2017 NC State Research Experience for Undergraduates in Mathematics: Modeling and Industrial Applied Mathematics
REU arrival May 29, first day May 30
Final day August 1, departure day August 2
REU+ (REU for underrepresented undergraduate students) has a different page.
Program Director: Hien Tran
This program will be similiar to those offered each summer since Summer 2005. Summer 2016 program.
The NSF and the NSA provide generous funding and support for this REU program.
Stipend and support: $4,500 for ten weeks, all housing provided, as well as a partial meal allowance. Travel funds up to $300 per participant provided as needed.
2017 REU and REU+ Students
REU Projects for Summer 2017
Project 1: Portfolio Optimization and Risk Analysis with Leveraged ETF
Project mentor: Tao Pang (NC State)
An exchanged-traded fund (ETF) provides a convenient vehicle for an individual investor to seek return from a stock market index or sector. For example, SPDR S&P 500 ETF (SPY) is an ETF that seeks to provide investment results that, before expenses, correspond generally to the price and yield performance of the S&P 500 Index. It is traded on the New York Stock Exchange like ordinary stocks. A leveraged ETF (LETF) with a leverage of β aims to replicate β times the underlying index returns on a daily basis. β can be negative, in which case the ETF provides a negative multiple of the underlying index returns. Market size for ETFs and LETFs has been growing rapidly in recent years.
In this project, we consider portfolio optimization and risk analysis of investments in LETFs. While normal distributions are widely used to model stock index returns, the returns of LETFs do not follow normal distributions. This provides extra challenges to the traditional mean-variance portfolio optimization problem. We will first derive the distributions of the LETF returns and then we will solve the portfolio optimization problem with LETFs. In particular, we will derive the optimal investment strategy and the efficient frontier. Further, we will investigate risk management for investments in LETFs. The traditional methods of risk management using value at risk (VaR), conditional value at risk (CVaR) and the GARCH model need to be modified to be applied to LETFs.
Students need to have background in calculus, linear algebra, probability and statistics. Background in finance is not required, but would be a plus.
Project 2: Physiologically Based Pharmacokinetic (PBPK) Modeling for a Persistent Chlorinated Water Contaminant: 1,2,3-Trichloropropane
Project mentor: Marina Villafane Evans (US Environmental Protection Agency)
1,2,3-trichloropropane (TCP) has been used as a pesticide, degreasing solvent and in synthesis of polymers. Since it is a volatile organic chemical, exposure can occur via inhalation, dermally, or by ingestion of contaminated water. TCP is a multi-site carcinogen in two rodent species as a result of chronic oral ingestion. Because of its potential presence and solubility in water, the US EPA is “requiring many large water utilities to monitor for TCP with a minimum reporting level of 0.03 µg/L” (https://www.epa.gov/sites/production/files/2014-03/documents/ffrrofactsheet_contaminant_tcp_january2014_final.pdf). PBPK modeling is an excellent tool for converting external exposure (i.e. drinking water) to internal dose (inside the organs). Estimation of internal dose is important since we need to know what concentrations are in the internal organs being affected. For halogenated chemicals such as TCP, the mechanism of action is considered to be metabolic conversion in liver and kidney. Both of these organs produce metabolites inside their space, and internal dose will determine the extent of tissue damage produced by the metabolites. A PBPK model for drinking water would quantify the internal dose being generated by environmental concentrations found in contaminated water. If there is time, a PBPK model will be developed for a binary mixture including TCP with another water contaminant chosen by the students. (This abstract does not reflect EPA policy).
Project 3: Computational Modeling of Thyroid Hormones Modulations by Chemical Exposure During Pregnancy
Project mentor: Hisham El-Masri (US Environmental Protection Agency)
Thyroid hormones (TH) are important for neurological development. Lack of adequate levels during pregnancy is associated with brain deficits in the offspring both in human and in animal models. Despite being implicated in TH disruption, the relationship between environmental chemicals and consequent decline in serum TH leading to neurological impairment is poorly understood. The purpose of this project is to develop a computational model that links exposure of Thyroid-disrupting chemicals to predicted levels of the TH hormones during pregnancy and fetal developments in rats. The project will build on existing models and modify them to include more pertinent physiological and biochemical process obtained from literature. The computational model will be tested against literature and lab-generated data.
Project 4: Program and Technical Baseline and Acquisition Strategy Optimization Using War-Gaming Applications
Project mentors: Tien M. Nguyen and Andy Guillen (The Aerospace Corporation), Hien Tran (NC State)
This proposed project continues the 2016 REU project with a focus on advanced mathematical war-gaming application concepts to address Program and Technical Baseline (PTB) and Acquisition Strategy (AS) optimization using war-gaming concepts and Bayesian games with complete, incomplete information and mixed strategy. The proposed project exposes mathematics and statistics students to real-world research problems and requires interdisciplinary research involving game theory, probability and statistics, non-linear programming and mathematical modeling components, as well as experience in a team approach to problem solving,
The objective for this project is to improve the Aerospace Corporation’s mathematical war-gaming models for PTB and AS optimization for acquiring future space systems, and implement the models in a commercial off-the-shelf (COTS) software platform such as MATLAB. The project will focus on: (i) PTB optimization using Bayesian games with incomplete information and mixed strategy, and (ii) AS optimization using Bayesian games with complete, incomplete information and mixed strategy for various contract types, including Cost Plus Incentive Fee (CPIF), Fixed-Price Award Fee (FPAF), Fixed-Price Economic Price Adjustment (FPEPA), Cost Plus Fixed Fee (CPFF) and Cost Plus Award Fee contract types.
Participant Background, Requirements and Selection
Participants are expected to meet the following criteria:
- Citizen or permanent resident of the United States or its possessions
- Full-time rising senior science major with strong mathematics preparation
- Committed to devote their full time to the program and not engage in any other course work or employment during the program
Participants will be selected on the basis of demonstrated mathematical creativity, motivation and good work habits as well as meeting the above requirements, as determined from the application materials and recommendation letters.
Week 1: REU Workshop on modeling. Reception with REU students and faculty.
Week 2: Introduction to projects and mentors. Project teams are determined and begin to work on projects.
Weeks 3–9: Work on projects. Progress reports are due each Friday. Every other week there will be presentations given by each group. In addition there may be seminars on:
- mathematics related to the student projects
- research ethics
- applying to graduate school
- how to give poster presentations
- how to give research talks
Week 10: Students complete their final reports and do poster presentations of their work.
Extracurricular activities may include weekly teas, organized game and movie nights, a trip to see the AAA Durham Bulls play a baseball game, as well as an excursion to the beach. The North Carolina beaches and North Carolina mountains are within 2 to 4 hours drive from Raleigh.
Places to visit:
All applicants will be notified by email about the completeness of their application a couple of days after the deadline date. Unless previously notified, a final notification that the search is closed will be emailed after all positions have been filled and confirmed (this could take a month). If you have any questions about the status of your application, especially if you are trying to make a decision on accepting another summer position, please email the program director who will be happy to send you a prompt response.