Honors Theses Open Access
 
Filters: Department: "Mathematics" Collection: "ir_htoa"
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CreatorTitleDescriptionSubjectDate
1 Fischer, PaulHigh-Performance Computing Performance Metric AnalysisAt present, a signi#12;cant amount of ongoing scienti#12;c research relies on computational models. High-performance computing (HPC) resources are often required to obtain results in a reasonable amount of time. However, as physical and practical limitations constrain the performance progression of ...2019
2 Halberg, CharlesOn causality in machine learningAlthough the studies of causal inference and machine learning arose independently, there are emerging intersections which are proving fruitful for both fields. One of the major modern challenges in AI is to develop robust, generalizable models which can perform across a number of different tasks wit...2022
3 McDaniel, TylerUtah's Pathways to Higher Education: a Critical, Quantitative AnalysisThis work uses linear and nonlinear models in order to predict student success and pathways in higher education in the state of Utah. Postsecondary Grade Point Average is used as a metric for success in higher education. Pathways are identified using clustering analyses, which group observations a...Higher education and state - Utah; Higher education and state - United States; Low-income students - United States
4 Bowen, BradyFractal geometry of melt ponds: Modeling the fractal geometry of arctic melt ponds using the level sets of random surfacesDuring the late spring, most of the Arctic Ocean is covered by sea ice with a layer of snow on top. As the snow and sea ice begin to melt, water collects on the surface to form melt ponds. As melting progresses, sparse, disconnected ponds coalesce to form complex, self-similar structures which are c...Melt pond geometry2016-04
5 Wang, WenyiImaging in a homogeneous aluminum plate by using ultrasonic wavesThis project is about detecting and imaging damage (such as cracks) in a plate by using ultrasonic waves. The waves are generated by a source (an ultrasonic transducer) that is part of a robot that can move on the plate. The waves traveling in the plate are recorded at a receiver (another ultrasonic...Ultrasonic transducer - Mathematics; Kirchoff migration - Research2014-12
6 Kroll, TylerNumerical floating-point code: precision-independence, base-independence, and other programming considerationsThe knowledge and skills of the floating-point-literate mathematician are seldom lauded, though central to the art of translating the world of mathematics into the language of computers. This thesis highlights the importance of floatingpoint literacy through various high-utility techniques relevant ...2020
7 Tang, AnnaMathematical model of drug resistance in ER+ breast Cancer: the role of the microenvironmentOne of the main obstacles to treating cancer is its ability to evolve and resist treatment. In this project, we are primarily interested mathematically modeling how the cancer microenvironment interacts with cancer cells and affects cancer's response to therapy. We aim to develop the mathematical mo...2023
8 Tse, JustinThe Linear Algebra of the Last Passage Percolation ModelWe study the linear algebra of the last passage percolation model. In this model, we want to find the statistics of maximal paths through a randomly weighted grid. Specifically we focus on bases of the set of path lengths made from paths. The maximum path length is a deterministic function of a much...2017
9 Zheng, KennethDyck Paths and Random TreesWe give an expository survey of random trees, focusing on the interplay between plane trees and Dyck paths. The material explained here summarizes what can be found in Aldous [1], Le Gall [10], and Drmota [6]. The bijection between plane trees and Dyck paths serves as motivation for the connection b...2017
10 Thomas, J PaytonStability of genetic oscillators with distributed delayed feedbackGenetic oscillators govern periodic phenomena in biology including circadian rhythms and are also the basis of biological clocks used in the design of synthetic genetic circuits. Models of genetic oscillators tend to neglect biological detail, however, because biological systems tend to be too compl...2023
11 Beams, AlexanderImplications of antibiotic use for co-infections when a fitness trade-off for resistance is presentHow much does indiscriminate antibiotic use promote the spread of antibiotic-resistant infections in a population? Assuming a fitness trade-off for resistance exists, it is possible for an antibiotic-vulnerable strain to outlast a resistant type within an untreated host carrying both. That means pru...Drug resistance in microorganisms -- Mathematical models Co-infections2015
12 Copinga, AidanOptimal transport and applications in partial differential equationsIn the 18th century, Gaspard Monge created a mathematical framework to find the best way to describe the optimal way to rearrange the dirt dug out from the land into castle walls or other desired shapes. More recently, in the 20th century, Leonid Kantorovich explored infinite dimensional optimizatio...2022
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