by Tong Pak Yee. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 12-16). / Acknowledgement --- p.i / List of Publications --- p.ii / Abstract --- p.iii / Chapter 1. --- Introduction / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Outline of the article --- p.5 / Chapter 1.2.1 --- Multifractal Scaling in Fractal Lattice --- p.6 / Chapter 1.2.2 --- Anomalous Multifractality in Percolation Model --- p.7 / Chapter 1.2.3 --- Anomalous Crossover Behavior in Two-Component Random Resistor Network --- p.8 / Chapter 1.2.4 --- Current Distribution in Two-Component Random Resistor Network --- p.10 / Chapter 1.2.5 --- Multif ractality in Wide Distribution Fractal Models --- p.11 / References --- p.12 / Chapter 2. --- Multifractal Analysis of Percolation Backbone and Fractal Lattices / Chapter 2.1 --- Multifractal Scaling in Fractal Lattice --- p.17 / Chapter 2.1.1 --- Multifractal Scaling in a Sierpinski Gasket --- p.18 / Chapter 2.1.2 --- Hierarchy of Critical Exponents on a Sierpinski Honeycomb --- p.38 / Chapter 2.2 --- Anomalous Multifractality in Percolation Model --- p.51 / Chapter 2.2.1 --- Anomalous Multifractality of Conductance Jumps in a Hierarchical Percolation Model --- p.52 / Chapter 2.3 --- Anomalous Crossover Behavior in Two-Component Random Resistor Network --- p.74 / Chapter 2.3.1 --- Anomalous Crossover Behaviors in the Two- Component Deterministic Percolation Model --- p.75 / Chapter 2.3.2 --- Minimum Current in the Two-Component Random Resistor Network --- p.90 / Chapter 2.4 --- Current Distribution in Two-Component Random Resistor Network --- p.105 / Chapter 2.4.1 --- Current Distribution in the Two-Component Hierarchical Percolation Model --- p.106 / Chapter 2.4.2 --- Current Distribution and Local Power Dissipation in the Two-Component Deterministic Percolation Model --- p.136 / Chapter 2.5 --- Multifractality in Wide Distribution Fractal Models --- p.174 / Chapter 2.5.1 --- Fractal Networks with a Wide Distribution of Conductivities --- p.175 / Chapter 2.5.2 --- Power Dissipation in an Exactly Solvable Wide Distribution Model --- p.193 / Chapter 3. --- Conclusion --- p.210

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

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Thesis. 1975. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / Vita. / Bibliography: leaves 132-133. / by Nguyen Quang Hien. / Ph.D.

