Mathematical Methods in Linguistics and Phylogenetics

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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.