Phylogentic Combinatorics And T-Theory

Since Combinatorics and Graph Theory has been widely used in Computer Science, Artificial Intelligence and Telecommunication, more and more people are doing research works in this area. And it is well known to all we can get better algorithm if we have better analysis of combinatorics and graph theory in advance.In biology, one of the important research works is to discuss evolutionary re-latedness among various groups of organisms (for example, species or populations). Depending on the experimental molecular data such as sequencing data and mor-phological data matrices, phylogenetics tree for species can be constructed. And it is just the evolutionary tree of life. However, the experimental data which can be used are not so accurate because some of them just come from the Fossil. Based on these imprecise resource data, different research method will lead to different phylogenetics tree. It means sometimes we can not get the unique phylogenetics tree. Since it is impossible to reproduce whole evolution history at the moment, one of the big issues is how can people determine which phylogenetics tree is correct among different ones. Over time, Phylogenetics Combinatorics has been created because people find that Mathematics can do a lot helpful to reconstruct accurate Phylogenetics tree.T-Theory is one of the hot topics in Phylogenetics Combinatorics, and Tight Span as well as Split Decomposition theory are two of most important topics in this area. In additional to the brief introduction of basic idea of T-Theory as well as its development recently, some of my new research results in this area can be found in the thesis. (1) Research works of Tight Span on sub-tree Metric are in Tight Span section. (2) New results in Split Decomposition area will show you the relationship between Split Decomposition and some kinds of Metrics. Based on the these results, we will get one important result which associates hyperbolicity and Split Decomposition. (3) In order to show the usage of T-Theory, you will find one real example of Phylogenetic tree re-construction in this paper. Furthermore, tree comparison based on Split theory is mentioned as well. All of them will help you get better understanding of T-Theory and its applications.