{"id":6,"date":"2013-08-11T02:14:37","date_gmt":"2013-08-11T02:14:37","guid":{"rendered":"https:\/\/jasoncantarella.com\/wordpress\/?page_id=6"},"modified":"2026-03-26T11:00:38","modified_gmt":"2026-03-26T15:00:38","slug":"papers","status":"publish","type":"page","link":"https:\/\/jasoncantarella.com\/wordpress\/papers\/","title":{"rendered":"Papers"},"content":{"rendered":"\n

To obtain a copy of any of the papers listed below, click on the title of the paper. The preprints should be cited by arXiv number (as they are all also available from the arXiv<\/a>). You can get citation information for these papers from my Google author profile<\/a> if you’re interested. The BibTeX citation information for all the papers is collected in <\/span>cantarella.bib<\/a>.<\/span><\/p>\n\n\n\n

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  1. Random knotting in very long off-lattice self-avoiding polygons.<\/a>
    Jason Cantarella, Tetsuo Deguchi, Henrik Schumacher, Clayton Shonkwiler, and Erica Uehara.
    Journal of Physics A,<\/em> to appear.<\/li>\n\n\n\n
  2. New Upper Bounds for Stick Number<\/a>.
    Jason Cantarella, Andrew Rechnitzer, Henrik Schumacher, Clayton Shonkwiler.
    Journal of Knot Theory and its Ramifications<\/em>, to appear. <\/li>\n\n\n\n
  3. Factoring the Graph Laplacian to Understand Topological Polymers.<\/a>
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, Erica Uehara.
    Europhysics Letters<\/em> 152 (2025), vol. 1, p. 12001<\/li>\n\n\n\n
  4. An exact formula for the <\/a>contraction<\/a> <\/a>factor of a subdivided Gaussian topological polymer. <\/a>
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, Erica Uehara.
    Journal of Physics A<\/em> 58 (2025), 355201.<\/li>\n\n\n\n
  5. On the average squared radius of gyration of a family of embeddings of subdivision graphs.<\/a>
    Jason Cantarella, Henrik Schumacher, and Clayton Shonkwiler.
    arXiv preprint 2409.18767<\/li>\n\n\n\n
  6. CoBarS: Fast reweighted sampling for polygons in any dimension.<\/a>
    Jason Cantarella and Henrik Schumacher.
    SIAM Journal on Applied Algebra and Geometry<\/em> 8 (2024), 756-781.
    C++ implementation on GitHub<\/a>
    Mathematica interface to library on GitHub<\/a><\/li>\n\n\n\n
  7. A faster direct sampling algorithm for equilateral polygons and the probability of unknotting.<\/a>
    Jason Cantarella, Henrik Schumacher, and Clayton Shonkwiler.
    Journal of Physics A<\/em> 57 (2024) p. 285205<\/li>\n\n\n\n
  8. Random graph embeddings with general edge potentials.<\/a>
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler and Erica Uehara.
    arXiv preprint 2205.09049<\/li>\n\n\n\n
  9. Exact Evaluation of the Mean Square Radius of Gyration for Gaussian Topological Polymer Chains.<\/a>
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler and Erica Uehara.
    in     Topological Polymer Chemistry,<\/em> Tezuka and Deguchi, eds, Springer, 2021.<\/a><\/li>\n\n\n\n
  10. Families of similar simplices inscribed in most smoothly embedded spheres.<\/a><\/div>Jason Cantarella, Elizabeth Denne, and John McCleary.<\/div><\/div>Forum of Mathematics, Sigma<\/em> 10 (2022) , e101.<\/li>\n\n\n\n
  11. Square-like quadrilaterals inscribed in embedded space curves.<\/a>
    Jason Cantarella, Elizabeth Denne, and John McCleary.
    arXiv preprint 2103.13848 <\/li>\n\n\n\n
  12.  Configuration Spaces, Multijet <\/a>Transversality<\/a>, and the Square-Peg Problem.<\/a>
    Jason Cantarella, Elizabeth Denne, and John McCleary.
    Illinois Journal of Mathematics<\/em> 66 (2022), no. 3, p. 385\u2013420.<\/li>\n\n\n\n
  13. Performance of the Uniform Closure Method for open knotting as a Bayes-type classifier.<\/a>
    Emily Tibor, Elizabeth Annoni, Erin Brine-Doyle, Nicole Kumerow, Madeline Shogren, Jason Cantarella, Clayton Shonkwiler, and Eric Rawdon.
    arXiv preprint 2011.08984 <\/li>\n\n\n\n
  14. Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers.<\/a>
    Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler, and Erica Uehara.
    Journal of Physics A<\/em> 55 (2022), no. 47, p. 475202.<\/li>\n\n\n\n
  15. Computing the Conformal Barycenter.<\/a>
    Jason Cantarella and Henrik Schumacher.
    SIAM Journal on Applied Algebra and Geometry <\/em>6 (2022), no. 3, p. 503-530.
