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- Creators: Barrett, The Honors College
- Resource Type: Text
ContributorsNunez, Christian (Author) / Koblenz, Blair (Thesis director) / Stapp, Mark (Committee member) / Barrett, The Honors College (Contributor) / Department of Finance (Contributor)
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
ContributorsLuca, Michael (Author) / Yan, Hao (Thesis director) / Stephanopoulos, Nicholas (Committee member) / Blattman, Joseph (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor) / School of International Letters and Cultures (Contributor) / School of Molecular Sciences (Contributor)
Created2024-05
Description
Our Idea: As a team of engineers, two in the engineering field and one in computer
science and software development, we wanted to find a way to put these skills to use in our
company. As we did not have a revolutionary idea to build our own product, we wanted to base our company on the assumption that people have great ideas and lack the ability to execute on these ideas. Our mission is to enable these people and companies to make their ideas a reality, and allow them to go to market with a clean and user friendly product. We are using our skills and experience in hardware and device prototyping and testing, as well as software design and development to make this happen.
Implementation: To this point, we have been working with a client building a human diagnostic and enhancement AI device. We have been consulting on mostly the design and creation of their first proof of concept, working on hardware and sensor interaction as well as developing the software allowing their platform to come to life. We have been working closely with the leaders of the company, who have the ideas and business knowledge, while we focus on the technology side. As for the scalability and market potential of our business, we believe that the potential market is not the limiting factor. Instead, the limiting factor to the growth of our business is the time we have to devote. We are currently only working with one client, and not looking to expand into new clients. We believe this would require the addition of new team members, but instead we are happy with the progress we are making at the moment. We believe we are not only building equity in business we believe in, but also building a product that could help the safety and wellness of our users.
ContributorsSchildgen, Nathan (Author) / Engerholm, Liam (Co-author) / Miller, Kyle (Co-author) / Byrne, Jared (Thesis director) / Lee, Christopher (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2024-05
Description
Our Idea: As a team of engineers, two in the engineering field and one in computer
science and software development, we wanted to find a way to put these skills to use in our
company. As we did not have a revolutionary idea to build our own product, we wanted to base
our company on the assumption that people have great ideas and lack the ability to execute on
these ideas. Our mission is to enable these people and companies to make their ideas a reality,
and allow them to go to market with a clean and user friendly product. We are using our skills
and experience in hardware and device prototyping and testing, as well as software design and
development to make this happen.
Implementation: To this point, we have been working with a client building a human
diagnostic and enhancement AI device. We have been consulting on mostly the design and
creation of their first proof of concept, working on hardware and sensor interaction as well as
developing the software allowing their platform to come to life. We have been working closely
with the leaders of the company, who have the ideas and business knowledge, while we focus on
the technology side. As for the scalability and market potential of our business, we believe that
the potential market is not the limiting factor. Instead, the limiting factor to the growth of our
business is the time we have to devote. We are currently only working with one client, and not
looking to expand into new clients. We believe this would require the addition of new team
members, but instead we are happy with the progress we are making at the moment. We believe
we are not only building equity in business we believe in, but also building a product that could
help the safety and wellness of our users.
ContributorsMiller, Kyle (Author) / Engerholm, Liam (Co-author) / Schildgen, Nathan (Co-author) / Byrne, Jared (Thesis director) / Lee, Christopher (Committee member) / Barrett, The Honors College (Contributor) / Mechanical and Aerospace Engineering Program (Contributor)
Created2024-05
Description
In this paper, a novel model of Hotelling duopoly is introduced that explains horizontal product variety as the result of consumer preferences, expanding on and meshing the works of Hotelling (1929) and Neven (1985). From this model, two opposing forces from consumer preferences are found that impact the variety and price decisions of firms: market share revenues and price revenues. As firms face consumers with highly linear (weak) preferences over variety, the profit incentive is to simply capture the market by offering products that appeal to the middle consumer. However, as firms face consumers with highly quadratic (strong) preferences over variety, the profit incentive is to carve out and exploit a market segment by offering a distinct variety. Thus, observed product variety between minimal and maximal differentiation is emergent from consumer preferences, as firms face a balance of price and market share incentives.
