Dr. Michael Mascagni

Curriculum Vitae

Biographical Information

Name: Michael V. A. Mascagni

Birth Date: on request

Birthplace: Bologna, Italy with given name Michele V. A. Mascagni

Citizenship: United States of America, Repubblica Italiana

Postal Contact Information:

Electronic Contact Information:

Academic Degrees:

Ph.D., Mathematics, October, 1987

Courant Institute of Mathematical Sciences, New York University, New York, NY; Dissertation Title: Negative Feedback in Neural Networks; Prof. Charles Peskin, Major Professor

M.S., Mathematics, October 1984

Courant Institute of Mathematical Sciences, New York University

B.S., Mathematics, with Highest Distinction, December 1981

University of Iowa, Iowa City, IA; Minor in Biological Sciences (formerly Zoology)

B.S.E., Biomedical Engineering, with Highest Distinction, May 1981

University of Iowa, Iowa City, IA

Awards:

2008

Fulbright Senior Specialist Roster, Council for International Exchange of Scholars, Washington, DC

2001

Developing Scholar (Associate Professor Research) Award, Florida State University, Tallahassee, FL

1988-1989

National Academy of Sciences/National Research Council Postdoctoral Fellowship used at Mathematical Research Branch, N.I.D.D.K., National Institutes of Health, Bethesda, MD

Academic Positions:

Summer 2007

Visiting Professor: Université de Toulon et du Var, Institut des Sciences de l'Ingénieur de Toulon et du Var, Modélisation Numérique et Couplages, Toulon, France; Prof. Sylvain Maire, Sponsor

Wintersemester 2005-06 - Sommersemeter 2006

Gastprofessor, Seminar für Angewandte Mathematik, Departement Mathematik, Eidgenössische Technische Hochschule (ETH), Swiss Federal Institute of Technology, Zürich, Switzerland; Prof. Dr. Rolf Jeltsch, Seminar Head, Prof. Dr. Wesley Petersen, Academic Host

2002-Present

Professor, Department of Computer Science, Florida State University, Tallahassee, FL; Dr. David Whalley, Chair

Sommersemeter 2002

Gastprofessor, Institut für Scientific Computing, Universität Salzburg, Salzburg, Austria; Prof. Dr. Peter Zinterhof, Chair

2001-Present

Professor, Department of Chemical and Biomedical Engineering, Florida State University, Tallahassee, FL; Dr. Michael H. Peters, Chair (Courtesy)

1999-Present

Professor, Department of Mathematics, Florida State University, Tallahassee, FL; Dr. Phillip Bowers, Chair (Courtesy)

1999-Present

Faculty Affiliate, School of Computational Science, Florida State University, Tallahassee, FL; Dr. Max Gunzburger, Director

1999-2002

Associate Professor, Department of Computer Science, Florida State University, Tallahassee, FL; Dr. Ted Baker, Chair

1997-1999

Director, University of Southern Mississippi/Center of Higher Learning Naval Oceanographic Office/Programming Environment and Training Research Program, Stennis Space Center, MS; Dr. Peter Ranelli, Technical Director, Center of Higher Learning

1997-1999

Coordinator, Ph.D. Program in Scientific Computing and Associate Professor of Mathematics: University of Southern Mississippi, Hattiesburg, MS; Dr. Grayson Rayborn, Director, School of Mathematical Sciences

1997-1999

Associate Professor, Department of Mathematics, University of Southern Mississippi, Hattiesburg, MS; Dr. Wallace Pye, Chairman

May 1996

Visiting Professor: Dipartimento di Metodi e Modelli Matematici per le Scienze Applicate (DMMMSA), Università degli Studi di Padova, Padova, Italy; Prof. Renato Spigler, Sponsor

1994-1995

Adjunct Professor: Georgetown University Department of Computer Science, Washington, D.C.; Dr. Timothy Law Snyder, Chair

1987

Adjunct Professor: Dept. of Computer Science, Courant Institute of Mathematical Sciences, New York University, New York, NY

1981-1983

Graduate Fellow in Biophysics; The Rockefeller University, New York, NY; Dr. Robert Shapley, Advisor

Other Professional Positions:

1989-1996

Research Staff Member: Center for Computing Sciences (formerly Supercomputing Research Center), Institute for Defense Analyses, Bowie, MD; Dr. Francis Sullivan, Director

1987-1996

NIH-NRC Research Associate/Guest Worker: Mathematical Research Branch, NIDDK, National Institutes of Health, Bethesda, MD; Dr. John Rinzel, Advisor

