纠缠、不变量和系统发生学
Entanglement, Invariants, and Phylogenetics
摘要：
本论文发展和扩展了已知的数学物理技术，与生物学中所需的系统发育树的流行马尔可夫模型的分析相关，以从生物分子序列数据重建分类单位的进化关系。数学物理的技术是过多的，已经发展了一段时间。遗传学的马尔可夫模型及其分析是一种相对较新的技术，迄今为止，大多数进展都是通过使用离散数学来实现的。这篇论文采取群论的方法来解决这个问题，从一个显着的数学平行粒子物理学中的散射过程开始。这被证明等同于分子单位进化历史中的分支事件。本论文的主要技术成果是推导出在多线性空间上计算多项式群不变函数的存在性证明和计算技巧，其中群作用是与马尔可夫时间演化相关的。本论文的实际结果是一个扩展的分析使用不变函数的距离为基础的方法和介绍一种新的重建技术的四叉树，这是符合最一般的马尔可夫模型的序列演化。
英文摘要：
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units from biomolecular sequence data. The techniques of mathematical physics are plethora and have been developed for some time. The Markov model of phylogenetics and its analysis is a relatively new technique where most progress to date has been achieved by using discrete mathematics. This thesis takes a group theoretical approach to the problem by beginning with a remarkable mathematical parallel to the process of scattering in particle physics. This is shown to equate to branching events in the evolutionary history of molecular units. The major technical result of this thesis is the derivation of existence proofs and computational techniques for calculating polynomial group invariant functions on a multi-linear space where the group action is that relevant to a Markovian time evolution. The practical results of this thesis are an extended analysis of the use of invariant functions in distance based methods and the presentation of a new reconstruction technique for quartet trees which is consistent with the most general Markov model of sequence evolution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
