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Topological Analysis of Syntactic Structures

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Abstract

We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality, of hierarchical clustering structures, and of non-trivial loops. We show there are relations that hold across language families and additional relations that are family-specific. We then analyze the trees describing the merging structure of persistent connected components for languages in different language families and we show that they partly correlate to historical phylogenetic trees but with significant differences. We also show the existence of interesting non-trivial persistent first homology groups in various language families. We give examples where explicit generators for the persistent first homology can be identified, some of which appear to correspond to homoplasy phenomena, while others may have an explanation in terms of historical linguistics, corresponding to known cases of syntactic borrowing across different language subfamilies.

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Acknowledgements

The third author was supported by NSF grants DMS-1707882 and DMS-2104330 and by NSERC Discovery Grant RGPIN-2018-04937 and Accelerator Supplement Grant RGPAS-2018-522593.

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Authors and Affiliations

  1. University of Southern California, Los Angeles, CA, USA

    Alexander Port

  2. California Institute of Technology, Pasadena, CA, USA

    Taelin Karidi & Matilde Marcolli

  3. Perimeter Institute for Theoretical Physics, Waterloo, ON, Canada

    Matilde Marcolli

  4. University of Toronto, Toronto, ON, Canada

    Matilde Marcolli

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  1. Alexander Port
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  2. Taelin Karidi
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Correspondence to Matilde Marcolli.

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Port, A., Karidi, T. & Marcolli, M. Topological Analysis of Syntactic Structures. Math.Comput.Sci. 16, 2 (2022). https://doi.org/10.1007/s11786-021-00520-5

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