博弈理論己貫穿於許多不同的研究領域中，成為了一種非常有用的研究工具。在演化博弈中，個體可以通過比較彼此在競爭中表現的好壞，從一個策略改變至另一個策略。當依賴於收益參數的競爭個體系統處於穩定態時，可以是一個所有個體都採用同一策略的均勻系統，或是使用不同策略的個體共同存在的非均勻系統。近年來，均勻態和混合態或是均勻相和混合相之間的轉變成為物理學家們的研究熱點。 / 在論文的第一部份(第二及第三章)中，我們研究了有空間關聯的群體在規則晶格上演化雪堆博弄(ESG) 。在文獻中的分析方法大多數是基於對近似法(pair approximation) 。但是對近似法的結果，就算是在定性上，都未能捕捉到電算模擬結果中顯現的重要特性。例如，對近似法未能給出全c 態和混合態之間以及混合態與全D 態之間的轉變特徵，其中c和D 分別表示演化雪堆博奔中的兩種策略。而這些轉變作為收益參數的函數，卻可於ESG 在不同的規則品格中的電算模擬中被觀察到。對近似法的這些缺陷引發了本論文的研究。當不同局域競爭組態的分佈形式假設為二項式分佈，並將之引入到c 個體數目隨時間演變的動態公式中，就能得出全D 態。當進一步深入考慮ESG 的演化後，我們得知在收益參數較小時，D 個體被孤立的局部組態的比例在二項式分佈假設中被高估。通過修正D 個體被孤立的局部組態比例，就能得出全C 態。通過適當調整收益參數較小時D 個體被孤立的局部組態的比例，和收益參數較大時適當調整C個體被孤立的局部組態的比例，我們就能得出與模擬結果吻合較好的結果。然後，我們還將這個方法推廣至線性鏈和六角品格結構中。該種方法比對近似法得到的結果更好。 / 在論文的第二部份(第四章)中，我們研究了有本懲罰者的存在對演化雪堆博弈在正方晶格上演化的影響。該博弈中相應地有三種策略。懲罰者願意支付額外成本以對不合作者造成顯外的損失。同時懲罰者與其他合作者之間是合作的。我們展示了在收益參數組成的空間下得出的詳盡相圖。我們從動態演化後期出現的最終生存形態(last surviving patterns) 出發，討論了相圖中的相邊界成因。 / Game theoretical methods have become a useful tool in research across many fields. In evolutionary games, agents could switch from one strategy to another based on how well they perform as compared with others. Depending on a payoff parameter, a system of competing agents may form a homogeneous system with all agents taking on the same strategy or an inhomogeneous system with the coexistence of different strategies in the steady state. The transitions between the homogeneous and mixed states or phases are of much interest to physicists in recent years. / In Part I (Chapter 2 and 3) of the thesis, the evolutionary snowdrift game (ESG) is studied in spatially structured populations on regular lattices. Analytic approaches in the literature are largely based on the pair approximation. However, results of the pair approximation cannot capture the key features in simulation results even qualitatively. For example, the pair approximation fails to give the transition between an All-C and the mixed phase and the transition between the mixed phase and an All-D phase as a function of a payoff parameter observed in ESG on different regular lattices, where C and D are the two strategies in ESG. The failure motivated the present work. By incorporating different local competing configurations within an assumption of binomial distribution into the dynamical equation for the time evolution of the number of C-agents, the All-D phase readily emerges. Further consideration of the dynamics of ESG informs us that the proportion of isolated-D local configurations is over-estimated in the binomial distribution when the payoffparameter is small. By modifying the proportion of isolated-D congurations, the All-C phase results. By suitably adjusting the weighings of isolated-D congurations for small payoff parameters and isolated-C congurations for large payoff parameters, good agreement with simulation results is obtained. The approach is then generalized to linear chain and hexagonal lattice. The present approach performs much better than the pair approximation. / In Part II (Chapter 4) of the thesis, the effects of the presence of costly punishers in ESG are studied in a square lattice. There are, thus, three strategies in the game. The punishers are willing to pay an extra cost so as to inflict an extra damage to a defector, and they cooperate with other cooperators. Detailed phase diagrams are presented in the space formed by the payoff parameters. The phase boundaries are discussed within the idea of last surviving patterns at the late stage of the dynamics. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chan, Wan Hang = 晶格上演化雪堆博弈及相關問題的研究 / 陳運亨. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 81-86). / Abstracts also in Chinese. / Chan, Wan Hang = Jing ge shang yan hua xue dui bo yi ji xiang guan wen ti de yan jiu / Chen Yunheng. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Game Theory --- p.2 / Chapter 1.1.1 --- Prisoner Dilemma --- p.3 / Chapter 1.1.2 --- Snowdrift Game --- p.3 / Chapter 1.1.3 --- Costly Punishment --- p.4 / Chapter 1.2 --- Evolutionary Game Theory --- p.6 / Chapter 1.2.1 --- Updating Rules --- p.6 / Chapter 1.2.2 --- Updating Schemes --- p.6 / Chapter 1.2.3 --- Spatial Structures --- p.8 / Chapter 1.3 --- Analytic Approaches --- p.9 / Chapter 1.3.1 --- Mean-field Approach --- p.9 / Chapter 1.3.2 --- Last Surviving Patterns --- p.10 / Chapter 2 --- Evolutionary Snowdrift Game on Square Lattice --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- Simulation Results --- p.12 / Chapter 2.3 --- Last Surviving Patterns --- p.15 / Chapter 2.4 --- Pair Approximation --- p.19 / Chapter 2.5 --- The Site Dynamical Equations --- p.22 / Chapter 2.5.1 --- Pure Binomial Approximation --- p.23 / Chapter 2.5.2 --- Modified Binomial Approximation --- p.24 / Chapter 2.5.3 --- Isolated Factor Correction --- p.27 / Chapter 2.5.4 --- The Zonal Correction --- p.31 / Chapter 2.6 --- Summary --- p.32 / Chapter 3 --- Evolutionary Snowdrift Game on Other Networks --- p.34 / Chapter 3.1 --- Snowdrift Game on Other Lattices --- p.34 / Chapter 3.1.1 --- Linear Chain --- p.34 / Chapter 3.1.2 --- Hexagonal Lattice --- p.40 / Chapter 3.2 --- Snowdrift Game on Small-world Network --- p.43 / Chapter 3.3 --- Summary --- p.50 / Chapter 4 --- Costly punishment in ESG on Lattices --- p.52 / Chapter 4.1 --- Introduction --- p.52 / Chapter 4.2 --- Model --- p.54 / Chapter 4.3 --- Simulation Results [1] --- p.56 / Chapter 4.3.1 --- Results with fixed α and β [1] --- p.56 / Chapter 4.3.2 --- Results with a fixed α [1] --- p.60 / Chapter 4.3.3 --- Consideration of special local structures --- p.65 / Chapter 4.3.4 --- Results of different α --- p.67 / Chapter 4.4 --- Pair Approximation Extended to Three Strategies [1] --- p.69 / Chapter 4.5 --- Summary --- p.76 / Chapter 5 --- Summary --- p.78 / Bibliography --- p.81 / Chapter A --- Uncertainty in Simulation Results --- p.87