1996

Visiting Researcher: National Institute of Standards and Technology, Gaithersburg, MD; Dr. Judy Devaney, Sponsor

Summer 1995

Visiting Scientist: Research Institute for Advanced Computer Science (RIACS), NASA Ames Research Center, Moffett Field, CA; Dr. Robert Schreiber, Sponsor

Summer 1984

Courant Institute/IBM Summer Student: Department of Mathematical Sciences, IBM T. J. Watson Research Center, Yorktown Heights, NY; Dr. Willard Miranker, Advisor

Summer 1983

Summer Student in Numerical Weather Prediction: NASA Goddard Space Flight Center, Greenbelt, MD; Dr. Eugenia Kalnay and Mr. Dean Duffy, Advisors

 

Professional Society Memberships:

 

Association of Computing Machinery (ACM)
International Association for Mathematics and Computers in Simulation (IMACS)

Society of Industrial and Applied Mathematics (SIAM)

Society of Industrial and Applied Mathematics, Supercomputing (SC) Activity Group

Society of Industrial and Applied Mathematics, Computational Science and Engineering (CSE) Activity Group
The Speedup Society, The Swiss Forum for Grid and High-Performance Computing

Honor Society Memberships:

Phi Beta Kappa (National Liberal Arts Honor Society), Iowa Alpha Chapter
Tau Beta Pi (National Engineering Honor Society), Iowa Beta Chapter

Other Honors:

2005-Present
          Member, Board of Directors, International Association for Mathematics and Computers in Simulation (IMACS)
2005-Present
          Member, Technical Committee on Monte Carlo Methods, International Association for Mathematics and Computers in Simulation (IMACS)
2004-Present
          Marquis Who's Who, Who's Who in Computational Science and Engineering
1999-Present
          Society of Industrial and Applied Mathematics (SIAM) Visiting Lecturer
1986-1987
          New York University, College of Arts and Science, New York, NY, Dean's Dissertation Fellowship
1983-1984
          New York University, Courant Institute of Mathematical Sciences, New York,  NY, Computational Fluid Dynamics Fellowship

Research and Creative Activity

Research Interests:

• Computational Science and Applications: Fast deterministic and stochastic numerical algorithms for computational materials science; computational biophysics; computational neuroscience; computational electrostatics; computational nanotechnology
• Computer Science: Parallel and distributed computing system software; commodity-off-the-shelf cluster computing; cryptography and computer security; computational number theory; derandomization of probabilistic algorithms; probabilistic algorithms for quantum computers
• Mathematical Biology: Numerical methods for neuronal modeling; reaction-diffusion equations; fast methods for branching nerve equations; particle methods; computational neuroscience; computational methods in biochemistry
• Monte Carlo Methods: Monte Carlo methods for partial differential equations; quasi-Monte Carlo methods for eigenproblems; first- and last-passage algorithms; applications to materials, biology, physics, and parallel computing
• Numerical Analysis: Deterministic particle and random gradient methods for reaction-diffusion equations; numerical integration; numerical linear algebra; graph partitioning; pseudo- and quasi random number generation
• Parallel/Distributed/Grid Computing: Scalable pseudorandom number generation; scalable quasirandom number generation; parallel Monte Carlo and quasi-Monte Carlo methods; methods for parallel domain decomposition; validation of volunteered computation; Grid-based infrastructures for Monte Carlo
• Random Number Generation: Splitting and parameterization methods for parallel computing; SIMD and MIMD parallel testing and implementation; ASCI-class random numbers; quasirandom number generation; fast scrambling techniques quasirandom numbers
• Software Engineering: Scalable libraries for pseudorandom number generation, numerical libraries; efficient and portable implementations; scalable libraries for quasirandom number generation; robust distributed/Grid infrastructure for Monte Carlo applications; validation of Grid computing

Refereed Chapters in Edited Volumes:

