28 citations · 187 across the 25 of their papers we have counts for
26 papers
Hard unknots are often easy from a different perspective
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
Recent attempts to train AI models to recognize knots have produced millions of ``hard'' unknot diagrams resistant to simplification by Reidemeister moves, pass moves, or random wa…
Random knotting in very long off-lattice self-avoiding polygons
Jason Cantarella, Tetsuo Deguchi, Henrik Schumacher +2
We present experimental results on knotting in off-lattice self-avoiding polygons in the bead-chain model. Using Clisby's tree data structure and the scale-free pivot algorithm, fo…
New Upper Bounds for Stick Numbers
Jason Cantarella, Andrew Rechnitzer, Henrik Schumacher +1
We use a version of simulated annealing with knot-type preserving moves to find polygonal representatives of various knot types with low stick number. These give better bounds on s…
An exact formula for the contraction factor of a subdivided Gaussian topological polymer
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler +1
We consider the radius of gyration of a Gaussian topological polymer formed by subdividing a graph of arbitrary topology (for instance, branched or multicyclic). We give a…
On the average squared radius of gyration of a family of embeddings of subdivision graphs
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
Suppose we have an embedding of a graph created by subdividing the edges of a simpler graph . The edges of can be divided into subsets which…
CoBarS: Fast reweighted sampling for polygon spaces in any dimension
Jason Cantarella, Henrik Schumacher
We present the first algorithm for sampling random configurations of closed -gons with any fixed edgelengths in any dimension which is proved to sample cor…
A faster direct sampling algorithm for equilateral closed polygons and the probability of knotting
Jason Cantarella, Henrik Schumacher, Clayton Shonkwiler
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 C…
Random graph embeddings with general edge potentials
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler +1
In this paper, we study random embeddings of polymer networks distributed according to any potential energy which can be expressed in terms of distances between pairs of monomers.…
Families of similar simplices inscribed in most smoothly embedded spheres
Jason Cantarella, Elizabeth Denne, John McCleary
Let denote a non-degenerate -simplex in . The set of simplices in similar to is diffeomorphic to $O(k)\times [0,\infty)\time…
Square-like quadrilaterals inscribed in embedded space curves
Jason Cantarella, Elizabeth Denne, John McCleary
The square-peg problem asks if every Jordan curve in the plane has four points which are the vertices of a square. The problem is open for continuous Jordan curves, but it has been…
Configuration Spaces, Multijet Transversality, and the Square-Peg Problem
Jason Cantarella, Elizabeth Denne, John McCleary
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: given a submanifold of configurations o…
Performance of the Uniform Closure Method for open knotting as a Bayes-type classifier
Emily Tibor, Elizabeth M. Annoni, Erin Brine-Doyle +5
The discovery of knotting in proteins and other macromolecular chains has motivated researchers to more carefully consider how to identify and classify knots in open arcs. Most def…
Computing the conformal barycenter
Jason Cantarella, Henrik Schumacher
The conformal barycenter of a point cloud on the sphere at infinity of the Poincaré ball model of hyperbolic space is a hyperbolic analogue of the geometric median of a point cloud…
Radius of Gyration, Contraction Factors, and Subdivisions of Topological Polymers
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler +1
We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropria…
Factoring the Laplacian to understand topological polymers
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler +1
A ring polymer is a random walk whose steps obey a single linear condition; their sum vanishes. Factoring the graph Laplacian into the product of the incidence matrix and its trans…
Open and closed random walks with fixed edgelengths in
Jason Cantarella, Kyle Chapman, Philipp Reiter +1
In this paper, we consider fixed edgelength -step random walks in . We give an explicit construction for the closest closed equilateral random walk to almost any o…
Random Triangles and Polygons in the Plane
Jason Cantarella, Tom Needham, Clayton Shonkwiler +1
We consider the problem of finding the probability that a random triangle is obtuse, which was first raised by Lewis Caroll. Our investigation leads us to a natural correspondence…
Knot Probabilities in Random Diagrams
Jason Cantarella, Harrison Chapman, Matt Mastin
We consider a natural model of random knotting- choose a knot diagram at random from the finite set of diagrams with n crossings. We tabulate diagrams with 10 and fewer crossings a…
A Fast Direct Sampling Algorithm for Equilateral Closed Polygons
Jason Cantarella, Bertrand Duplantier, Clayton Shonkwiler +1
Sampling equilateral closed polygons is of interest in the statistical study of ring polymers. Over the past 30 years, previous authors have proposed a variety of simple Markov cha…
Transversality for Configuration Spaces and the "Square-Peg" Theorem
Jason Cantarella, Elizabeth Denne, John McCleary
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of po…
The symplectic geometry of closed equilateral random walks in 3-space
Jason Cantarella, Clayton Shonkwiler
A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. Th…
The Expected Total Curvature of Random Polygons
Jason Cantarella, Alexander Y Grosberg, Robert B. Kusner +1
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference be…
Symmetric Criticality for Tight Knots
Jason Cantarella, Jennifer Ellis, Joseph H. G. Fu +1
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configu…
Probability Theory of Random Polygons from the Quaternionic Viewpoint
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler
We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the comp…