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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.
ContributorsMusfeldt, Caleb (Author) / Panagiotou, Eleni (Thesis director) / Richa, Andrea (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Historical, Philosophical & Religious Studies, Sch (Contributor)
Created2024-05
Description
Mid-air ultrasound haptic technology can enhance user interaction and immersion in extended reality (XR) applications through contactless touch feedback. However, existing design tools for mid-air haptics primarily support the creation of static tactile sensations (tactons), which lack adaptability at runtime. These tactons do not offer the required expressiveness in interactive scenarios where a continuous closed-loop response to user movement or environmental states is desirable. This thesis proposes AdapTics, a toolkit featuring a graphical interface for the rapid prototyping of adaptive tactons—dynamic sensations that can adjust at runtime based on user interactions, environmental changes, or other inputs. A software library and a Unity package accompany the graphical interface to enable integration of adaptive tactons in existing applications. The design space provided by AdapTics for creating adaptive mid-air ultrasound tactons is presented, along with evidence that the design tool enhances Creativity Support Index ratings for Exploration and Expressiveness, as demonstrated in a user study involving 12 XR and haptic designers.
ContributorsJohn, Kevin (Author) / Seifi, Hasti (Thesis advisor) / Bryan, Chris (Committee member) / Schneider, Oliver (Committee member) / Arizona State University (Publisher)
Created2024