1. Y. Li and M. Mascagni (2006), "An Overview of Grid-Based Monte Carlo Computing," Grid Technologies, Emerging from Distributed Architectures to Virtual Organizations, WIT Press, ISBN: 978-1-84564-055-2, M. P. Bekakos, G. A. Gravvanis and H. R. Arabnia, editors, pp. 391-421.  This paper provides an overview of computational infrastructure for parallel, distributed, and Grid-based Monte Carlo computations.  The starting point is the Scalable Parallel Random Number Generators (SPRNG) Library, and its uses for parallel and distributed Monte Carlo, and the discussion continues with a description of our Grid-Computing Infrastructure for Monte Carlo Applications (GCIMCA), and an extension of this point-of-view to workflows.  The paper then continues with consideration of quasi-Monte Carlo and the differences that arise in computing in this manner on the Grid with quasirandom numbers.  The work concludes with a summary and many open problems.
2. C.-O. Hwang, J. A. Given, and M. Mascagni (2004), "First- and Last-Passage Algorithms for Diffusion Monte Carlo," New Vistas in Statistical Physics: Applications in Econophysics, Bioinformatics, and Pattern Recognition, L. T. Wille, editor, Springer Verlag: Berlin/New York, pp.  47-65.  This invited review paper summarizes first- and last-passage methods developed by our research group for solving problems in electrostatics, material science, and biochemistry.
3. C.-O. Hwang, M. Mascagni and N. A. Simonov (2003), Monte Carlo Methods for the Linearized Poisson-Boltzmann Equation, Advances in Numerical Analysis, Nova Science Publishers, Inc., Hauppauge, NY, 20 pages.  This paper reviews several methods for the solution of the linear Poisson-Boltzmann equation via Monte Carlo methods.  In addition, the effectiveness of the various methods are illustrated on several examples.  Finally, one of the methods is applied to a complex application where the solution is used in a biochemical setting.  The Poisson-Boltzmann equation is becoming more important in applications where biomolecules are studied in solution.
4. M. Mascagni (2003), "Random Number Generation," in CRC Standard Mathematical Tables and Formulae 31st Edition, D. Zwillinger, editor, Chapman and Hall/CRC, Boca Raton, pp. 644-649.  This invited chapter gives a review of the use of pseudorandom numbers to produce uniform real and integer variables and how to transform them into nonuniform distribution.  The volume where this chapter appears is a widely used reference for Mathematics and computational technique.
5. M. Mascagni (2003), "Deterministic Monte Carlo Methods and Parallelism," Sourcebook on Parallel Computing, J. Dongarra, I. Foster, F. Fox, W. Gropp, K. Kennedy, L. Torcson, and A. White, editors, Morgan Kaufman Publishers, San Francisco, pp. 249-258.  This invited review of parallel quasi-Monte Carlo methods provides an overview of the subject and some new results for single eigenvalue computations.  This work is part of the summary document to be produced by the NSF funded Center for Research in Parallel Computing.
6. A. Srinivasan, D. M. Ceperley, and M. Mascagni (1999), "Random Number Generators for Parallel Applications," in Monte Carlo Methods in Chemical Physics, D. M. Ferguson, J. I. Siepmann, and D. G. Truhlar, editors, Advances in Chemical Physics Series, Volume 105, John Wiley and Sons, New York, pp. 13-36.  This invited review presents an overview of parallel random number generation and the SPRNG library for the Monte Carlo community working in Physical Chemistry and Molecular Physics.
7. M. Mascagni (1999), "Serial and Parallel Random Number Generation," in Quantum Monte Carlo in Physics and Chemistry, P. Nightingale and C. Umrigar, editors, Springer-Verlag: New York, Berlin, pp. 277-288.  This invited review presents an overview of parallel random number generation and the SPRNG library for the Quantum Monte Carlo community.  This paper was presented at the NATO Advanced Study Institute on Quantum Monte Carlo Methods in Physics and Chemistry.
8. M. Mascagni (1997), "Some Methods of Parallel Pseudorandom Number Generation," in Algorithms for Parallel Processing, R. Schreiber, M. Heath and A. Ranade editors, Springer Verlag: New York, Berlin, pp. 277-288.  This invited review presents the discrete mathematics and number theory behind the use of parameterized pseudorandom number generators in parallel.  This paper was presented at the Institute for Mathematics and Its Applications during a special year in High Performance Computing Workshop on Algorithms for Parallel Processing.
9. M. Mascagni and A. Sherman (1996), "Numerical Methods for Neuronal Modeling," in Methods of Neuronal Modeling: From Ions to Networks, Second Edition, C. Koch and I. Segev editors, MIT Press: Cambridge, Massachusetts, pp. 569-606.  This invited review is a second edition update of the review done in 1989 that is listed below.
10. M. Mascagni (1996), "Parallel Wiener Integral Methods for Elliptic Boundary Value Problems: A Tale of Two Architectures," in Applications on Advanced Architecture Computers.  This invited chapter looks at SIMD and MIMD implementations of random walk based Monte Carlo algorithms for the solution of elliptic boundary value problems.
11. M. Mascagni (1996), "Random Number Generation," in CRC Standard Mathematical Tables and Formulae 30th Edition, D. Zwillinger, editor, pp. 593-598.  This invited chapter gives a review of the use of pseudorandom numbers to produce uniform real and integer variables and how to transform them into nonuniform distribution.  The volume where this chapter appears is a widely used reference for Mathematics and Computational technique.
12. M. Mascagni (1989), "Numerical Methods for Neuronal Modeling," in Methods of Neuronal Modeling: From to Networks to Ions, C. Koch and I. Segev editors, MIT Press: Cambridge, pp. 439-484.  This invited chapter reviews numerical methods for the solution of problems that arise in the quantitative simulation of the nervous system.  It presents finite-difference methods for the solution of ordinary and partial differential equations that arise, as well as methods for solving neural network type systems.  This chapter was based on material the author developed for the Methods in Computational Neuroscience course taught at the Marine Biological Laboratory for four summers.

