Matheamatical Sciences: University-Industry Postdoctoral Fellow Support for Research in Optimal Design and Control ofFluids

9501570刘摘要（技术） 多序列比对是研究基因结构和功能的重要手段 产品，通过促进序列基序的检测和描述; 在蛋白质建模、结构预测和工程方面的努力; 分子系统学中的分子进化和系统发育构建。 我们最近 提出了新的局部比对算法（Lawrence等人，1993，1994），基于贝叶斯 建模和Gibbs抽样。在这个项目中，我们建议开发几个扩展 我们原来的贝叶斯模型，以适应各种实际情况，并 研究我们对对齐问题的研究中出现的几个统计问题。对 在应用方面，我们希望做到以下几点：（1）放松存在性假设 并开发贝叶斯模型，以同时检测和对齐公倍数， （2）联合收割机结合马尔可夫结构建模的思想， 序列数据（例如，隐马尔可夫模型）与劳伦斯等人的基于块的方法。 （1993）以增强多个基序的对齐;（3）修改和应用 以前和本项目中开发的方法用于其他几种重要的生物学 问题：检测非编码区的细微序列信号; 蛋白质二级结构的预测;以及线程和对齐的组合。 在理论方面，我们试图（4）理解预测的性质和潜力 更新与引导，贝叶斯引导，和一般 非参数问题;（5）制定模型选择标准， 对准问题中图形宽度的确定;（6）研究了先验知识对对准精度的影响 结果的规范和这些结果在贝叶斯中的频率属性 分类问题;最后，（7）研究几种抽样的收敛性质 算法 在获奖期间，我将在概率导论的教学中发展自己的风格 和统计课程，重点是统计思维，并参与一个 该计划旨在吸引有才华的本科生进入我们的领域。我也会努力的 开发新的研究生水平的课程，目前的研究领域，如图像处理， 缺失数据，马尔可夫链蒙特卡罗，遗传学和生物学。我的指导方针是 研究生的特点是：独立性、联系和创造力。 小行星9501570 摘要（非技术性） 大量关于生命的基本分子，蛋白质和核酸的数据已经出现 从生物技术革命。人类基因组计划加速了 这些数据。从多个来源的同源蛋白质或核酸序列的多次观察 不同的生物体通常是可用的。 然而，由于突变和序列错误 由于这些数据不一致，多序列比对已经成为一种必要的和有价值的 了解这些分子的结构和功能的工具， 蛋白质建模、结构预测和工程;以及 揭示了分子 分子系统学中的进化和系统发生学构建。 传统算法 发现这样的对准或者在计算上太昂贵，从而限制了它们的 应用程序或过于启发式，从而失去了对微妙模式的敏感性。 我们最近 提出了新的局部对齐算法（Lawrence等人，1993，1994），该算法基于 序列的概率模型和称为 吉布斯取样器。在这个项目中，我们建议开发几个扩展我们原来的 概率模型，以适应各种实际情况，并调查几个 我们对对齐问题的研究中出现了统计问题。在应用方面， 我们希望做到：（1）放宽生存假设，发展 更通用的混合模型，以同时检测和对齐 常见模式 多个同源的生物序列;（2）研究我们之间的联系 方法和其他成功的方法，如隐马尔可夫模型;（3）修改 并将以前和本项目中开发的方法应用于其他几个项目， 重要的生物学问题：检测非编码DNA中的细微序列信号 区域;蛋白质二级结构的预测;以及线程和 对齐。在理论方面，我们试图（4）理解的性质和潜力 提出了一种新的迭代模拟方法， 结合该 自助法、贝叶斯自助法和一般非参数问题;（5）建立模型 在对准问题中用于确定图案宽度的选择标准;（6） 研究先验规范对最终对准结果的影响;最后，（7） 几种随机模拟收敛性研究 算法 在获奖期间，我将在概率导论的教学中发展自己的风格 和统计课程，重点是统计思维，并参与一个 该计划旨在吸引有才华的本科生进入我们的领域。我也会努力的 开发新的研究生水平的课程，目前的研究领域，如图像处理， 缺失数据，马尔可夫链蒙特卡罗，遗传学和生物学。我的指导方针是 研究生的特点是：独立性、联系和创造力。

9501570 Liu Abstract (technical) Multiple sequence alignment is crucial in research on the structure and function of gene products, through promoting the detection and description of sequence motifs; aiding efforts at protein modeling, structure prediction and engineering; and shedding light on molecular evolution and phylogeny construction in molecular systematics. We recently presented new local alignment algorithms (Lawrence et al. 1993, 1994) based on Bayesian modeling and Gibbs sampling. In this project, we propose to develop several extensions of our original Bayesian model to accommodate various practical situations, and to investigate several statistical problems arisen from our study of the alignment problem. On the applied side, we wish to accomplish the following: (1) relax the existence assumption and develop Bayesian models to simultaneously detect and align the common multiple motifs in the sequences; (2) combine the idea of Markovian structure modeling of sequence data (e.g., hidden Markov Model) with the block-based method of Lawrence et. al. (1993) to enhance the alignment of multiple motifs; (3) modify and apply the methodology developed previously and in this project to several other important biological problems: the detection of subtle sequence signals in noncoding DNA region; the prediction of protein secondary structures; and the combination of threading and alignment. On the theoretical side, we attempt to (4) understand the nature and potential of predictive updating in connection with the bootstrap, the Bayesian bootstrap, and general nonparametric problems; (5) develop model selection criteria that are useful for determining pattern width in alignment problems; (6) study the influence of prior specifications on the results and frequency properties of these results in Bayesian classification problems; and finally, (7) study convergence