    Mathematica implementation on GitHub.<\/a><\/li>\n\n\n\n
  16. Open and closed random walks with fixed edgelengths in R^d<\/a>
    Jason Cantarella, Kyle Chapman, Philipp Reiter, and Clayton Shonkwiler.
    Journal of Physics A <\/em>51 (2018), no. 43, p. 434002<\/li>\n\n\n\n
  17. Random Triangles and Polygons in the Plane.<\/a>
    Jason Cantarella, Thomas Needham, and Clayton Shonkwiler.
    American Mathematical Monthly <\/em>126 (2019), no. 2, p.113-134<\/li>\n\n\n\n
  18. Knot Fertility and Lineage.<\/a>
    Jason Cantarella, Allison Henrich, Elsa Magness, Oliver O’Keefe, Kayla Perez, Eric Rawdon, Brianna Zimmer.
    Journal of Knot Theory and Its Ramifications<\/i> 26 (2017), no. 13, p. 1750093<\/li>\n\n\n\n
  19. Knot Probabilities in Random Diagrams.<\/a>
    Jason Cantarella, Harrison Chapman and Matt Mastin.
    Journal of Physics A<\/em> 49 (2016), p. 405001
    This paper comes with a tabulation of knot diagrams up to 10 crossings (including pictures) as     supplementary data (53M).<\/a><\/li>\n\n\n\n
  20. A Fast Direct Sampling Algorithm for Equilateral Closed Polygons.<\/a>
    Jason Cantarella, Bertrand Duplantier, Clayton Shonkwiler and Erica Uehara.
    Journal of Physics A<\/i> 49 (2016), no. 27, p. 275205.
    This paper was one of the     highlights of the year for 2016 in Mathematical Physics.<\/a><\/li>\n\n\n\n
  21. Rigid Origami Vertices: Conditions and Forcing Sets.<\/a>
    Zachary Abel, Jason Cantarella, Erik D. Demaine, David Eppstein, Thomas C. Hull, Jason S. Ku, Robert J. Lang, Tomohiro Tachi.
    Journal of Computational Geometry<\/em> 7 (2016), no. 1, p. 171-184.<\/li>\n\n\n\n
  22. Transversality in Configuration Spaces and the Square Peg Problem.<\/a>
    Jason Cantarella, Elizabeth Denne and John McCleary.
    arXiv:1402.6174<\/li>\n\n\n\n
  23. The Symplectic Geometry of Closed Equilateral Random Walks in 3-space<\/a>
    Jason Cantarella and Clayton Shonkwiler.
    Annals of Applied Probability <\/em>26 (2016), no. 1, p. 549-596
    A     30-minute talk <\/a> on this paper for physicists and biologists
     Slides from the talk<\/a><\/li>\n\n\n\n
  24. The tight knot spectrum in QCD<\/a>. <\/em>
    Roman Buniy, Jason Cantarella, Thomas Kephart and Eric Rawdon.
    Physical Review D<\/em> 89 (2014), no. 5, p. 054513
    PhysRevD.89.054513
    This paper comes with a data set of     tight knot and link vertex coordinates and summary data<\/a> (including prime and composite knots and links and curvature information) and a low-resolution archive of tight knot and link vertex coordinates<\/a>.<\/li>\n\n\n\n
  25. The Expected Total Curvature of Random Polygons<\/a>.
    Jason Cantarella, Alexander Y Grosberg, Robert B Kusner and Clayton Shonkwiler.
    American Journal of Mathematics 137<\/em>, (2015), no. 2, p. 411-438 .
    arXiv:1210.6537.
    2012arXiv1206.3161C<\/li>\n\n\n\n
  26. Symmetric Criticality for Tight Knots<\/a>.
    Jason Cantarella, Jennifer Ellis, Joseph H.G. Fu and Matt Mastin.
    Journal of Knot Theory and its Ramifications 23<\/a> <\/em>(2014), 1450008-1-17
    arXiv:1208.3879.
    doi:10.1142\/S0218216514500084<\/li>\n\n\n\n
  27. Probability Theory of Random Polyg<\/a>ons from the Quaternionic Viewpoint.<\/a>
    Jason Cantarella, Tetsuo Deguchi and Clayton Shonkwiler.
    Communications on Pure and Applied Mathematics<\/em> 67 (2014), no. 10, p. 1658-1699.
    CPA:CPA21480
    ANSI C code for generating random polygons according to the methods of this paper is included in our plCurve library.<\/li>\n\n\n\n
  28. Ropelength Criticality<\/a>.
    Jason Cantarella, Joseph H.G. Fu, Rob Kusner, John Sullivan.
    Geometry and Topology<\/em> 18 (2014), no. 4, p. 1973-2043.
    gtropelengthcriticality<\/li>\n\n\n\n
  29. The 27 possible intrinsic symmetry groups of 2-component links<\/a>.
    Jason Cantarella, James Cornish, Matt Mastin and Jason Parsley.
    Symmetry<\/em> 4 (2012), no. 1, p. 129-142
    sym4010129<\/li>\n\n\n\n
  30. The Shapes of Tight Composite Knots<\/a>
    Jason Cantarella, Al LaPointe and Eric Rawdon.
