Mathematical Methods in Linguistics and Phylogenetics

拟议的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，涉及数学建模和使用真实数据；第三个是系统发育学，主要是理论上的，尽管考虑到长期的应用。语言平实与清晰--沟通的一个重要方面是，说话人可以在不同的语境中调整自己的讲话风格。王悦在旧金山大学的实验室通过实验研究了清晰和朴素言语之间的许多差异，其中清晰言语是指在困难的交流环境中产生的任何言语。这给我的团队带来了两个挑战，我们将同时进行以下两个挑战：(I)明确和朴素言语之间的区别。这涉及到分析王的实验室产生的丰富数据集。(2)发展一种可证伪的清晰言语理论，该理论可以涵盖我们观察到的许多经验现象。我们将把演讲分析为说话人和听话人之间的游戏，并使用博弈论来做出可实验验证的预测。语音错误数据库和语音产生模型-有关语音产生机制的一个重要信息来源是语音中的错误。约翰·阿尔德雷特(SFU语言学)及其合作者收集了大量自然发生的语音错误的高质量数据库。我们将使用这个新可用的数据库来识别语音错误发生方式的规律性，然后看看哪些语音产生模型体现了同样的规律性。我们最终将提供一个语音产生的模型，该模型既能捕捉语音的基本特征，又能捕捉数据中的统计规律。系统发育学--随机过程的紧密跨度系统发育学是根据一组生物的遗传数据来确定其进化历史的任务。实现这一点的一个重要方法是根据每对生物体的遗传信息的相似性来定义它们之间的距离。这给出了一个有限的度量空间，现在可以用度量几何的工具来分析它。一个这样的工具是紧跨度，它给出了有限度量空间到多面体复形中的规范嵌入。然后可以研究这个复合体的组合学来刻画原始的度量空间。这种系统发育学方法的一个缺点是，从每个生物体的数据中推导出一个度量标准会抛出大量信息。事实上，遗传数据可以被建模为以有机体集合为指标集的随机过程的分布的观测。这项研究试图推导出随机过程的紧跨度的一个类比，然后发展它在系统发育学和数据科学的其他应用中的应用。

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.