Refereed International Journal Papers:

1. C.-O. Hwang, M. Mascagni and T. Won (2008), "Monte Carlo Methods for Computing the Capacitance of the Unit Cube: A Review,"  Mathematics and Computers in Simulation, 11 pages, in the press.  This paper reviews Monte Carlo methods for computing the capacitance of the unit cube to high accuracy.  Based on this, the walk-on-planes (WOB) and walk-on-the-boundary (WOB) methods are analyzed for their computational efficiency.  WOB is found to be superior and is subsequently used to provide a more accurate, and confirmatory, numerical result.
2. N. Simonov, M. Mascagni and M. O. Fenley (2007), "Monte Carlo Based Linear Poisson-Boltzmann Approach Makes Accurate Salt-Dependent Solvation Free Energy Predictions Possible," Journal of Chemical Physics, 127: 18505.  This paper uses Monte Carlo techniques developed by the authors to make computations of the solvation free energy over a wide range of salt concentrations.  The problems solved involve the implicit solvent model, Poisson-Boltzmann equation, and the results obtained agree with other computational results as well as experimental results.  In addition, these computations explicitly benefit from another advantage of using Monte Carlo in these computations, the ability to use a single simulation to compute the energies at all of the different salt concentrations.
3. Y. Li and M. Mascagni (2005), "Grid-based Quasi-Monte Carlo Applications," Monte Carlo Methods and Applications, 11: 39-55.  This paper presents preliminary results on extending the Grid-based Monte Carlo services to quasi-Monte Carlo.  Experiments using scrambled quasirandom numbers are also presented.
4. H. Chi, M. Mascagni, and T. Warnock (2005), "On the Scrambled Halton Sequence," Mathematics and Computers in Simulation, 70(1): 9-21.  This paper analyzes the two-dimensional correlations in the Halton sequence, and based on this analysis presents a new way to find an optimal scrambling (derandomization) of the Halton sequence.  The efficacy of this new scrambling is numerically demonstrated to be far superior to the unscrambled Halton sequence on a very difficult high-dimensional integral.  This paper is joint with Tony Warnock, a Halton student.
5. M. Mascagni and N. A. Simonov (2004), "Monte Carlo Methods for Calculating Some Physical Properties of Large Molecules," SIAM Journal on Scientific Computing, 26(1): 339-357.  This paper carefully presents a Monte Carlo algorithm for computing the solution of an internal Poisson and external linearized Poisson-Boltzmann problem for molecular geometries.  An analysis of the Monte Carlo estimators is given, as well as a detailed computational complexity analysis.  Finally, a simple problem involving two spherical molecules is solved with the methods described in the paper.
6. M. Mascagni and H. Chi (2004), "Parallel Linear Congruential Generators with Sophie-Germain Moduli," Parallel Computing, 30: 1217-1231.  This paper considers the use of Sophie-Germain primes, primes of the form m=2p+1 where p is also prime, for use in parameterized linear congruential generators.  It is shown that this choice minimizes initialization time, maximizes the number of streams for a given prime modulus, and provides fast generation when particular Sophie-Germain moduli are used.
7. A. Karaivanova, M. Mascagni and N. Simonov (2004), "Parallel Quasirandom Walks on the Boundary," Monte Carlo Methods and Applications, 10: 311-320.  This paper studies the us of quasirandom numbers in the solution problems using the "random walk on the boundary" Monte Carlo algorithm.  The analysis and numerical results show that a small but significant improvement in convergence rate is seen over traditional Monte Carlo on this algorithm.
8. M. Mascagni and H. Chi (2004), "On the Scrambled Halton Sequence," Monte Carlo Methods and Applications, 10: 435-442.  This paper analyzes the two-dimensional correlations in the Halton sequence, and based on this analysis presents a new way to find an optimal scrambling (derandomization) of the Halton sequence.  The efficacy of this new scrambling is numerically demonstrated to be far superior to the unscrambled Halton sequence on a very difficult high-dimensional integral.
