Physical Sciences and Mathematics Commons^™

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Theses

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

Split Classification Model For Complex Clustered Data, Katherine Gerot

Honors Theses

Classification in high-dimensional data has generated tremendous interest in a multitude of fields. Data in higher dimensions often tend to reside in non-Euclidean metric space. This prevents Euclidean-based classification methodologies, such as regression, from reliably modeling the data. Many proposed models rely on computationally-complex embedding to convert the data to a more usable format. Others, namely the Support Vector Machine, rely on kernel manipulation to implicitly describe the "feature space" to arrive at a non-linear decision boundary. The proposed methodology in this paper seeks to classify complex data in a relatively computationally-simple and explainable manner.

Quantitative Appraisal Of Non-Irrigated Cropland In South Dakota, Shelby Riggs

Honors Theses

This appraisal attempts to remove subjectivity from the appraisal process and replace it with quantitative analysis of known data to generate a fair market value of the subject property. Two methods of appraisal were used, the income approach and the comparable sales approach. For the income approach, I used the average cash rent for the region, the current property taxes for the subject property, and a capitalization rate based on Stokes' (2018) capitalization rate formula to arrive at my income-based valuation. For the comparable sales approach, I utilized Stokes' (2018) research in optimization modeling to estimate a market value for …