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Heat Kernel Analysis of Syntactic Structures

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Abstract

We consider two different data sets of syntactic parameters and we discuss how to detect relations between parameters through a heat kernel method developed by Belkin–Niyogi, which produces low dimensional representations of the data, based on Laplace eigenfunctions, that preserve neighborhood information. We analyze the different connectivity and clustering structures that arise in the two datasets, and the regions of maximal variance in the two-parameter space of the Belkin–Niyogi construction, which identify preferable choices of independent variables. We compute clustering coefficients and their variance.

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Authors and Affiliations

  1. California Institute of Technology, Pasadena, USA

    Andrew Ortegaray & Matilde Marcolli

  2. Massachusetts Institute of Technology, Cambridge, USA

    Robert C. Berwick

  3. Perimeter Institute for Theoretical Physics, Waterloo, Canada

    Matilde Marcolli

  4. University of Toronto, Toronto, Canada

    Matilde Marcolli

Authors
  1. Andrew Ortegaray
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  2. Robert C. Berwick
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  3. Matilde Marcolli
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Correspondence to Matilde Marcolli.

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Ortegaray, A., Berwick, R.C. & Marcolli, M. Heat Kernel Analysis of Syntactic Structures. Math.Comput.Sci. 15, 643–660 (2021). https://doi.org/10.1007/s11786-021-00498-0

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  • DOI: https://doi.org/10.1007/s11786-021-00498-0

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