9. Y. Li, M. Mascagni, R. van Engelen and Q. Cai (2004), "A Grid Workflow-Based Monte Carlo Simulation Environment," Neural Parallel and Scientific Computations, 12: 439-454.  This paper takes our previous work on grid services for Monte Carlo and views these services in a workflow setting.
10. N. A. Simonov and M. Mascagni (2004), "Random Walk Algorithms for Estimating Effective Properties of Digitized Porous Media," Monte Carlo Methods and Applications, 10: 599-608.  This paper describes a Monte Carlo method for permeability calculations in complex digitized porous structures.  The results of computational experiments for some random models of porous media confirm the log-normality hypothesis for the permeability distribution.
11. A. Rasulov, A. Karaivanova and M. Mascagni (2004), "Quasirandom in Branching Random Walks," Monte Carlo Methods and Applications, 10: 551-558.  This paper studies the effects of using quasirandom numbers in the generation of branching walks used to solved certain nonlinear boundary-value problems.  A slight improvement in convergence rate is seen.
12. M. Mascagni and N. A. Simonov (2004), "The Random Walk on the Boundary Method for Calculating Capacitance," Journal of Computational Physics, 195(2): 465-473. This paper describes the random walk on the boundary Monte Carlo method, and applies it to the calculation of the capacitance of the unit cube. This calculation is the most accurate known.
13. C.-O. Hwang and M. Mascagni (2004), "Electrical Capacitance of the Unit Cube," Journal of Applied Physics, 95(7): 3798-3802.  This paper presents a new computation of the capacitance of the unit cube using a first-passage variant based on walks on planes.  The computed results are consistent with our previous computations, and has a slightly smaller set of error bars.
14. M. Mascagni and A. Srinivasan (2004), "Parameterizing Parallel Multiplicative Lagged-Fibonacci Generators," Parallel Computing, 30: 899-916.  This paper shows how to parameterize full-period multiplicative lagged-Fibonacci generators via the seed, and then how to use this to produce a parallel version of the generator.  This generator is now used in the SPRNG library.
15. C.-O. Hwang and M. Mascagni (2003), "Analysis and Comparison of Green's Function First-Passage Algorithms with "Walk on Spheres" Algorithms," Mathematics and Computers in Simulation, 63: 605-613.  This paper shows that the Green's function first-passage (GFFP) algorithm is always more efficient that the "walk on spheres" algorithm for solving elliptic PDEs.  In addition, the complexity of GFFP is analyzed.
16. M. Mascagni and C.-O. Hwang (2003), "e-Shell Error Analysis of Walk on Spheres Algorithms," Mathematics and Computers in Simulation, 63: 605-613.  This paper provides analytic and empirical evidence that the error associated the the e-shell used in Walk on Spheres algorithms is linear in e.  This result motivates the preferential usage of the Green's function first-passage method over Walk on Spheres when both are applicable.
17. C.-O. Hwang, M. Mascagni and J. A. Given (2003), "A Feynman-Kac Path-Integral Implementation for Poisson's Equation Using an h-conditioned Green's Function," Mathematics and Computers in Simulation, 62: 347-355.  This paper presents a new random walk method for solving the Poisson equation using the Feynman-Kac formula using only a small number of points in a Brownian trajectory.
18. Y. Li and M. Mascagni (2003), "Analysis of Large-scale Grid-based Monte Carlo Applications,"  International Journal of High Performance Computing Applications (IJHPCA), 17(4): 369-382.  This paper provides an overview of the M-out-of-N technique for Grid-based Monte Carlo.  Also, methods for producing trustworthy Monte Carlo computations are presented.
19. A. Srinivasan, M. Mascagni, and D. Ceperley  (2003), "Testing Parallel Random Number Generators,"  Parallel Computing, 29: 69-94.  This paper provides a mathematical framework for testing parallel random number generators and also motivates the construction of the SPRNG test suite.  In addition, results from extensive parallel testing of multiplicative lagged-Fibonacci generators, candidates for SPRNG, are presented.
