Bio

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As of August 2019, I am a second year graduate student and teaching assistant at University of Nebraska–Lincoln pursuing a joint Ph.D. in computer science and mathematics. I am interested in computational complexity and algorithm development and analysis. As an undergraduate, I majored in both computer science and electrical engineering at Dordt College and minored in mathematics. Most of the research I have done to date has been in statistical and computational genetics, though I did get the opportunity to spend one summer working on a mathematical problem in graph theory and abstract algebra. For more information on any of those projects, see my research page which includes links within each project page to my publications and presentations for that project. Alternatively, you can view this information in my CV.

Research

Computational Space Complexity

As part of my computer science qualifying exam I wrote a survey paper on the space complexity of varitions of the reachability problem.

Plant Genome Imputation

I ported the LB-Impute plant genetics imputation algorithm from Java to R to improve usability for researchers after which I developed improved methods to enable better statistical analysis of the results. The improved algorithm (LaByRInth) is available on GitHub.

Powers of Ideals of Graphs

We proved a previously conjectured relationship between abstract algebraic objects (edge ideals of cyclic graphs) and discovered an equality relation involving these objects that was stronger and more general. We also established a means of calculating various metrics of interest regarding these relationships.

Genetic Analysis Workshop 20 (GAW20)

We researched and evaluated the performance of novel gene-based statistical tests of association and demonstrated proof of concept for a new data aggregation method using simulated data. I served as the primary programmer and technical support for two groups and lead author for one of the group's papers.

E. Coli Gene Activity States

I conducted exploratory research on modeling E. coli gene activity states using regulatory networks and created a modeling process that had potential to be more informative than the current standard models. The results were used in an NSF-MCB grant proposal to secure funding for further research.

Computational
Space Complexity

Survey Paper

Paper from November 2019 surveying results in space complexity related to the reachability problem

Survey Presentation

Presentation from December 2, 2019

Plant Genome Imputation

LaByRInth R-Package

LaByRInth is available on GitHub as an installable package for the R programming language.

Dordt Presentation

This presentation was given at Dordt College in May of 2018 and was targeted at a general audience.

Michigan Presentation

During the summer of 2018, while conducting research at Dordt College, the interns presented their research projects for faculty and students in the Department of Computational Medicine and Bioinformatics at the University of Michigan. The latter half of the presentation discusses one of the fundamental improvements in LaByRInth as compared to LB-Impute which was better genetic recombination rate estimation.

Comparing Symbolic
Powers of Edge Ideals
of Cyclic Graphs

Published Article

Published in the Journal of Algebra and Its Applications

arXiv Preprint

This is the initial submission to the journal and while the content is largely the same as the published version, there were a number of significant changes to the proofs of our claims including some corrections.

Dordt Summer Seminar Presentation

This presentation was given at Dordt College during the summer of 2017 as part of the research project and was targeted at a general audience. The presentation mostly discusses a way of graphically interpreting monomials in the context of the problem—a pivotal technique that we used in the proof of our central theorem in the paper.

Math on the Norther Plains Presentation

During the spring of 2018 we presented on this project at Math on the Northern Plains held at University of Sioux Falls in Sioux Falls, South Dakota. The audience was primarily undergraduate math majors and the presentation was an adaption of the one given at Dordt but with more detail given to our monomial deconstruction technique.