Multi-scale Jones polynomial and persistent Jones polynomial for knot data analysis.

Authors

Ruzhi Song, Fengling Li, Jie Wu, Fengchun Lei, Guo-Wei Wei

Published in

AIMS mathematics. Volume 10. Issue 1. Pages 1463-1487. Epub Jan 22, 2025.

Abstract

Many structures in science, engineering, and art can be viewed as curves in 3-space. The entanglement of these curves plays a crucial role in determining the functionality and physical properties of materials. Many concepts in knot theory provide theoretical tools to explore the complexity and entanglement of curves in 3-space. However, classical knot theory focuses on global topological properties and lacks the consideration of local structural information, which is critical in practical applications. In this work, two localized models based on the Jones polynomial were proposed, namely, the multi-scale Jones polynomial and the persistent Jones polynomial. The stability of these models, especially the insensitivity of the multi-scale and persistent Jones polynomial models to small perturbations in curve collections, was analyzed, thus ensuring their robustness for real-world applications.

PMID:
40838040
Bibliographic data and abstract were imported from PubMed on 21 Aug 2025.

Read full publication at:
Please sign in to see all details.

Stats

1-terrible, 9-excellent. How would you rate this publication? Sign in in to submit your rating.

Post a comment

You need to be signed in to post comments. You can sign in here.

Comments

There are no comments yet.