20. J. A. Given, C.-O. Hwang and M. Mascagni (2002), "First- and last-passage Monte Carlo algorithms for the charge density distribution on a conducting surface," Physical Review E, 66, 056704, 8 pages.  This paper presents two new Monte Carlo algorithms based on the concept of "last-passage" diffusion.  These methods are compared with each other and with the best first-passage algorithm for computing the charge density on a circular disk held at unit potential.
21. C.-O. Hwang, J. A. Given and M. Mascagni (2001), "The Simulation-Tabulation Method for Classical Diffusion Monte Carlo," Journal of Computational Physics, 174: 925-946.  This paper shows how simulated Green's functions, simulation-tabulation, can be used to augment our Green's function first-passage Monte Carlo method.  The utility of simulation-tabulation is verified by solving problems from materials science and biochemistry.
22. M. Mascagni, A. Karaivanova and Y. Li (2001), "A Quasi-Monte Carlo Method for Elliptic Partial Differential Equations," Monte Carlo Methods and Applications, 7: 283-294.  This paper presents new bounds on errors associated with the use of quasirandom numbers in Markov chain-based methods for the solution of elliptic partial differential equations.
23. C.-O. Hwang, M. Mascagni and J. A. Given (2001), "Rapid Diffusion Monte Carlo Algorithms for Fluid Dynamic Permeability," Monte Carlo Methods and Applications, 7: 213-222.  This paper uses our Green's function first-passage Monte Carlo method to compute the permeability of a wide class of porous media models considerably extending our previous results. 
24. C.-O. Hwang and  M. Mascagni (2001), "Efficient Modified Walk on Spheres Algorithm for the Linearized Poisson-Boltzmann Equation," Applied Physics Letters, 76: 787-789.  This paper presents an improved method for using the Feynman-Kac formula as the basis for a Monte Carlo algorithm to solve the linearized Poisson-Boltzmann equation.  This is accomplished with a new probability that is used to terminate random walks in the linearized Poisson-Boltzmann case.
25. M. Mascagni and A. Karaivanova (2000), "Matrix Computations Using Quasirandom Sequences,"  Springer Verlag Lecture Notes in Computer Science, 1988: 552-559.  This paper presents new methods and error bounds for using quasi-Monte Carlo methods for computing eigenvalues of large, sparse matrices.
26. M. Mascagni and A. Srinivasan (2000), "Algorithm 806: SPRNG: A Scalable Library for Pseudorandom Number Generation," ACM Transactions on Mathematical Software, 26: 436-461.  This paper describes the SPRNG library and gives an overview of the mathematical foundation for the random number generators in SPRNG, the computational techniques used in parallelization, the randomness testing suite in SPRNG, and shows how the library can be used to provide reliable and reproducible parallel Monte Carlo computations.  SPRNG is the first library of its kind.
27. C.-O. Hwang, J. A. Given and M. Mascagni (2000), "On the Rapid Calculation of Permeability for Porous Media Using Brownian Motion Paths," Physics of Fluids, 12: 1699-1709.  This paper derives our Green's function first-passage Monte Carlo method and applies it to the computation of the fluid permeability of porous media made up of overlapping and nonoverlapping monosized spheres.  This new method is the fastest method known for doing these kinds of calculations.
28. M. Mascagni (1998), "Parallel Linear Congruential Generators with Prime Moduli," Parallel Computing, 24: 923-936.  This paper derives a method for parameterizing primitive roots modulo a prime and uses this as the basis for providing parallel linear congruential random numbers.  In addition, an efficient algorithm for finding the ith integer relatively prime to given, factored, integer is presented.
29. M. Mascagni, M. L. Robinson, D. V. Pryor and S. A. Cuccaro (1995), "Parallel Pseudorandom Number Generation Using Additive Lagged-Fibonacci Recursions", Springer Verlag Lecture Notes in Statistics, 106: 263-277.  This paper proves bounds on exponential sum bounds used to estimate the cross-correlation between different random number streams produced using our parallelization of additive lagged-Fibonacci generators.
