The NSF and the NSA provide generous funding and support for this
REU program.
Where: NC State University, Raleigh, NC .
Stipend and support: $4000 for ten weeks, all
housing provided, as well as a partial meal allowance. Travel
funds up to $300 per participant provided as needed.
Topics for 2011 REU program: Other projects are being negotiated and will be listed
when they are finalized.
Project 1: Sensitivity Analysis Tools for Nonlinear ODE Models and Applications in Biological Systems
Advisors: Michael Zager (Pfizer), Mary Spilker (Pfizer), Paolo Vicini (Pfizer) and Hien Tran (NCSU)
Graduate Student Assistant: Adam Attarian
Modeling and simulation is becoming a highly sought-after discipline within drug research and development, being used to address a wide range of challenging questions. Since the onset of systems approaches that have resulted from the genomic revolution, the pharmaceutical industry has begun to embrace more and more highly mechanistic models of disease, pathways, and pharmacology. These models are being employed to help investigate and validate potential drug targets for a range of diseases, including diabetes and cancer. However, as these models become more complex, modelers working in industry need tools of appropriate sophistication and speed to analyze model behavior. Sensitivity analysis quantifies the influence of model parameter and state variable changes on model predictions. It is perhaps one of the most useful engineering methods applied to systems biological models. In principle, it provides an understanding of which parameters (such as binding, synthesis, degradation and phosphorylation rates) and which state variables (typically representing proteins, hormones or drug molecules) are most important to understand and measure in a given pathway. However, calculating these sensitivities in closed form is cumbersome, and often impossible for complex systems. Although there are numerous methods in the literature for estimating sensitivity via numerical approximations (e.g. finite differencing), these methods vary in behavior and reliability. Alternatively, automatic differentiation is a very attractive approach, especially for large models, due to the accuracy of the derivatives that it provides.
In this REU project, students will learn the concept of sensitivity analysis and will develop both local and global sensitivity analysis tools for applications in biological systems modeling. No prior knowledge of the biology is required but a good background in ordinary differential equations and computer programming experience including knowledge of MATLAB are desirable.
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Project 2: Development and Calibration of an Ozone Inhalation Model
Advisors: Hisham El-Masri (U.S. EPA) and William LeFew (U.S. EPA)
Graduate Student Assistant: Bryan Conklin
The US Environmental Protection Agency’s mission to protect human and environmental health depends in large measure on generation of relevant scientific knowledge in the laboratory and interpretation of this knowledge to refine our understanding of the related potential health risks. Biologically based dose-response (BBDR) modeling integrates exposure, dose, mode of action, and effect data to generate predictions of dose-response and time-course behaviors. The validity of these predictions depends largely on the datasets that are used as inputs to the model and the technical quality of the model development process itself. Ultimately, coordinated BBDR modeling efforts will lead to
improved health risk predictions by augmenting our understanding of exposure, dosimetry, and the modes of action. The goal of this project is develop an exposure/dose model as part of a larger BBDR model for effects of inhaled ozone on the respiratory tract. This project will involve the simulation of ozone as it passes into the lung and the
consequences of the reactions that take place therein. The uptake of ozone will be described by a transport equation which describes the flow, propagation, diffusion, and flux into the lung layers. Simulation of this process will involve work with linear algebra, numerical solutions to partial differential equations (PDE's), examinations into stability, consistency, and convergence of solutions, and some programming in MATLAB.
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Project 3: Quantitative Financial Risk Analysis
Advisors: Tao Pang (NCSU) and Jeffrey Scroggs (NCSU)
Graduate Student Assistant: Anran Wang
In this project, students will learn how to quantify the financial risks associated with each financial asset as well as financial portfolio. We will consider some popular financial risk measures such as value at risk (VaR), conditional value at risk (CVaR) and their connection with financial regulations such as Basel Accord. The advantage and challenge of different risk measures are to be discussed.
Certain probability distributions, such as Gaussian, Lognormal, etc. have been used to model the financial data, and many risk management are based on those models. However, the recent financial crisis and its severe impacts suggest that the risks might have been underestimated. Distributions with heavier tail should be considered. In addition, when we consider a financial portfolio of several assets, the correlations between the assets should be considered. Copula method will be introduced and
students will be asked to implement certain copula with real financial data for risk management purpose.
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Project 4: Stochastic vs. Deterministic Modeling in HIV/FIV Infections
Advisors: H.T. Banks (NCSU), Shuhua Hu (NCSU) and Michele Joyner (East Tennessee State University)
Graduate Student Assistant:
This project will concern modeling of HIV and FIV during both short term (acute) and long term (chronic) periods. We will develop and compare through analysis and simulation both stochastic and deterministic models involving populations of uninfected and infected target cells, virions, and immune response effectors. No prior knowledge of the biology is required but a background introduction to ordinary differential equations and probability theory or statistics along with elementary knowledge of MATLAB is desirable.
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Project 5: Cell Rearrangements in Tissues
Advisor: Sharon Lubkin (NCSU)
Graduate Student Assistant: K. Krisna
Developmental biology is the study of how we go from a spherically symmetric egg to a complex dynamic structure with dozens of differentiated cell types in spatially complex and useful arrangements, such as lungs, hands, and brains. Part of the mechanism of development is cell rearrangements, which are due to forces generated by the cell interacting with forces applied to the cell. We will model the rearrangements of cells in morphogenesis using a stochastic simulation technique.
Some computer programming experience is necessary.
