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Creators/Authors contains: "Cantarella, Jason"

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  1. ; ; ; (, Journal of Physics A: Mathematical and Theoretical)
    We consider the radius of gyration of a Gaussian topological polymer G formed by subdividing a graph G' of arbitrary topology (for instance, branched or multicyclic). We give a new exact formula for the expected radius of gyration and contraction factor of G in terms of the number of subdivisions of each edge of G' and a new weighted Kirchhoff index for G'. The formula explains and extends previous results for the contraction factor and Kirchhoff index of subdivided graphs. 
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    Free, publicly-accessible full text available September 2, 2026
  2. ; ; (, Journal of Physics A: Mathematical and Theoretical)
    Abstract We present a faster direct sampling algorithm for random equilateral closed polygons in three-dimensional space. This method improves on the moment polytope sampling algorithm of Cantarellaet al(2016J. Phys. A: Math. Theor.49275202) and has (expected) time per sample quadratic in the number of edges in the polygon. We use our new sampling method and a new code for computing invariants based on the Alexander polynomial to investigate the probability of finding unknots among equilateral closed polygons. 
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