapter 3.4 --- CVP Algorithm Using the Reduce-and-Enumerate Approach --- p.71 / Chapter 3.5 --- CVP Algorithm with Improved Average-Case Complexity --- p.72 / Chapter 3.5.1 --- CVP Algorithm for Norms Induced by Orthogonalization --- p.73 / Chapter 3.5.2 --- Improved CVP Algorithm using Norm Approximation --- p.76 / Chapter 4 --- MLSE Algorithm --- p.79 / Chapter 4.1 --- MLSE Algorithm for PAM Systems --- p.79 / Chapter 4.2 --- MLSE Algorithm for Unimodular Channel --- p.82 / Chapter 4.3 --- Reducing the Boundary Effect for PAM Systems --- p.83 / Chapter 4.4 --- Simulation Results and Performance Investigation for Example Channels --- p.86 / Chapter 4.5 --- MLSE Algorithm for Other Lattice-Type Modulation Systems --- p.91 / Chapter 4.6 --- Some Potential Applications --- p.92 / Chapter 4.7 --- Further Research Directions --- p.94 / Chapter 5 --- Conclusion --- p.96 / Bibliography --- p.104

Lai Kim Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 55-57). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Likelihood Ratio Test Statistic --- p.6 / Chapter 2.1 --- Introduction --- p.6 / Chapter 2.2 --- Formulation --- p.6 / Chapter 2.3 --- Likelihood Ratio Type Statistic --- p.7 / Chapter 2.4 --- Dirichlet Distribution --- p.8 / Chapter 2.5 --- Edgeworth Expansion --- p.12 / Chapter 3 --- Divided Difference --- p.15 / Chapter 3.1 --- Introduction --- p.15 / Chapter 3.2 --- Definition of Divided Difference --- p.15 / Chapter 3.3 --- Theorem --- p.17 / Chapter 3.4 --- Proof of the Theorem --- p.18 / Chapter 3.5 --- Application of Theorem --- p.19 / Chapter 4 --- Computational Results --- p.22 / Chapter 4.1 --- Introduction --- p.22 / Chapter 4.2 --- Critical Values for Moderate and Large Sample Sizes --- p.22 / Chapter 4.3 --- Critical Values for Small Sample Sizes --- p.23 / Chapter 4.3.1 --- Exact Critical Values --- p.23 / Chapter 4.3.2 --- Edgeworth Expansion Results --- p.23 / Chapter 4.3.3 --- Simulation Results --- p.23 / Chapter 4.4 --- Power --- p.24 / Chapter 5 --- Illustrative Examples --- p.29 / Chapter 5.1 --- Stanford Heart Transplant Data --- p.29 / Chapter 5.1.1 --- The Data --- p.29 / Chapter 5.1.2 --- Result --- p.31 / Chapter 5.2 --- Air Conditioning Data --- p.31 / Chapter 5.2.1 --- The Data --- p.31 / Chapter 5.2.2 --- Result --- p.32 / Chapter 5.3 --- Insulating Fluid Failure Data --- p.33 / Chapter 5.3.1 --- The Data --- p.33 / Chapter 5.3.2 --- Result --- p.33 / Chapter 6 --- Conclusion and Further Research Topic --- p.35 / Chapter 6.1 --- Conclusion --- p.35 / Chapter 6.2 --- Further Research Topic --- p.38 / Appendix A --- p.39 / Appendix B --- p.46 / Bibliography --- p.55

Kwan Ho-yuet. / "April 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 98-[103]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

Li, Qiwei. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (p. 75-85). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Repetitive DNA Sequence --- p.3 / Chapter 1.1.1 --- Definition and Categorization of Repeti- tive DNA Sequence --- p.3 / Chapter 1.1.2 --- Definition and Categorization of Tandem Repeats --- p.4 / Chapter 1.1.3 --- Definition and Categorization of Interspersed Repeats --- p.6 / Chapter 1.2 --- Research Significance --- p.7 / Chapter 1.3 --- Contributions --- p.9 / Chapter 1.4 --- Thesis Organization --- p.11 / Chapter 2 --- Literature Review and Overview of Our Method --- p.13 / Chapter 2.1 --- Existing Methods --- p.14 / Chapter 2.2 --- Overview of Our Method --- p.17 / Chapter 3 --- Theoretical Background --- p.22 / Chapter 3.1 --- Multinomial Distributions --- p.23 / Chapter 3.2 --- Dirichlet Distribution --- p.23 / Chapter 3.3 --- Metropolis-Hastings Sampling --- p.25 / Chapter 3.4 --- Gibbs Sampling --- p.26 / Chapter 4 --- Problem Description --- p.28 / Chapter 4.1 --- Generative Model --- p.29 / Chapter 4.1.1 --- Input Data R --- p.31 / Chapter 4.1.2 --- Parameters A (Repeat Segment Starting Positions) --- p.32 / Chapter 4.1.3 --- Parameters S (Repeat Segment Structures) --- p.33 / Chapter 4.1.4 --- Parameters θ(Motif Matrix) --- p.35 / Chapter 4.1.5 --- Parameters Φ (Background Distribution) . --- p.36 / Chapter 4.1.6 --- An Example of the Model Schematic Di- agram --- p.37 / Chapter 4.2 --- Parameter Structure --- p.38 / Chapter 4.3 --- Posterior Distribution --- p.40 / Chapter 4.3.1 --- The Full Posterior Distribution --- p.41 / Chapter 4.3.2 --- The Collapsed Posterior Distribution --- p.42 / Chapter 4.4 --- Conclusion --- p.43 / Chapter 5 --- Methodology --- p.45 / Chapter 5.1 --- Schematic Procedure --- p.46 / Chapter 5.1.1 --- The Basic Schematic Procedure --- p.46 / Chapter 5.1.2 --- The Improved Schematic Procedure --- p.47 / Chapter 5.2 --- Initialization --- p.49 / Chapter 5.3 --- Predictive Update Step for θn and Φn --- p.50 / Chapter 5.4 --- Gibbs Sampling Step for an --- p.50 / Chapter 5.5 --- Metropolis-Hastings Sampling Step for sn --- p.51 / Chapter 5.5.1 --- Rear Indel Move --- p.53 / Chapter 5.5.2 --- Partial Shift Move --- p.56 / Chapter 5.5.3 --- Front Indel Move --- p.56 / Chapter 5.6 --- Phase Shifts --- p.57 / Chapter 5.7 --- Conclusion --- p.58 / Chapter 6 --- Results and Discussion --- p.60 / Chapter 6.1 --- Settings --- p.61 / Chapter 6.2 --- Experiment on Synthetic Data --- p.63 / Chapter 6.3 --- Experiment on Real Data --- p.69 / Chapter 7 --- Conclusion and Future Work --- p.72 / Chapter 7.1 --- Conclusion --- p.72 / Chapter 7.2 --- Future Work --- p.74 / Bibliography --- p.75

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 120-124).