72 citations · 109 across the 4 of their papers we have counts for
4 papers
Knot Tightening By Constrained Gradient Descent
Ted Ashton, Jason Cantarella, Michael Piatek +1
We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fi…
Polygonal knot space near ropelength-minimized knots
Kenneth C. Millett, Michael Piatek, Eric J. Rawdon
For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r<R(K) de…
Self-contact Sets for 50 Tightly Knotted and Linked Tubes
Ted Ashton, Jason Cantarella, Michael Piatek +1
We report on new numerical computations of the set of self-contacts in tightly knotted tubes of uniform circular cross-section. Such contact sets have been obtained before for the…
Tsnnls: A solver for large sparse least squares problems with non-negative variables
Jason Cantarella, Michael Piatek
The solution of large, sparse constrained least-squares problems is a staple in scientific and engineering applications. However, currently available codes for such problems are pr…