Browsing marked-up documents by traversing hyperlinks has become probably the most important means by which documents are accessed, both via the World Wide Web (WWW) and organisational Intranets. However, there is a pressing demand for document management and retrieval systems to deal appropriately with the massive number of documents available. There are two classes of solution: general search engines, whether for the WWW or an Intranet, which make little use of specific domain knowledge or hand-crafted specialised systems which are costly to build and maintain. The aim of this thesis was to develop a document management and retrieval system suitable for small communities as well as individuals in specialised domains on the Web. The aim was to allow users to easily create and maintain their own organisation of documents while ensuring continual improvement in the retrieval performance of the system as it evolves. The system developed is based on the free annotation of documents by users and is browsed using the concept lattice of Formal Concept Analysis (FCA). A number of annotation support tools were developed to aid the annotation process so that a suitable system evolved. Experiments were conducted in using the system to assist in finding staff and student home pages at the School of Computer Science and Engineering, University of New South Wales. Results indicated that the annotation tools provided a good level of assistance so that documents were easily organised and a lattice-based browsing structure that evolves in an ad hoc fashion provided good efficiency in retrieval performance. An interesting result suggested that although an established external taxonomy can be useful in proposing annotation terms, users appear to be very selective in their use of terms proposed. Results also supported the hypothesis that the concept lattice of FCA helped take users beyond a narrow search to find other useful documents. In general, lattice-based browsing was considered as a more helpful method than Boolean queries or hierarchical browsing for searching a specialised domain. We conclude that the concept lattice of Formal Concept Analysis, supported by annotation techniques is a useful way of supporting the flexible open management of documents required by individuals, small communities and in specialised domains. It seems likely that this approach can be readily integrated with other developments such as further improvements in search engines and the use of semantically marked-up documents, and provide a unique advantage in supporting autonomous management of documents by individuals and groups - in a way that is closely aligned with the autonomy of the WWW.

Copies of author's previously published works inserted. Bibliography: p. 56-57.

"October 2002" Bibliography: p. 129-136. 1. Introduction -- 2. QCD and the standard model -- 3. The Lattice -- 4. Symanzik improvement in the Static Quark Potential -- 5. Scale determination for an improved Gluon Action -- 6. Fat-link Irrelevant Clover Fermion actions -- 7. Excited Baryons in Lattice QCD -- 8. Spin 3/2 Baryons -- 9. Conclusion. This thesis reports work done in conducting numerical simulations of Lattice QCD.

There are many problems in mathematical finance which require the evaluation of a multivariate integral. Since these problems typically involve the discretisation of a continuous random variable, the dimension of the integrand can be in the thousands, tens of thousands or even more. For such problems the Monte Carlo method has been a powerful and popular technique. This is largely related to the fact that the performance of the method is independent of the number of dimensions. Traditional quasi-Monte Carlo techniques are typically not independent of the dimension and as such have not been suitable for high-dimensional problems. However, recent work has developed new types of quasi-Monte Carlo point sets which can be used in practically limitless dimension. Among these types of point sets are Sobol' sequences, Faure sequences, Niederreiter-Xing sequences, digital nets and lattice rules. In this thesis, we will concentrate on results concerning lattice rules. The typical setting for analysis of these new quasi-Monte Carlo point sets is the worst-case error in a weighted function space. There has been much work on constructing point sets with small worst-case errors in the weighted Korobov and Sobolev spaces. However, many of the integrands which arise in the area of mathematical finance do not lie in either of these spaces. One common problem is that the integrands are unbounded on the boundaries of the unit cube. In this thesis we construct function spaces which admit such integrands and present algorithms to construct lattice rules where the worst-case error in this new function space is small. Lattice rules differ from other quasi-Monte Carlo techniques in that the points can not be used sequentially. That is, the entire lattice is needed to keep the worst-case error small. It has been shown that there exist generating vectors for lattice rules which are good for many different numbers of points. This is a desirable property for a practitioner, as it allows them to keep increasing the number of points until some error criterion is met. In this thesis, we will develop fast algorithms to construct such generating vectors. Finally, we apply a similar technique to show how a particular type of generating vector known as the Korobov form can be made extensible in dimension.

"October 2002" / Bibliography: p. 129-136. / ix, 136 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis reports work done in conducting numerical simulations of Lattice QCD. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002