Matching Items (5)
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- All Subjects: Mathematics
- Resource Type: Text
- Status: Published
Description
Cellular and molecular biologists often perform cellular assays to obtain a better understanding of how cells work. However, in order to obtain a measurable response by the end of an experiment, the cells must reach an ideal cell confluency. Prior to conducting the cellular assays, range-finding experiments need to be conducted to determine an initial plating density that will result in this ideal confluency, which can be costly. To help alleviate this common issue, a mathematical model was developed that describes the dynamics of the cell population used in these experiments. To develop the model, images of cells from different three-day experiments were analyzed in Photoshop®, giving a measure of cell count and confluency (the percentage of surface area covered by cells). The cell count data were then fitted into an exponential growth model and were correlated to the cell confluency to obtain a relationship between the two. The resulting mathematical model was then evaluated with data from an independent experiment. Overall, the exponential growth model provided a reasonable and robust prediction of the cell confluency, though improvements to the model can be made with a larger dataset. The approach used to develop this model can be adapted to generate similar models of different cell-lines, which will reduce the number of preliminary range-finding experiments. Reducing the number of these preliminary experiments can save valuable time and experimental resources needed to conduct studies using cellular assays.
ContributorsGuerrero, Victor Dominick (Co-author) / Guerrero, Victor (Co-author) / Watanabe, Karen (Thesis director) / Jurutka, Peter (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
The spread of urbanization leads to habitat fragmentation and deterioration and changes the composition of ecosystems for species all over the world. Different groups of organisms are impacted differently, and insects have experienced loss in diversity and abundance due to changing environmental factors. Here, I collected seed beetles across 12 urban and rural sites in Phoenix, Arizona, to analyze the effects of urbanization and habitat variation on beetle diversity and abundance. I found that urbanization, host tree origin, and environmental factors such as tree diversity and density had no impact on overall beetle diversity and abundance. Beetles were found to have higher density on hosts with a higher density of pods. In assessing individual beetle species, some beetles exhibited higher density in rural sites with native trees, and some were found more commonly on nonnative tree species. The observed differences in beetle density demonstrate the range of effects urbanization and environmental features can have on insect species. By studying ecosystem interactions alongside changing environments, we can better predict the role urbanization and human development can have on different organisms.
ContributorsPaduano, Gabrielle (Author) / Savalli, Udo (Thesis director) / Sweat, Ken (Committee member) / Division of Teacher Preparation (Contributor) / School of Mathematical and Natural Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Adderall remains to be one of the most commonly abused drug among college campuses. Although it is a prescription drug that is primarily used to treat attention deficit hyperactivity disorder (ADHD), it has become one of the many "study drugs" due to its usage among college students during stressful school times, such as exams, where increased concentration and energy levels are thought to improve work efficiency. However, Adderall is notable for having a high potential for abuse and a risk of psychological and physical side effects. In this paper, we conducted a mathematical analysis on an existing epidemiological model of Adderall abuse. We started by verifying the positivity of solutions using techniques from dynamical systems because this is a population model dealing with people. Then, we found and investigated different equilibrium solutions to analyze their stability using both analytical and graphical approaches. Finally, the results were tied back into the Adderall model and conclusions were drawn.
ContributorsKerseg, Cassidy (Author) / Wirkus, Stephen (Thesis director) / Brager, Danielle (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
ContributorsHum, Aaron (Author) / Nishimura, Joel (Thesis director) / Wang, Haiyan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)
Created2023-05
Description
This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.
ContributorsHum, Aaron (Author) / Nishimura, Joel (Thesis director) / Wang, Haiyan (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Natural Sciences (Contributor)
Created2023-05