    J. Phys A: Math Theor<\/em>.<\/a> 45 (2012), p. 1-19
     arXiv:1110.3262<\/a>
    1751-8121-45-22-225202
    This paper comes with several data files:     tight knot and link vertex coordinates<\/a> (including prime and composite knots and links and curvature information) and a low-resolution version of tight knot and link vertex coordinates.<\/a> This data was generated with support from NSF grants 1115722 and 0810415 (to Rawdon). This paper was the source of the cover image of the Journal of Physics A the month it was published\"JphysAcover\"<\/li>\n\n\n\n
  31. Intrinsic Symmetry Groups of Links with 8 and fewer crossings<\/a>
    Michael Berglund, Jason Cantarella, Meredith Perrie Casey,
    Ellie Dannenberg, Whitney George, Aja Johnson, Amelia Kelly,
    Al LaPointe, Matt Mastin, Jason Parsley, Jacob Rooney and Rachel Whitaker.
    Symmetry<\/em> 4 (2012), no. 1, p. 143-207.
     arXiv:1010.3234<\/a> sym4010143<\/li>\n\n\n\n
  32. Knot Tightening by Constrained Gradient Descent<\/a>.
    Ted Ashton, Jason Cantarella, Michael Piatek, and Eric Rawdon.
    Experimental Mathematics<\/em> 20 (2011), no. 1, p. 57-90.
    arXiv:1002.1723<\/a>
    acprtightening
    See also     Self contact sets for 50 Tightly Knotted and Linked Tubes<\/a>, which is an early version of this paper. The data sets corresponding to this paper are the Atlas of Tight Knots and Links<\/a>, the archive of Tight Knot and Link Vertex Coordinates<\/a> and a text file summary of ropelengths for knots and links<\/a>. This paper was the source of the cover image for Experimental Math when published:
    \"Experimental<\/a><\/li>\n\n\n\n
  33. A new cohomological formula for helicity in $\\R^{2k+1}$ reveals the effect of a diffeomorphism on helicity<\/a>.
    Jason Cantarella and Jason Parsley.
    Journal of Geometry and Physics<\/em> 60 (2010), p. 1127-1155.
     arxiv: math.GT\/09031465 <\/a>
    Cantarella20101127<\/li>\n\n\n\n
  34. Criticality for the Gehring Link Problem<\/a>.
    Jason Cantarella, Joseph H.G. Fu, Rob Kusner, John M. Sullivan, and Nancy Wrinkle.
    Geometry and Topology<\/em> 10 (2006), p. 2055-2116.
     arXiv: math.DG\/0402212<\/a>
    MR2284052<\/li>\n\n\n\n
  35. On Comparing the Writhe of a Smooth Curve to the Writhe of an Inscribed Polygon<\/a>.
    Jason Cantarella.
    SIAM Journal of Numerical Analysis<\/em> 42 (2005) no. 4, p. 1846-1861.
    arXiv: math.DG\/0202236
    MR2139226<\/li>\n\n\n\n
  36.  Visualizing the tightening of knots<\/a>
    Jason Cantarella, Michael Piatek, and Eric Rawdon.
    Proceedings of IEEE Visualization 2005<\/em>, p. 575-582.
    cprvis<\/li>\n\n\n\n
  37.  A fast octree-based algorithm for computing ropelength<\/a>
    Ted Ashton and Jason Cantarella
    In Physical and Numerical Models in Knot Theory<\/em>
    and their Application to the Life Sciences<\/em>,
    World Scientific Press (2005), p. 323-341
     arxiv <\/a>
    MR2197947
    This is the algorithm implemented by the Octrope library.<\/li>\n\n\n\n
  38. TSNNLS: A solver for large sparse least squares problems with non-negative variables<\/a>
    Jason Cantarella and Michael Piatek.
    Unpublished (2004).
     arxiv:cs.MS\/0408029<\/a>
    tsnnls
    This unpublished manuscript describes the algorithm implemented in our open-source TSNNLS library. The library is used around the world for solving sparse constrained least squares problems of moderate size (matrices dimensions of a few thousand by a few thousand). TSNNLS was very fast for its day, but it is not an actively updated package and it is probably somewhat behind the times at this point. If you want to do more general or much larger problems of this type, I’d look at the     COIN-OR<\/a> project (specifically IpOPT).<\/li>\n\n\n\n
  39. An Energy-Driven Approach to Linkage Unfolding<\/a>.
    Jason Cantarella, Erik Demaine, Hayley Iben and James O’Brien.
    SCG ’04: Proceedings of the twentieth annual symposium on Computational geometry<\/em>, p. 134-143
    Abstract (not posted) in Proceedings of the 12th Annual DIMACS Fall Workshop<\/em>
    on Computational Geometry<\/em>, Piscataway, New Jersey, November 14-15, 2002.
    James O’Brien and Hayley Iben prepared     some cool movies and wrote a nice Java applet<\/a> to demonstrate some of the results from this paper. Here are some updated video files showing the unfolding\n