30. M. Mascagni, S. A. Cuccaro, D. V. Pryor and M. L. Robinson (1995), "A Fast, High Quality, and Reproducible Parallel Lagged-Fibonacci Pseudorandom Number Generator", Journal of Computational Physics, 119: 211-219.  This paper presents a novel parameterization of additive lagged-Fibonacci generators based on seeding.  This approach is used as the basis of providing a parallel version of this generator that requires no interprocessor communication while assuring that different processors get distinct random number streams.
31. A. Sherman and M. Mascagni (1994), "A Gradient Random Walk Method for Two-Dimensional Reaction-Diffusion Equations'', SIAM Journal on Scientific Computing, 15: 1280-1293.  This paper presents and analyzes a Monte Carlo method for solving two-dimensional reaction-diffusion equations.  The method is related to the random vortex method for the two-dimensional incompressible Navier-Stokes equations, and the paper also presents numerical evidence of it's effectiveness.
32. M. Mascagni (1991), "A Parallelizing Algorithm for Computing Solutions to Arbitrarily Branched Neuron Models," Journal of Neuroscience Methods, 36: 105-114.  This paper presents a parallel algorithm for solving coupled, branching, one-dimensional nonlinear reaction-diffusion equations based on finite-difference methods.  These kinds of equations arise in the realistic modeling of the nervous system.
33. M. Mascagni (1991), "High-Dimensional Numerical Integration and Massively Parallel Computing," Contemporary Mathematics, 115: 53-73.  This paper presents parallel data-parallel methods for doing deterministic and Monte Carlo high-dimensional numerical integration using parallel prefix methods.  In addition, data-parallel techniques for Monte Carlo solution of partial differential equations based on random walks is presented along with numerical examples performed on the CM-2 massively parallel computer.
34. M. Mascagni (1990), "The Backward Euler Method for Numerical Solution of the Hodgkin-Huxley Equations of Nerve Conduction," SIAM Journal on Numerical Analysis, 27: 941-962.  This method analyzed the convergence of the backward Euler method for the finite-difference solution of the Neumann initial-boundary value problem for the Hodgkin-Huxley equations of nerve conduction.  Convergence is proved with the help of derived a priori bounds for solutions to the nonlinear difference equations.
35. M. Mascagni (1990), "In Initial-Boundary Value Problem of Physiological Importance for Equations of Nerve Conduction," Communications on Pure and Applied Mathematics, 42: 213-227.  The paper proves well-posedness in the sense of Hadamard for the Neumann initial-boundary value problem for the Hodgkin-Huxley equations of nerve conduction.  In addition, a priori bounds on the solution of this nonlinear system of partial differential equations.
36. M. Mascagni (1989), "Animation's Role in Mathematically Modeling the Nervous System," Iris Universe, Winter 1989: 6-18.  This paper presents computational results obtained in the numerical modeling of a ring of Hodgkin-Huxley neurons with passive dendritic segments.  In particular, a presentation level visualization of the results is presented as well as a discussion of new visualization tools that allow rapid qualitative analysis of the large data sets produced in realistic neural modeling.
37. M. Mascagni and W. L. Miranker (1985), "Arithmetically Improved Algorithmic Performance," Computing, 35: 153-175.  This paper presents theoretical and numerical evidence that numerical algorithms sensitive to numerical accuracy can be significantly improved by using augmented floating-point arithmetic to exactly compute inner products.  This augmented arithmetic was implemented in hardware in IBM 370 series mainframe with the ACRITH product.
38. W. L. Miranker, M. Mascagni, and S. Rump (1985), "Case Studies for Augmented Floating-Point Arithmetic," Lecture Notes in Computer Science, 235: 86-118.  This paper provides numerical examples from poorly posed problems arising from finite-difference solutions of ordinary and partial differential equations, and numerical linear algebra to  motivate the use of augmented floating-point arithmetic to exactly compute inner products.

