Zhang Yuanxiu. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 38-39). / Abstracts in English and Chinese.

by Tse, Yan Tung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 75-76). / Abstracts in English and Chinese. / Abstract --- p.i / 摘要 --- p.i / Acknowledgements --- p.ii / Table of Contents --- p.iii / List of Figures --- p.vi / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Types of 2D Barcodes --- p.3 / Chapter 1.2 --- Reading 2D Barcodes --- p.5 / Chapter 1.3 --- Thesis Organization --- p.8 / Chapter Chapter 2 --- Related Works --- p.9 / Chapter 2.1 --- DataMatrix --- p.9 / Chapter 2.2 --- Original MaxiCode --- p.11 / Chapter 2.3 --- Spatial Methods for MaxiCode --- p.12 / Chapter 2.4 --- Summary --- p.14 / Chapter Chapter 3 --- Reading 2D Barcode on Uneven Surfaces --- p.15 / Chapter 3.1 --- The Image Processing Framework --- p.15 / Chapter 3.2 --- The Scanning Environment --- p.17 / Chapter 3.3 --- Perspective Transform --- p.20 / Chapter Chapter 4 --- Uneven Surface Models --- p.23 / Chapter 4.1 --- Cylindrical Surfaces --- p.24 / Chapter 4.2 --- General Uneven Surfaces --- p.26 / Chapter Chapter 5 --- """Patch-wise"" Barcode Reading" --- p.28 / Chapter 5.1 --- The Inputs --- p.28 / Chapter 5.2 --- The Registration Process --- p.29 / Chapter 5.3 --- Patch Cutting --- p.33 / Chapter Chapter 6 --- Registering Cells in a Patch --- p.37 / Chapter 6.1 --- Document Skew Detection: Projection Profiles --- p.38 / Chapter 6.2 --- Radon Transform Based Orientation Detection --- p.41 / Chapter 6.3 --- Identifying Row/column Boundaries --- p.45 / Chapter 6.4 --- Detecting Cell Width --- p.50 / Chapter 6.5 --- Calculating Transform Parameters --- p.53 / Chapter Chapter 7 --- Patch Registration --- p.57 / Chapter 7.1 --- Matching Adjacent patches --- p.57 / Chapter 7.2 --- Expanding to the Entire Code Area --- p.60 / Chapter Chapter 8 --- Simulation and Results --- p.61 / Chapter 8.1 --- Implementation Details --- p.61 / Chapter 8.2 --- Comparison Methods --- p.63 / Chapter 8.3 --- Results --- p.63 / Chapter 8.4 --- Computation Costs --- p.68 / Chapter Chapter 9 --- Conclusion and Further Works --- p.73 / Bibliography --- p.75

The overall theme of this thesis work concerns the problem of handling measurement error and sources of variation in functional data models. The first part introduces a wavelet-based sparse principal component analysis approach for characterizing the variability of multilevel functional data that are characterized by spatial heterogeneity and local features. The total covariance of the data can be decomposed into three hierarchical levels: between subjects, between sessions and measurement error. Sparse principal component analysis in the wavelet domain allows for reducing dimension and deriving main directions of random effects that may vary for each hierarchical level. The method is illustrated by application to data from a study of human vision. The second part considers the problem of scalar-on-function regression when the functional regressors are observed with measurement error. We develop a simulation-extrapolation method for scalar-on-function regression, which first estimates the error variance, establishes the relationship between a sequence of added error variance and the corresponding estimates of coefficient functions, and then extrapolates to the zero-error. We introduce three methods to extrapolate the sequence of estimated coefficient functions. In a simulation study, we compare the performance of the simulation-extrapolation method with two pre-smoothing methods based on smoothing splines and functional principal component analysis. The third part discusses several extensions of the simulation-extrapolation method developed in the second part. Some of the extensions are illustrated by application to diffusion tensor imaging data.

