Performance of the Uniform Closure Method for open knotting as a Bayes-type classifier

• Main Authors: Tibor, Emily, Annoni, Elizabeth M, Brine-Doyle, Erin, Kumerow, Nicole, Shogren, Madeline, Cantarella, Jason, Shonkwiler, Clayton, Rawdon, Eric J
• Format: Journal Article
• Language: English
• Published: 17.11.2020
• Subjects: Mathematics - Geometric Topology
• DOI: 10.48550/arxiv.2011.08984

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 definitions classify knotting in open arcs by constructing an ensemble of closures and measuring the probability of different knot types among these closures. In this paper, we think of assigning knot types to open curves as a classification problem and compare the performance of the Bayes MAP classifier to the standard Uniform Closure Method. Surprisingly, we find that both methods are essentially equivalent as classifiers, having comparable accuracy and positive predictive value across a wide range of input arc lengths and knot types.