SIAM Undergraduate Research Online (SIURO)
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Undergraduate Student Research
Optimal Control in Discrete Pest Control Models
Published electronically January 18, 2013.
Author: Kathryn Dabbs (University of Tennessee)
Sponsor: Suzanne Lenhart (University of Tennessee)
Abstract: We use discrete time models to represent the dynamics of two interacting populations, a “valuable" population and a “pest" population. We investigate optimal control in the form of decreasing the growth rate of the “pest" population with the goal of maximizing the “valuable" population while minimizing the cost of the control. We compare different types of growth functions for the “valuable" population and their impact on the optimal control.
Assessment of Statistical Methods for Water Quality Monitoring in Maryland's Tidal Waterways
Published electronically April 17, 2013.
Author: Rosemary K. Le (Brown University), Christopher V. Rackauckas (Oberlin College), Anne S. Ross (Colorado State University) and Nehemias Ulloa (California State University, Bakersfield)
Sponsor: Matthias K. Gobbert (University of Maryland, Baltimore County)
Abstract: The Chesapeake Bay and its surrounding tributaries are home to over 3,600 species of plants and animals. In order to assess the health of the region, the Maryland Department of Natural Resources (DNR) monitors various parameters, such as dissolved oxygen, with monitoring stations located throughout the tidal waterways. Utilizing data provided by DNR, we assessed the waterways for areas of water quality concern. We analyzed the percentage of the readings taken for each parameter that failed to meet the threshold values and used the Wilcoxon Signed-Rank Test to determine the statuses of the stations. In order to assess the applicability of the Wilcoxon Test given the positive skew in the data, a simulation was performed. This simulation demonstrated that log-transforming the data prior to performing the Wilcoxon Test was not enough to reduce the Type I Error to reasonable levels. Thus, our team developed a relative ranking using a set of multiple comparison methods: a version of the Tukey Test on variance-transformed proportions, the Bonferroni adjustment method, a Bayesian method, and the Benjamini-Hochberg rejection method. From the ranking results we identified when each ranking technique is most applicable to our data.
Published electronically May 8, 2013.
Authors: Aleksey Chernobelskiy, Vineet Dixit, Agostino Cala, Siddharth Pandya, and Hector Javier Rosas (University of Arizona)
Sponsor: Scott Hottovy (University of Arizona)
Abstract: In this paper, we describe the general framework of neural networks and how such frameworks can be adapted to model human game play and the learning that takes place during iterative games. We introduce a method of pre-processing game matrices in an effort to produce cooperative strategies in games with non-cooperative dominant strategies, such as the Nash Equilibrium solution to the Prisoner's Dilemma. We find that the introduction of the pre-processed matrix increases the probability that the network plays a cooperative strategy significantly when compared to the network behavior without pre-processing.