Li Guo-Yin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 105-107). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Examples for the variational inequality problem --- p.2 / Chapter 1.2 --- Approaches for variational inequality problem --- p.7 / Chapter 1.3 --- Error bounds results for variational inequality problem --- p.8 / Chapter 1.4 --- Organization --- p.9 / Chapter 2 --- Solution Theory --- p.11 / Chapter 2.1 --- "Elementary Convex Analysis, Nonsmooth Analysis and Degree theory" --- p.11 / Chapter 2.1.1 --- Elementary Convex Analysis --- p.11 / Chapter 2.1.2 --- Elementary Nonsmooth Analysis --- p.16 / Chapter 2.1.3 --- Degree Theory --- p.18 / Chapter 2.2 --- Existence and Uniqueness Theory --- p.24 / Chapter 3 --- Merit Functions for variational inequalities problem --- p.36 / Chapter 3.1 --- Regularized gap function --- p.38 / Chapter 3.2 --- D-gap function --- p.44 / Chapter 3.3 --- Generalized Regularize gap function and Generalized D-gap function --- p.61 / Chapter 4 --- Error bound results for the merit functions --- p.74 / Chapter 4.1 --- Error bound results for Regularized gap function --- p.77 / Chapter 4.2 --- Error bound results for D-gap function --- p.78 / Chapter 4.3 --- Error bound results for Generalized Regularized gap function --- p.92 / Chapter 4.4 --- Error bound results for Generalized D-gap function --- p.93 / Bibliography --- p.105

Wang Xin. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 61-63). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction and Literature Review --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- The Objective --- p.2 / Chapter 1.3 --- Literature Review --- p.3 / Chapter Chapter 2 --- The Model --- p.7 / Chapter Chapter 3 --- The Consistent Estimation of Chang-Point --- p.11 / Chapter 3.1 --- The Consistency of ιT --- p.11 / Chapter 3.2 --- The Case of Single Regressor --- p.15 / Chapter Chapter 4 --- The SupWald Test and Sample-Splitting Method --- p.20 / Chapter 4.1 --- The SupWald Test --- p.20 / Chapter 4.2 --- " The Distribution of WT (ι,0,1)" --- p.23 / Chapter 4.3 --- The Sample-Splitting Method --- p.25 / Chapter Chapter 5 --- Experimental Results --- p.27 / Chapter Chapter 6 --- Empirical Example --- p.41 / Chapter Chapter 7 --- Conclusion --- p.44 / Appendix --- p.46 / References --- p.61

Chan Ka Man. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 46-48). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Multiple comparison procedures and their applications --- p.1 / Chapter 1.2 --- Different types of error control --- p.3 / Chapter 1.3 --- Single-step and stepwise procedures --- p.5 / Chapter 1.4 --- From familywise error rate control to false discovery rate control --- p.8 / Chapter 1.5 --- The FDR procedure of BH --- p.10 / Chapter 1.6 --- Application of the FDR procedure --- p.11 / Chapter 1.7 --- Family size and family size robustness --- p.16 / Chapter 1.8 --- Objectives of the thesis --- p.17 / Chapter 2 --- The Familywise Robustness Criteria --- p.18 / Chapter 2.1 --- The basic idea of familywise robustness --- p.18 / Chapter 2.2 --- Definitions and notations --- p.19 / Chapter 2.3 --- The measurement of robustness to changing family size --- p.21 / Chapter 2.4 --- Main Theorems --- p.21 / Chapter 2.5 --- Example --- p.23 / Chapter 2.6 --- Summary --- p.24 / Chapter 3 --- FDR and FWR --- p.26 / Chapter 3.1 --- Positive false discovery rate --- p.26 / Chapter 3.2 --- A unified approach to FDR --- p.29 / Chapter 3.3 --- The S procedure --- p.30 / Chapter 3.4 --- Family wise robustness criteria and the S procedure --- p.32 / Chapter 4 --- Simulation Study --- p.41 / Chapter 4.1 --- The setup --- p.41 / Chapter 4.2 --- Simulation result --- p.43 / Chapter 4.3 --- Conclusions --- p.44 / Bibliography --- p.46

