Quasi-Monte Carlo Methods: Where Randomness and Determinism Collide

Name:    Prof. Michael Mascagni         
Address: Department of Computer Science and
         School of Computational Science
         Florida State University
         Tallahassee, FL  32306-4530  USA
Offices: 498 Dirac Science Library/172 Love Building
Phone:   +1.850.644.3290
FAX:     +1.850.644.0098
e-mail:  mascagni@fsu.edu

Title: Quasi-Monte Carlo Methods: Where Randomness and Determinism Collide

Abstract:

We will give a brief overview of Monte Carlo methods, methods for solving problems that involve the use of random numbers. Pseudorandom numbers are used in these simulations because they mimic the behavior of "real" random numbers. However, there are many Monte Carlo applications that do not really require randomness, but instead need numbers that uniformly cover the sample space. To meet these different requirements, quasirandom numbers have been developed. These are numbers that are very evenly distributed, but do not behave like truly random numbers. In fact, for certain problems one obtains deterministic, not probabilistic, bounds for Quasi-Monte Carlo methods. We present some of the fundamental results about this deterministic method to solve random number driven problems. We also describe some simple methods for quasirandom number generation and discuss open problems in the field.

This talk is more of a subject overview than a research presentation. Dr. Mascagni will be in need of a large number of graduate students for two projects that are about to start. These projects offer substantial opportunities to graduate students to find funded research opportunities working in a state-of-the-art computational environment that includes access to the latest high-performance computing hardware and software. The research topics that make up these projects include Monte Carlo methods, Quasi-Monte Carlo methods, pseudorandom number generation, quasirandom number generation, high-performance computing, parallel and distributed computing, interactive web design, web-enhanced collaboration, descriptive statistics, and tests of randomness. These projects will involve considerable collaborations with colleagues at Sandia, Lawrence Livermore, and Los Alamos National Laboratories as well as foreign colleagues in Salzburg, Austria and Sofia, Bulgaria. Graduate students will be encouraged to form their own collaborations with these groups and will be likewise encouraged to visit them to further these collaborations.