ContributorsMalaki, Adam (Author) / Leiva Bertran, Fernando (Thesis director) / Hanemann, Michael (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Economics Program in CLAS (Contributor) / School for the Future of Innovation in Society (Contributor)
Created2024-05
Description
Alzheimer’s disease (AD) is projected to increase, and understanding risk and protective factors could help mitigate this increase. Deficits in Choline, a B-like vitamin, intake or issues with endogenous choline production can lead to an increased risk for AD development. To better understand the effects of endogenous choline through the lifespan in the context of Alzheimer pathology, Male and Female 3xTg-AD and NonTg mice, were aged to 16.81 ± 0.13 months. Body weight, food consumption data, and blood plasma samples were collected across the lifespan. A behavioral battery, that consisted of Rotarod, Elevated Plus Maze, and Intellicage, was performed to assess differences across a range of tasks. Hippocampal and cortical tissue were collected to assess pathology. Overall, 3xTg-AD mice had lower choline levels than NonTg at multiple timepoints and Males had higher choline than Females. Furthermore, 3xTg-AD Females had higher levels of both Aβ and Tau pathology than their Male counterparts. In the Intellicage, Females made fewer Percent of Correct Responses during Place Preference. Together these findings show that choline levels through the lifespan, impact the severity of pathology between Males and Female 3xTg-AD mice and behavioral differences between the 3xTg-AD and NonTg mouse models.
ContributorsMistry, Faizan (Author) / Velazquez, Ramon (Thesis director) / Judd, Jessica (Committee member) / Barrett, The Honors College (Contributor) / Department of Psychology (Contributor) / School of Life Sciences (Contributor)
Created2024-05
Description
Quantum entanglement is a phenomenon in which a group of particles that are either generated, interacting with each other, or close in proximity to each other, have a property that the quantum states of each particle cannot be described independently of the states of the other particles. This phenomenon was initially investigated by Albert Einstein, Boris Poldosky, and Nathan Rosen in their landmark paper known as the EPR paradox, in which Einstein described this behavior as
"spooky action at a distance''. This thesis presents a mathematical and theoretical approach in defining quantum entanglement by detecting photons in their entangled state through a set of photon-number-resolving (PNR) detectors and threshold detectors. This theoretical approach is made rigorous by including the notion of a dark count, a phenomenon in which a detector incidentally detects a photon when it should not have been detected. With this dark count model, we define the probabilities of finding a coincidence of such entangled photons through a combination and configuration of PNR detectors and threshold detectors. Then, we find the coincidence probabilities of detecting a single coincidence of photons within the detector system, the total coincidence probabilities of detecting this coincidence with respect to ground truth, and the effective density matrix that characterizes how well each combination and configuration of detectors can detect photon coincidences. By making mathematical and probabilistic assumptions on the distribution of photon types and counts with respect to ground truth, we are able to compute these quantities and analyze their expressions based on a mathematical and conceptual context.
ContributorsTruong, Taman (Author) / Lukens, Joseph (Thesis director) / Arenz, Christian (Committee member) / Barrett, The Honors College (Contributor) / Computer Systems Engineering (Contributor)
Created2024-05
Description
The events industry provides an integral service to society but fails to understand and incorporate the three pillars of sustainability. The purpose of this paper is to identify the cause of the lack of awareness and motivation from event managers to make their events more sustainable. Utilizing both dated and recent research papers to understand the gap of awareness, the data demonstrated that there is not a clear understanding of sustainability from a holistic perspective. The most notable issue was the focus on environmental sustainability and the lack of awareness of social and economic sustainability. This paper analyzes one specific event, the Boys & Girls Clubs of Greater Scottsdale, Celebrate Youth Gala, and dives deeper into how the event can be made more sustainable. The findings demonstrated that event managers often are unaware of the sustainable options available to them and the costs associated with them. This paper offered recommendations for event managers and started the necessary conversation to create change within the industry.
ContributorsMertz, Carly (Author) / Goodman, Rebekka (Thesis director) / Schneiderman, Erin (Committee member) / Barrett, The Honors College (Contributor) / Department of Marketing (Contributor) / Dean, W.P. Carey School of Business (Contributor) / School of Community Resources and Development (Contributor)
Created2024-05
ContributorsLuca, Michael (Author) / Yan, Hao (Thesis director) / Stephanopoulos, Nicholas (Committee member) / Blattman, Joseph (Committee member) / Barrett, The Honors College (Contributor) / School of Life Sciences (Contributor) / School of International Letters and Cultures (Contributor) / School of Molecular Sciences (Contributor)
Created2024-05