Based on the weight properties of network codes, we present the refined versions of the Hamming bound, the Singleton bound and the Gilbert-Varshamov bound for linear network codes. We give two different algorithms to construct network codes with minimum distance constraints, both of which can achieve the refined Singleton bound. The first algorithm finds a codebook based on a given set of local encoding kernels defining a linear network code. The second algorithm finds a set of of local encoding kernels based on a given classical error-correcting code satisfying a certain minimum distance requirement. / First, the error correction/detection correction capabilities of a network code is completely characterized by a parameter which is equivalent to the minimum Hamming distance when the network code is linear and the weight measure on the error vectors is the Hamming weight. Our results imply that for a linear network code with the Hamming weight being the weight measure on the error vectors, the capability of the code is fully characterized by a single minimum distance. By contrast, for a nonlinear network code, two different minimum distances are needed for characterizing the capabilities of the code for error correction and for error detection. This leads to the surprising discovery that for a nonlinear network code, the number of correctable errors can be more than half of the number of detectable errors. (For classical algebraic codes, the number of correctable errors is always the largest integer not greater than half of the number of detectable errors.) / Network error correction provides a new method to correct errors in network communications by extending the strength of classical error-correcting codes from a point-to-point model to networks. This thesis considers a number of fundamental problems in coherent network error correction. / We further define equivalence classes of weight measures with respect to a general channel model. Specifically, for any given channel, the minimum weight decoders for two different weight measures are equivalent if the two weight measures belong to the same equivalence class. In the special case of network coding, we study four weight measures and show that all the four weight measures are in the same equivalent class for linear network codes. Hence they are all equivalent for error correction and detection when applying minimum weight decoding. / Yang, Shenghao. / Adviser: Raymond W.H. Yeung. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3708. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 89-93). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Zheng Xi Yin. / "December 2002." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (p. 117-121). / 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.

by Yang Weihong. / "March 2003." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 89-92). / 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.

Eukaryotic DNA replication is composed of a complex array of molecular biological activities compounded by the pressure for faithful replication in order to maintain genetic and genomic integrity. The constraints governing DNA replication biology is of fundamental importance to understand the degree of replication error and strategies employed by organisms to tackle the threats to replication fidelity from such errors. We apply a simple conceptual model, formalized by the use of probability theory and statistics, to discern fundamental pressures and constraints that optimise complete DNA replication in genomes of different size scales (10 Megabases to 10 Gigabases), spanning the whole eukaryota. We show in yeasts (genome size ~10 Megabases) that the replication origins (sites on DNA where replication can be initiated) are biased towards equal spacing on the genome and the largest gap between adjacent origins is limited compared to that is expected by chance, as well as origins are placed very close to the telomeric ends in order to minimize the replication errors arising from occasional irreversible failures of replication forks. Replication origin mapping data from five different yeasts confirm to all of these predictions. We derive an estimate of ~5.8×10-8 for the fork stalling rate per nucleotide, the one unknown parameter in our theory, which conforms to previous experimental estimates. We show in higher eukaryotes (genome size 100 Megabases to 10 Gigabases) that the bias for equal origin spacing is absent, larger origin gaps contribute more to the errors while the permissible origin separations are restricted by the rate of fork stalling per nucleotide, and in the larger genomes ( > 100 Megabases) errors become increasingly inevitable, yet with low net number of events, that follows a Poisson with small mean. We show, in very large genomes e.g. human genome, that larger gaps contributing most to the error are distributed as a power law to spread the risk of damage from the error, and post-replicative error-correction mechanisms are necessary for containment of the inevitable errors. Replication origin mapping data from yeast, Arabidopsis, Drosophila and human cell lines as well as experimental observations of post replicative error markers validate these predictions. We show that replication errors can be quantified from the nucleosome scale minimum inter-origin distance permissible under the known DNA structure and we propose a universal replication constant maintained across all eukaryotes independent of their architectural complexity. We show this molecular biological constant relates the genome length and developmental robustness of organisms and this is confirmed by early embryonic mortality rates from different organisms. Good agreement of the biologically obtained data to the model predictions in all cases suggests our model efficiently captures the biological complexity involved in containing errors in the DNA replication process. Conceptually, the model thus portrays how simple ideas can help complex biology to elevate our understanding of the continuously increasing knowledge of biological details.