National Research Experience for Undergraduates Program

Acknowledgement

This program is an MAA activity funded by NSA (grant H98230-13-1-0270) and NSF (grant DMS-1156582).

Summary

Jan Rychtar (UNCG), Tsvetlanka Sendova (Bennett College) and Hyunju Oh (Bennett College) received funding from the Mathematical Association of America (MAA) for the for the “Game Theory and Applications” project. The award is part of the National Research Experience for Undergraduates Program funded through MAA by the National Science Foundation's Division of Mathematical Sciences and the National Security Agency. During the 6 weeks, from May 1, 2013 to June 15, 2013, we will engage 5 African-American female undergraduate students from Bennett College, Greensboro, NC in the research projects. The students will work in groups under the supervision of project directors. We will introduce the students to the fundamental game-theoretical concepts such as Nash equilibria and evolutionarily stable strategy and teach them how to use computational tools (such as Maple or a freeware program NetLogo) as well as analytical tools (optimization and linear algebra) to identify such strategies in real game theoretical models with applications in biology or medicine (such as Asian Carp invasion in Mississippi River, or emergence of invasive tumor cells). The students will further be trained in all aspects of research, starting with the ethics code, going through the workshops on using library and online resources and ending with training in delivering oral presentations as well as in using LaTeX to write mathematical papers. We expect that each group of students will submit at least one research paper and present the finding during at least 2 conferences (held in NC during Fall 2013).

Students

1. Hakimah Smith
2. Marwah Jasim
3. Jasmine Everett
4. KeYona Barton
5. Corbin Smith

Projects

The Invasion of Asian Carp of the Upper Mississippi River

Asian carps were imported from China in the 1970s to help clean commercial ponds. However, they subsequently migrated from ponds into the Mississippi, where they quickly reached high population density. They are considered invasive species, highly detrimental to the ecological balance, as they threaten the native fish population, eating up the algae and other organisms essential for the survival of the native fish. The Asian carp now threatens the Great Lakes. In July 2012 Congress enacted the "Stop Invasive Species Act", which requires the U.S. Corp of Engineers to implement measures, which will prevent Asian Carp from invading the Great Lakes from the Mississippi through the Chicago area canal system. The goal of this project is to gain a better understanding of the interaction between native species and Asian carp. Students will develop and analyze gametheoretical models related to the Hawk-Dove-Retaliator game to study the Mississippi invasion of the Asian Carp and its competition with native fish. Specifically, students will study the speed of the invasion and how it depends on various parameters of the game; with the aim to identify values that slow down (or even stop) the invasion. With the help of computer simulations, they will also study how the spatial structure of the river (or the canals) affects the invasion process. H. Smith, M. Jasim and J. Everett work on this project.

The emergence of invasive tumor cells

The tumor cells can come in different phenotypes which in turn gain different advantage under various metabolic conditions. Basanta et al. 2008 (Evolutionary game theory elucidates the role of glycolysis in glioma progression and invasion) describe three different phenotypes: AG (autonomous growth), GLY (anaerobic glycolysis) and INV (invasive) and study an evolutionary game between those phenotypes. The game can be described as generalized Rock-Paper-Scissors game and authors’ main objective was to identify conditions for which the INV phenotype appears (as in those cases, the tumor spreads). As part of this proposed project, the students will a) completely analyze the above game with 3 phenotypes, and then build on this work to b) incorporate more phenotypes into the game and c) incorporate spatial aspects of the tumors that have been neglected in previous models. The main objective will stay the same as in the original – identify conditions that allow (or prevent) INV phenotype to appear in order to help device tumor treatment strategies. K. Barton and C. Smith work on this project

Outcomes

• Presentation at NC A&T, June 5, 2013