Summer Institute 2007
Carnegie Mellon University
May 31 - July 17
Projects:
- Green Oxidation
Participants: Tarek Elgindi (University of Wisconsin)
Project description:
- Understand how a system of ODEs can arise in green chemistry oxidation processes
- Investigate existence of exact solution by looking at some special cases
- If no exact solution can be found, analyse its numerical properties
- Try to predict correct values for rate constants from the equations
- Analyze phase space behaviour, identify any possible limit cycles and try to see what implications that can have for the chemical problem
Current plan: pdf
Progress report: pdf
- Voronoi
Participants: Morgan Shaffer (Mount Holoyoke College), Michelle Baker (Shippensburg University)
Project description:
- Understand Newton's method and its use in accelerating numerical methods.
- Study the concept of
centroidal Voronoi tessellations (CVTs) and its use in physical and engineering applications, such as data compression and segmentation.
- Develop the set of routines for accelerating data analysis by coupling Lloyd algorithm with Newton, explore possible shortcomings and alternatives.
Current plan:pdf
Progress report: pdf
- Random walks: finance applications
Participants: Jian Wang (UT Knoxville), Keith Rogers (Alabama State)
Project description:
- Review binomial options pricing
- Study the principles of discrete time finance focusing on European calls and random trees
- Develop understanding of the Brownian motion representation for a random walk and the use Black-Scholes equation in modeling option pricing
- Taking a model problem, formulate and analyze corresponding Black-Scholes equation
- Develop numerical techniques for solving the derived PDEs
Current plan:pdf
Progress report: pdf
- PageRank
Participants: Alexander Chun (Northwestern University)
Project description:
- Understand the math behind Google's million-dollar worth search engine.
- Study the relationship between the structure of the network and convergence of the numerical algorithms as well as their well-posedness.
- Investigate possible ways to compute dominant eigenvalues and their advantages and drawbacks.
- Taking as an example some model large matrix representation of the internet, develop a set of routines for computing page rank using existing methods such as power method and Gaussian elimination, as well as their possible modifications.
- Compare the results of the test and try to answer some of the open questions.
Current plan: pdf
Progress report: pdf