准度量、相似性和相似性：蛋白质数据集几何学方面
Quasi-metrics, Similarities and Searches: aspects of geometry of protein datasets
摘要：
准度量是满足三角不等式但不对称的距离函数：它可以被认为是非对称度量。本论文的中心结果，在第3章中发展，是一个自然的对应关系之间存在的生物（核苷酸或蛋白质）序列和准度量之间的相似性措施。第二章介绍了拟距离空间理论的基本概念，并介绍了一个新的例子：泛可数有理拟距离空间及其双完备性，泛双完备可分拟距离空间。第4章致力于发展具有Borel概率测度的拟度量空间或pq-空间的概念。本章的主要结果表明，“高维拟度量空间接近于度量空间”。第五章研究了数据库相似性搜索理论的几何方面。关于$pq$ -空间的结果被用来产生新的理论界的索引方案的性能。最后，本文介绍了一些生物应用。第6章介绍了FSIndex，这是一种索引方案，可以显著加速短蛋白质片段数据集的相似性搜索。第七章介绍了用于发现短功能蛋白质基序的系统PFMFind的原型，该系统依赖于FSIndex进行相似性搜索。
英文摘要：
A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. The central result of this thesis, developed in Chapter 3, is that a natural correspondence exists between similarity measures between biological (nucleotide or protein) sequences and quasi-metrics. Chapter 2 presents basic concepts of the theory of quasi-metric spaces and introduces a new examples of them: the universal countable rational quasi-metric space and its bicompletion, the universal bicomplete separable quasi-metric space. Chapter 4 is dedicated to development of a notion of the quasi-metric space with Borel probability measure, or pq-space. The main result of this chapter indicates that `a high dimensional quasi-metric space is close to being a metric space'. Chapter 5 investigates the geometric aspects of the theory of database similarity search in the context of quasi-metrics. The results about $pq$-spaces are used to produce novel theoretical bounds on performance of indexing schemes. Finally, the thesis presents some biological applications. Chapter 6 introduces FSIndex, an indexing scheme that significantly accelerates similarity searches of short protein fragment datasets. Chapter 7 presents the prototype of the system for discovery of short functional protein motifs called PFMFind, which relies on FSIndex for similarity searches.
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。
