Peer-Reviewed Journal Articles
- Isolating phyllotactic patterns embedded in the secondary growth of sweet cherry (Prunus avium L.) using magnetic resonance imaging, with Elizabeth Munch, Daniel H. Chitwood, Gregory Lang and James Larson. Plant Methods, vol. 15 (2019). [Read]
- An all-encompassing global convergence result for processive multisite phosphorylation systems, with Anne Shiu. Mathematical Biosciences, vol. 291, pp. 1-9 (2017). doi.org/10.1016/j.mbs.2017.05.006 [Read]
- Long-term versus short-term strategy in the game of Monopoly, with McKenzie Lamb and Andrea Young. Journal of Undergraduate Mathematics and Its Applications, vol. 38, issue 1, pp. 35-57 (2017). [Read]
Peer-Reviewed Conference Papers
- Topological Mapper for 3D Volumetric Images, with Elizabeth Munch, Daniel H. Chitwood and Tim Ophelders. Proceedings of the 14th International Symposium on Mathematical Morphology (2019). [Read]
- Bringing Computational Science to Collegiate Education. Proceedings of the American Society for Engineering Education, North Central Section Conference (2019). [Read]
Patterns in Sweet Cherry
In collaboration with plant scientists, I applied imaging processing techniques to an MRI scan of a cherry log to visualize internal structures and analyze growth patterns. Using Mathematical Phyllotaxy, we confirmed that grow sweet cherry follows a Fibonacci pattern. I wrote the code for the project, visualized the specimen and set the work in its mathematical context.
Isolating phyllotactic patterns embedded in the secondary growth of sweet cherry (Prunus avium L.) using magnetic resonance imaging, with Elizabeth Munch, Daniel H. Chitwood, Gregory Lang and James Larson. Plant Methods, vol. 15 (2019).
Visualizing Barley Using 3D Mapper
Click here to see a web visualization using node.js
We extended a method from topological data analysis called Mapper for 3D, voxel-based images from x-ray CT and MRI. Using different parameters, we showed how the algorithm reveals different features of an image of barley. I wrote the implementation, generated figures and drafted the paper.
Topological Mapper for 3D Volumetric Images, with Elizabeth Munch, Daniel H. Chitwood and Tim Ophelders. Proceedings of the 14th International Symposium on Mathematical Morphology (2019).
Segmenting Citrus
I developed a GPU-algorithm using image and signal processing techniques to segment anatomical structures from about 150 x-ray CT images of citrus. In addition, I began work on aligning citrus scans along an axis using Principal Component Analysis. Future lab researchers will use this data to study the relative sizes of citrus segments.
Museum Layouts in London
Click here to enter the Museum Graph Layout website
During 2018 I spent four weeks in London with the “Digital Humanities and the Arts in London” programs sponsored by the Digital Humanities at Michigan State University. As I toured more than a dozen museums, I wondered how I could see every room without repeating a room. This lead to a project in which I modeled museum floorpans using graph theory. Other projects I completed in London: Historical Timeline of St Paul’s Cathedral & Tourist Map.
Super Mario Bros. AI
I used a neuroevolutionary algorithm called Spectrum-diverse Unified Nueroevolution Architecture (SUNA) to learn to play Super Mario Bros. Neural networks mapped items on the screen to controller inputs and were evaluated by distance traveled in the game. (This independent project satisfied the capstone requirement for a Computer Science major from Ripon College.)
Semi-discrete Curve Shortening Flows
The curve shortening flow uses the heat equation to smoothly transform a closed curve into a circle. I implemented discrete versions of the curve shortening flow on polygons to study asymptotic behavior. (This independent project satisfied the capstone requirement for a Mathematics major from Ripon College. Click here to see this project in 2017 Ripon Senior Showcase.)
Monopoly Simulation
I created a Monopoly simulator in Python and evaluated the success of different strategies.
Long-term versus short-term strategy in the game of Monopoly, with McKenzie Lamb and Andrea Young. Journal of Undergraduate Mathematics and Its Applications, vol. 38, issue 1, pp. 35-57 (2017).