Jan Rychtář

National Research Experience for Undergraduates Program

[2013] [2014] [2015] [2016]

Acknowledgement

This program is an MAA activity funded by NSF NSF (grant DMS-1359016) and NSA (grant H98230-15-1-0020).

Summary

Jan Rychtar (UNCG), Hyunju Oh (Bennett College) and Joon-Yeoul Oh (Texas A&M University-Kingsville) 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 25, 2015 to July 3, 2015, we will engage 4 African-American female undergraduate students from Bennett College, Greensboro, NC in research projects. The students will work under the supervision of project directors Jan Rychtar (University of North Carolina at Greensboro), Hyunju Oh (Bennett College) and Joon-Yeoul Oh (Texas A&M University-Kingsville). We will introduce fundamental game-theoretical concepts such as Nash equilibria (NE), and the usage of computational (Maple/Matlab) and analytical tools (optimization and linear algebra) to identify NEs in real game theoretical models with applications to hurricane evacuation and border patrolling. 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 student will submit at least one research paper and present her findings at least 2 conferences (held in NC during Fall 2015). This project is part of the growing collaboration between UNCG and Bennett College (HBCU) and a starting collaboration with Texas A&M University-Kingsville (HSI).

Students

  1. Aaleah Lancaster
  2. Rhoni Moffit
  3. Qaleelah Smith
  4. KeeAera Hood

Projects

Hurricane evacuation.

During the hurricane season, residents in southeast coast area experience frequent warnings for hurricanes. The residents need to be evacuated to safety at least 20 to 50 miles away from the impacted area. With a mass evacuation, even 24-hour notice may not be enough since necessities such as lodging are limited and the actual evacuation distance can easily be more than 100 miles. When a hurricane is approaching, the residents prepare with installing blocks on windows, buying gas/food and deciding if and when to evacuate. In general, if they are getting ready too early, the cost to prepare is too high due to the frequent false warnings (long term hurricane path predictions are not yet reliable). However, if the residents wait almost till the end, their lives get threatened (short term predictions are relatively accurate). Moreover, when everybody evacuates at the same time, there will be logistical issues such as traffic congestions and no fuel in gas stations. The goal of this project is to find an optimal evacuation time. The optimal time depends on individual circumstances and risks (for example, a family with young children is in a different situation than a single healthy young person) and the objective is to find the time as a function of the individual risk and the rick distribution within the population.

Patrolling the US Border.

U.S. Customs and Border Protection (CBP), is responsible for securing the border between U.S. ports of entry and has divided the 2,000-mile U.S. border with Mexico among nine Border Patrol sectors. CBP reported spending about $3 billion to support Border Patrol's efforts on the southwest border in fiscal year 2010 alone, and apprehending over 445,000 illegal entries and seizing over 2.4 million pounds of marijuana. The number of border patrol officers has been increased but because of the limitation of patrolling personnel and budget, it is critical to allocate resources appropriately. The goal of this project is to optimize border patrol routes. The infiltrators' goal is to enter US successfully while patrols intend to capture infiltrators to prevent illegal cross-border activities. Students will develop various models with the objective to find optimal routes and patrolling patterns for the optimal border protection.

Outcomes

  • Aaleah Lancaster and Qaleelah Smith: Patrolling the US Border, UNCG RMSC, November 12, 2016, Greensboro, NC
  • Aaleah Lancaster, Qaleelah Smith, Hyunju Oh and Jan Rychtar: Patrolling the US Border, submitted
  • KeeAera Hood, Rhoni Moffit, Hyunju Oh and Jan Rychtar: Game theory and Hurricane evacuation, submitted
  • Rhoni Moffit: Hurricane evacuation, UNCG RMSC, November 7, 2015, Greensboro, NC
  • Aaleah Lancaster and Qaleelah Smith: Patrolling the US Border, UNCG RMSC, November 7, 2015, Greensboro, NC
  • KeeAera Hood and Rhoni Moffit: Hurricane evacuation, International Conference of Undergraduate Research, September 29, 2015. http://www.icurportal.com/
  • Aaleah Lancaster and Qaleelah Smith: Patrolling the US Border, International Conference of Undergraduate Research, September 29, 2015. http://www.icurportal.com/
  • KeeAera Hood and Rhoni Moffit: Hurricane evacuation, Math biology minisymposium, Duke University, June 18, 2015
  • Aaleah Lancaster and Qaleelah Smith: Patrolling the US Border, Math biology minisymposium, Duke University, June 18, 2015
  • Aaleah Lancaster, participated in the North Carolina A&T in the EMCOR REU Program in 2016 on Computational Modeling: Research Topic - “Numerical Modeling of a Soft Polymer using finite element simulations”
  • Qaleelah Smith, Michigan State University Summer Research Opportunity Program in 2016: Research Topic - “Characterizing E. coli Motile Behavior in Various Viscous Environments”