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Project 6: Modeling blood pressure control during head-up tilt
Advisor: Mette Olufsen (NCSU)
Graduate Student Assistant: Nakeya Williams
A simple change of the body from supine to sitting or standing position requires activation of a series of control mechanisms to maintain blood flow and pressure. The control mechanisms activated are part of the autonomic control system. In particular, we focus on the baroreceptor control system, which regulate heart rate, cardiac contractility, and vascular resistance. The autonomic nervous system is very complex with many interacting components. Typical clinical studies investigate this system by analyzing potential malfunction of the system by analysis of each separate element. However, since the system is complex this approach does not provide essential insight into the complex function of the system. In this project, we will focus on building a model that can predict blood flow and pressure regulation, validating the model using measured and literature data, and investigating several theories put forward in an attempt to explain what mechanisms that trigger syncope (or fainting) for a given group of patients. This project is interdisciplinary and you will be exposed to both mathematics mostly related to ordinary differential equations and physiology of blood flow. Mathematically, this project will teach you to model and build a model using Matlab, you will learn techniques for sensitivity analysis and for identification and estimation of model parameters, and finally, you will be learning how to develop a set of computer simulations for model prediction.
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Project 7: Cluster Analytics and Visualization
Advisor: Carl Meyer (NCSU)
Graduate Student Assistant: Ralph Abbey
Given unorganized data that may be derived from text, images, or simply raw numerics, the objective is to develop new and innovative techniques for detecting, revealing, and analyzing hidden patterns and clusters of information that exhibit some sort of similarity
or commonality. The size and diverse nature of the data sets of interest make this a formidable but extremely important problem. The first part of the project will be to learn and understand how to use some of the state-of-the art techniques by analyzing some selected practical applications. This will be followed by exploring the possibilities of
developing some new methodologies and algorithms. Finally, the challenge of developing and building visualization techniques that can allow researchers to interact with their data in a dynamical fashion will be explored.
Prerequisites: The mathematics employed involves linear algebra, elementary probability and statistics, networks and graphs, and some numerical analysis coupled with scientific computing principles.
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Project 8: Randomized Algorithms for Matrix Computations
Advisor: Ilse Ipsen (NCSU)
Graduate Student Assistant: Thomas Wentworth
We will investigate numerical methods that use "random sampling" to approximate a matrix by one of lower rank.
Randomized algorithms are starting to find their way into a wide variety of applications that give rise to enormously large matrices, including pattern recognition, social network analysis, population genetics, circuit testing, and text classification. Randomized
algorithms downsize the enormous matrices by picking and choosing only particular columns or rows, thereby producing potentially huge savings in storage and computing speed.
Although randomized algorithms are fast and efficient, not much is known about their numerical properties. We will determine how accurate and reliable these randomized algorithms are in comparison to their deterministic counterparts, and we will try to answer questions like: Is the matrix dimension large enough to benefit from a randomized algorithm? How many correct digits does the output of a randomized algorithm have, in the worst case? Exactly how much sampling is necessary to achieve a user specified error? Is there a point where more sampling is counter productive? The algorithms under
consideration include randomized versions of QR, singular value and CUR decompositions.
The tools we will use include linear algebra, numerical analysis, programming in Matlab, and probability theory.
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Project 9: Antimicrobial Resistance: Assessing the Importance of Agricultural Drug Use
Advisor: Alun Lloyd (NCSU)
Graduate Student Assistant: Michael Robert
Antimicrobials have saved millions of lives since their introduction in the
mid-twentieth century. Overuse of these drugs, however, threatens to reduce their effectiveness as antimicrobial-resistant pathogens emerge and spread. Agricultural use of antimicrobials is a particular concern: antimicrobials are often pre-emptively given to healthy animals, and it has been estimated that this represents as much as 70% of US antimicrobial usage.
In this project, we will model the spread of antimicrobial resistance in pork production facilities, considering both direct animal to animal transmission and environmental transmission via contaminated swine waste products. We shall compare how different rearing practices impact the spread and develop strategies to mitigate or control spread.
Initially, we shall use simple ordinary differential equation models (ODEs). The environmental component may involve partial differential equations (PDEs) to describe the movement of bacteria through the environment, but previous experience of PDEs will not be necessary.
The results of this project will be used to design experiments to determine the risk
factors and measure the spread of antimicrobial resistance on pig farms in North
Carolina (collaborative project with Sid Thakur, College of Veterinary Medicine, NC
State).
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Project 10: Application of physiologically based pharmacokientic (PBPK) modeling to discriminate between different metabolic pathways for the water disinfection by-product bromochloromethane.
Advisor: M. Evans (U.S. EPA)
Graduate Student Assistant: Megan Sawyer
The application of mathematical models that take into account physiological and chemical information is now well established as a risk assessment tool, especially for extrapolation across species and different exposure scenarios. These PBPK models are usually calibrated using data collected in rodents and used to predict internal dose to
humans. Many volatile compounds are transformed into carcinogens after metabolism by a liver enzyme known as CYP2E1. This enzyme is known to metabolize volatiles, which are small molecules, as well as intermediate and large molecules, such as fatty acids. The molecular structure of the human CYP2E1 has been recently deciphered, allowing for the application of modeling tools to help predict biological effects. The purpose of this project is to use inhalation data designed to measure metabolism in rats an apply different mechanistic ideas to explain how CYP2E1 metabolizes bromochloromethane, a by-product of water chlorination. The current null hypothesis states that this compound is probably metabolized by two distinct liver enzymes. Recent information about the
ability of CYP2E1's active to adapt to larger molecules opens the possibility to the idea that CYP2E1 alone could perform all metabolism. In short, the students will make use of different enzymatic models to determine which one describes the inhalation data optimally. The students involved in this project will make use of mathematics to test
different hypotheses using scientific principles, apply their mathematical background to a real world problem, and learn basic kinetics and biology in the process.
