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Abstract: |
Electrostatic forces and the electrostatic properties of molecules in solution are among the most important issues in understanding the structure and function of large biomolecules. The use of implicit-solvent models, such as the Poisson-Boltzmann equation (PBE), have been used with great success as a way of computationally deriving electrostatics properties such molecules. We discuss how to solve an elliptic system of partial differential equations (PDEs) involving the Poisson and the PBEs using path-integral based probabilistic, Feynman-Kac, representations. This leads to a Monte Carlo method for the solution of this system which is specified with a stochastic process, and a score function. We use several techniques to simplify the Monte Carlo method and the stochastic process used in the simulation, such as the walk-on-spheres (WOS) algorithm, and an auxiliary sphere technique to handle internal boundary conditions. We then specify some optimizations using the error (bias) and variance to balance the CPU time. We show that our approach is as accurate as widely used deterministic codes, but has many desirable properties that these methods do not. In addition, the currently optimized codes consume comparable CPU times to the widely used deterministic codes. Thus, we have an very clear example where a Monte Carlo calculation of a low-dimensional PDE is as fast or faster than deterministic techniques at similar accuracy levels. |
| Affiliation: |
Michael Mascagni was born in Bologna, Italy of one American and one Italian parent. However, by the age of four he was in the US confusing his Lake Forest, Illinois kindergarten teacher (and American grandmother) by correctly answering her Italian. This confusion continued though High School in Clinton, Iowa and College at the University of Iowa. At Iowa, he obtained a B.S.E. in Biomedical Engineering, and a B.S. in Mathematics and was a member of Phi Beta Kappa and Tau Beta Pi, the top liberal arts and engineering academic honor societies.
After graduation, he seriously considered going to Medical School, and declined two such offers to instead study Neurobiology at the Rockefeller University, which is located on the East River the middle of Manhattan. Since "the Rock" is such a small and specialized University, he also took graduate classes uptown, at Columbia University, and downtown, at the Courant Institute of Mathematical Sciences of New York University. Eventually, downtown trumped midtown and uptown, and Mathematics trumped Neurobiology, and he obtained his M.S. and Ph.D. in Mathematics from Courant. Perhaps more importantly, his social contacts at "the Rock" introduced him to his future wife, Becky Fandrei, at a party during an historic snow storm in New York. They were married between the Masters and Doctoral degrees.
Upon graduation, he obtained a post-doctoral research position in the Mathematical Research Branch of an institute of the National Institutes of Health, in Bethesda, MD and they moved to Washington, DC. It was during this period his research moved away from modeling the nervous system to studying the high-performance computing implications of the algorithms he developed and used. He was one of the first to use random number-based algorithms on the massively parallel Connection Machine at the Naval Research Lab in DC. In fact, after two years at NIH he moved to the Institute for Defense Analyses' Supercomputing Research Center in Bowie, MD. This organization works for the National Security Agency, and it was here that his interests in parallel computing, random number generation, number theory, and discrete mathematics were nurtured. During his time at SRC his oldest sons Alexander and Marcus were born.
After many happy years at SRC, he decided to rejoin academia, and went to the University of Southern Mississippi to run the Graduate Program in Scientific Computing. After a few years there, a desire to join a Computer Science department arose, and he moved to Florida State University as an Associate Professor of Computer Science, he has since been promoted to Full Professor. While at FSU his youngest son, Evan, was born,
Dr. Mascagni is on the editorial board of three journals in his field, and is a member of the ACM (Association of Computing Machinery), SIAM (Society of Applied Mathematics), and IMACS (International Association of Mathematics and Computers in Simulation). He is also a member of the Board of Directors of IMACS. He has approximately 100 refereed technical papers that have appeared in a wide variety of publications in areas including Applied Mathematics, Computer Science, Simulation Science, Monte Carlo Methods, Computational Science, High-Performance Computing, Scientific Computing, Computational Physics, and Computational Neuroscience. He has been a visiting professor at the University of Padova in Italy, the University of Salzburg in Austria, and the Swiss Federal Technical Institute-Zürich in Switzerland, and is a consultant to industry and government. He has made technical presentations in 18 countries and in most of the 50 U.S. states.
At present Dr. Mascagni's research group consists of post-doctoral associates, graduate students, and undergraduate workers. The areas they work on are parallel and distributed computing, Grid computing, random number generation, Monte Carlo methods, computational number theory and discrete algorithms, and applications to materials science, biochemistry, electrostatics, and finance.
His hobbies include swimming and biking, which arise from his misspent youth at NYU where he commuted by bicycle and swam each day, and playing the violin. In fact, he has been the concertmaster of the Big Bend Community Orchestra in Tallahassee, has played with several orchestras in places like Washington, DC and Salzburg, Austria. By the way, he is always looking for others to play chamber music. |