properties of several sampling algorithms. During the award period, I will develop my own styles on teaching introductory probability and statistics courses with an emphasis on statistical thinking, and get involved in a program designed to attract talented undergraduates into our field. I will also make an effort to develop new graduate level courses on current research areas such as image processing, missing data, Markov Chain Monte Carlo, genetics and biology. My guideline for directing graduate students is: independence, connections, and creativity. 9501570 Liu Abstract (nontechnical) A wealth of data concerning life's basic molecules, proteins and nucleic acids, has emerged from the biotechnology revolution. The human genome project has accelerated the growth of these data. Multiple observations of homologous protein or nucleic acid sequences from different organisms are often available. However, since mutations and sequence errors misalign these data, multiple sequence alignment has become an essential and valuable tool for understanding the structures and functions of these molecule, aiding efforts at protein modeling, structure prediction and engineering; and shedding light on molecular evolution and phylogeny construction in molecular systematics. Traditional algorithms for finding such alignment are either too computationally expensive so as to limit their applications or too heuristic so that the sensitivity to subtle patterns is lost. We recently presented new local alignment algorithms (Lawrence et al. 1993, 1994) based on a probabilistic model of the sequences and a stochastic simulation technique called the Gibbs sampler. In this project, we propose to develop several extensions of our original probabilistic model to accommodate various practical situations, and to investigate several statistical problems arisen from our study of the alignment problem. On the applied side, we wish to accomplish the following: (1) relax the existence assum ption and develop more general mixture models to simultaneously detect and align common patterns in multiple homologous biological sequences; (2) investigate the connection between our method and other successful approaches such as the hidden Markov modeling; (3) modify and apply the methodology developed previously and in this project to several other important biological problems: the detection of subtle sequence signals in noncoding DNA region; the prediction of protein secondary structures; and the combination of threading and alignment. On the theoretical side, we attempt to (4) understand the nature and potential of the predictive updating, a new iterative simulation method, in connection with the bootstrap, the Bayesian bootstrap, and general nonparametric problems; (5) develop model selection criteria that are useful for determining pattern width in alignment problems; (6) study the influence of prior specifications on the final alignment results; and finally, (7) study convergence properties of several stochastic simulation algorithms. During the award period, I will develop my own styles on teaching introductory probability and statistics courses with an emphasis on statistical thinking, and get involved in a program designed to attract talented undergraduates into our field. I will also make an effort to develop new graduate level courses on current research areas such as image processing, missing data, Markov Chain Monte Carlo, genetics and biology. My guideline for directing graduate students is: independence, connections, and creativity.