Among all existing alignment-free methods for comparing biological sequences, the sequence graphical representation provides a simple approach to view, sort, and compare gene structures. The aim of graphical representation is to display DNA or protein sequences graphically so that we can easily find out visually how similar or how different they are. Of course, only the visual comparison of sequences is not enough for the follow-up research work. We need more accurate comparison. This leads us to develop the application of the graphical representation for biological sequences. / In this thesis, we have two main contributions: (1) We construct a protein map with the help of our proposed new graphical representation for protein sequences. Each protein sequence can be represented as a point in this map, and cluster analysis of proteins can be performed for comparison between the points. This protein map can be used to mathematically specify the similarity of two proteins and predict properties of an unknown protein based on its amino acid sequence. (2) We construct a novel genome space with biological geometry, which is a subspace in RN . In this space each point corresponds to a genome. The natural distance between two points in the genome space reflects the biological distance between these two genomes. Our genome space will provide a new powerful tool for analyzing the classification of genomes and their phylogenetic relationships. / Yu, Chenglong. / Adviser: Luk Hing Sun. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 59-64). / 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. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.