Mathematical Methods in Linguistics and Phylogenetics

该研究由三个主要项目组成，这些项目大多相互独立。前两个是数学语言学，涉及数学建模和真实的数据，第三个是遗传学，主要是理论性的，尽管考虑到长期的应用。语言学 * 简明与清晰的演讲- * 交流的一个重要方面是说话者可以在不同的语境中调整他们的演讲风格。SFU的Yue Wang实验室通过实验研究了清晰语音和普通语音之间的许多对比，其中清晰语音是在困难的交际环境中产生的任何语音。* 这给我的小组带来了两个挑战，我们将同时进行：（i）描述清楚和简单讲话之间的区别。这涉及分析王的实验室产生的丰富数据集。(ii)发展一个清晰言语的可证伪理论，可以涵盖我们观察到的许多经验现象。我们将把言语分析为说话者和听话者之间的游戏，并使用博弈论来做出实验上可检验的预测。一个语音错误数据库和语音产生模型-* 关于语音产生机制的一个重要信息来源是语音中的错误。约翰Alderete（SFU语言学）和合作者已经收集了广泛的高质量的数据库自然发生的语音错误。我们将使用这个新的可用数据库来识别语音错误发生的方式，然后看看哪些语音产生模型体现了相同的错误。我们最终将提供一个语音生成模型，它既能捕获语音的基本特征，也能沿着数据中的统计特征。**系统发生学-随机过程的一个紧密的跨度 * 系统发生学是从一组生物的遗传数据中确定其进化历史的任务。一个重要的方法是根据遗传信息的相似性来确定每对生物体之间的距离。这给出了一个有限的度量空间，现在可以使用度量几何的工具进行分析。一个这样的工具是紧跨度，它给出了一个典型的嵌入有限度量空间到一个多面体复杂。然后可以研究这个复形的组合学来刻画原来的度量空间。这种方法的缺点是，从每个生物体的数据中推导出一个指标会抛出大量信息。事实上，遗传数据可以建模为一个随机过程的分布与指标集的生物体的集合的观察。这项研究旨在推导出随机过程的紧跨度的模拟，然后在遗传学和数据科学的其他应用中开发其用途。

The proposed research consists of three major projects that are mostly independent of each other. The first two are in mathematical linguistics and involve both mathematical modelling and working with real data, and the third is in phylogenetics, and is mostly theoretical, though with applications in mind for the long term.******Linguistics***Plain vs Clear Speech- ***An important aspect of communication is that speakers can adjust the style of their speech in different contexts. Yue Wang's lab at SFU experimentally investigates the many contrasts between clear and plain speech, where clear speech is any speech that is produced in difficult communicative circumstances. ***This provides two challenges to my group which we will pursue in tandem (i) characterizing the differences between clear and plain speech. This involves analyzing the rich data sets Wang's lab produces. (ii) Developing a falsifiable theory of clear speech that can encompass many of the empirical phenomena we observe. We will analyze speech as a game played between a speaker and a hearer and use game theory to make experimentally testable predictions.***A Speech Error Database and Models of Speech Production- ***An important source of information about the mechanisms of speech production is the errors that are made in speech. John Alderete (SFU Linguistics) and collaborators have collected an extensive high-quality data base of naturally occurring speech errors. We will use this newly available database to identify regularities in the way that speech errors occur and then see which speech production models embody the same regularities. We will eventually provide a model of speech production that captures both the basic features of speech along with statistical regularities in the data.******Phylogenetics - A tight span for stochastic processes***Phylogenetics is the task of determining the evolutionary history of a group of organisms from their genetic data. An important way this has been done is to define a distance between each pair of organisms based on the similarity of their genetic information. This gives a finite metric space which now can be analyzed using the tools of metric geometry. One such tool is the tight span which gives a canonical embedding of the finite metric space into a polyhedral complex. The combinatorics of this complex can then be studied to characterize the original metric space. A downside of this approach to phylogenetics is that deriving a metric from the data for each organism throws out a lot of information. In fact, genetic data can be modeled as the observation of the distribution of a stochastic process with index set the set of organisms. This research seeks to derive an analogue of the tight span for stochastic processes, and then develop its use in phylogenetics and other applications in data science.