Development of a Python-Based Software for Calculating the Jones Polynomial: Insights into the Behavior of Polymers and Biopolymers
Description
This thesis details a Python-based software designed to calculate the Jones polynomial,
a vital mathematical tool from Knot Theory used for characterizing the topological and
geometrical complexity of curves in 3-space, which is essential in understanding physical
systems of filaments, including the behavior of polymers and biopolymers. The Jones
polynomial serves as a topological invariant capable of distinguishing between different
knot structures. This capability is fundamental to characterizing the architecture of
molecular chains, such as proteins and DNA. Traditional computational methods for
deriving the Jones polynomial have been limited by closure-schemes and high execu-
tion costs, which can be impractical for complex structures like those that appear in
real life. This software implements methods that significantly reduce calculation times,
allowing for more efficient and practical applications in the study of biological poly-
mers. It utilizes a divide-and-conquer approach combined with parallel computing and
applies recursive Reidemeister moves to optimize the computation, transitioning from
an exponential to a near-linear runtime for specific configurations. This thesis provides
an overview of the software’s functions, detailed performance evaluations using protein
structures as test cases, and a discussion of the implications for future research and
potential algorithmic improvements.
Date Created
The date the item was original created (prior to any relationship with the ASU Digital Repositories.)
2024-05
Agent
- Author (aut): Musfeldt, Caleb
- Thesis director: Panagiotou, Eleni
- Committee member: Richa, Andrea
- Contributor (ctb): Barrett, The Honors College
- Contributor (ctb): School of Mathematical and Statistical Sciences
- Contributor (ctb): Historical, Philosophical & Religious Studies, Sch