Mathematical Sciences: "Markov Dependence in Statistics andInformation Theory and Statistical Problems in Physical Mapping"

人类基因组计划的主要目标之一是绘制人类染色体的物理图谱。 这种图谱是染色体完全测序的重要步骤，也有其他重要的应用，如帮助定位疾病基因。 构建物理图谱的一种常见方法是基于随机克隆的指纹。拟议的研究使用信息理论的概念来量化完成物理地图所需的信息，以及从随机克隆数据中获得的信息。 最大化的配置变量和数据之间的互信息也提出了作为一个设计标准，以选择杂交概率参数。 数值和解析近似的标准将被认为是在简单的成对比较的情况下，最新的物理映射策略的基础上。 然后，可以使用这些近似来获得参数的最佳值。 最后，它将解决如何利用映射信息定位的染色体上的感兴趣的基因的位置。 拟议的研究是应用信息论的物理映射问题所产生的人类基因组计划。 提出了一种信息论方法来解决人类基因组计划中物理作图所产生的某些问题。 物理地图的目标将被阐明，我们将回答有关我们需要的信息量和我们对地图的了解量的问题。 一个3-克隆的方法，预计提取更多的信息映射数据比从2-克隆数据，和使用映射数据定位生物学感兴趣的基因的可能性将得到更好的理解。

One of the main goals of the Human Genome Project is to produce physical maps of the human chromosomes. Such maps are important steps on the path to the complete sequencing of chromosomes, and have other important applications, such as assisting in the localizing of disease genes. A common method for constructing physical maps is based on fingerprinting random clones. The proposed research uses information theory notions to quantify information needed for the completion of a physical map, and information obtained from random clone data. Maximizing the mutual information between a configuration variable and data is also proposed as a design criterion to select the hybridization probability parameter. Numerical and analytic approximations to the criterion will be considered in the simple pairwise comparison case, on which most current physical mapping strategies are based. Optimal values of the parameter can then be obtained using these approximations. Finally, it will be addressed how to utilize mapping information to localize positions of genes of interest on the chromosomes. The proposed research is on applying information theory to physical mapping problems arising from the Human Genome Project. An information-theoretic approach is proposed to address certain problems arising from physical mapping in the Human Genome Project. The goals of a physical map will be clarified and we will answer questions regarding the amount of information we need for and the amount we learn about the map. A 3-clone approach is expected to extract more information out of mapping data than from 2-clone data, and the possibility of using mapping data to locate genes of biological interest will be better understood.