5 papers
Trefoil Probabilities and Polyhedra
Joseph Geisz, Chris Peterson, Clayton Shonkwiler
We determine the exact probability that the closed hexagonal polygon obtained by cyclically joining six independent points uniformly distributed on the unit sphere is knotted. The…
Looping Animations Using the Modular Flow and Elliptic Functions
Clayton Shonkwiler
This paper describes an approach to generating looping animations using the modular flow and elliptic functions. The modular flow is a flow on lattices with many periodic orbits, a…
A Land of Oblique Duality for Frames and Probabilistic Frames
Dongwei Chen, Emily J. King, Clayton Shonkwiler
Functions or distributions used to sample and to reconstruct signals often occur in different domains, like the Dirac delta and a band-limited bump function in classical sampling.…
Sampling Finite Unit Norm Tight Frames Using Symplectic Geometry
Mason Faldet, Clayton Shonkwiler
Unit-norm tight frames in finite-dimensional Hilbert spaces (FUNTFs) are fundamental in signal processing, offering optimal robustness to noise and measurement loss. In this paper…
Direct Sampling of Confined Polygons in Linear Time
Clayton Shonkwiler, Kandin Theis
We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges. Using symplectic geometry,…