Invited International Publications:

1. M. Mascagni (1999), "Parallel Pseudorandom Number Generation," SIAM News, August, pp. 1,8-10.  This article provides a general presentation of the mathematical and computational underpinnings of parallel random number generation.  In particular, the problem of parallel reproducibility and the solution of parameterized random number generations id discussed.
2. M. Mascagni (1998), "High-Performance Monte Carlo Tools," IEEE Computational Science and Engineering, 5(2): 97-98.  This article summarizes the results of a workshop on High-Performance Monte Carlo Tools.
3. M. Mascagni (1990), "Parallel Wiener Integral Methods for Elliptic Boundary Value Problems: A Tale of Two Architectures," SIAM News, July, pp. 27-33.  This article looks at SIMD and MIMD implementations of random walk based Monte Carlo algorithms for the solution of elliptic boundary value problems.  It was reprinted as item 6 among the refereed book chapters, above.

Refereed International Conference Papers:

1. M. Mascagni and J. Ren (2008), "New Development in the Scalable Parallel Random Number Generator (SPRNG) Library," The Institute of Statistical Mathematics Cooperative Research Report, 210: 120-125.  The Scalable Parallel Random Number Generators (SPRNG) Library is a widely used software package for random number generation in high-performance computing settings.  In this paper, we provide an overview of SPRNG and especially discuss its recent developments. First, we give a very short review of random number generators and their applications to Monte Carlo computations. Then, we discuss some methods of parallel random number generation, and give the rationale for SPRNG. We next discuss about the past versions of SPRNG and the most recent version, version 4.0. Finally, webriefly discuss the impact of SPRNG and speculate on possible future work to SPRNG.
2. M. Mascagni (2008), "Random Number Generation : A Practitioner's Overview," The Institute of Statistical Mathematics Cooperative Research Report, 210: 97-119.  This gives a comprehensive overview of pseudorandom number generation, parallel pseudorandom number generation, and quasirandom number generation.  The presentation is motivated by an applications-based point-of-view.
3. Y. Li, M. Mascagni and A. Gorin (2007), "Decentralized Replica Exchange Parallel Tempering: An Efficient Implementation of Parallel Tempering Using MPI and SPRNG," Lecture Notes in Computer Science, 4707: 507-519.  This was a paper given at the international conference entitled Computational Science and Its Applications (ICCSA 2007) in Kuala Lumpur, Malaysia in August, 2007.  This paper discusses parallel Tempering (PT), also known as Replica Exchange, which is a powerful Markov Chain Monte Carlo sampling approach which aims at reducing the relaxation time in simulations of physical systems. In this paper, we present a novel implementation of PT, so-called decentralized replica exchange PT, using MPI and the Scalable Parallel Random Number Generators (SPRNG) libraries. By adjusting the replica exchange operations in the original PT algorithm, and taking advantage of the characteristics of pseudorandom number generators, this implementation minimizes the overhead caused by interprocessor communication in replica exchange in PT. This enables one to efficiently apply PT to large-scale massively parallel systems. The efficiency of this implementation has been demonstrated in the context of various benchmark energy functions, such as the high-dimensional Rosenbrock function, and a rugged funnel-like function.
4. H. Chi and M. Mascagni (2007), "Efficient Generation of Parallel Quasirandom Sequences via Scrambling," Lecture Notes in Computer Science, 4487: 723-730.  This was a paper given at the international conference entitled International Conference on Computational Science 2007 (ICCS 2007), held May 2007 in Beijing, People's Republic of China.  This paper proposes an alternative approach for generating parallel quasirandom sequences. We take a single quasirandom sequence and provide different random digit scramblings of the given sequence. The exact meaning of the digit scrambling we use depends on the mathematical details of the quasirandom number sequence's method of generation. For the Faure sequence we scramble by modifying the generator matrices in the definition. The obtained sequences are very interesting as the scrambled versions used in individual processes are of higher quality than the original Faure sequence. Thus, we not only obtain the expected near-perfect speedup of the naturally parallel Monte Carlo methods, but the errors in the parallel computation is even smaller than if the computation were done with the same quantity of quasirandom numbers using the original, unscrambled, Faure sequence.
5. N. A. Simonov and M. Mascagni (2005), "The Method of Random Walk on Sphere for Solving Boundary-Value problems for Molecular Electrostatics, Proceedings of the 17th IMACS World Congress, 5 pages published on compact disc, July, 2005.  This paper presents preliminary results for a new method for evaluating internal boundary conditions that arise in molecular electrostatics computations.  The methods were developed to work in concert with existing Monte Carlo methods for solving the entire PDE system, and are a significant improvement on a finite-difference based method previously developed.  Not only is performance enhanced by an order of magnitude, but a bias from the finite-difference based method is eliminated. 
6. Y. Li and M. Mascagni (2005), "A Bio-inspired Job Scheduling Algorithm for Monte Carlo Applications on a Computational Grid," Proceedings of the 17th IMACS World Congress, 7 pages published on compact disc, July, 2005.  In this paper we present a bio-inspired job scheduling mechanism that enables the adaptation of large-scale, naturally parallel and compute-intensive Monte Carlo tasks to clustered computational farms, such as large-scale computational grids, with heterogeneous and dynamic performance.  The kernel of this scheduling mechanism is a swarm intelligent algorithm, which is inspired from the ants’ behavior in a social insect colony.
7. C. Fleming, M. Mascagni and N. A. Simonov (2005), "An Efficient Monte Carlo Approach for Solving Linear Problems in Biomolecular Electrostatics," Proceedings of the Fifth International Conference on Computational Science (ICCS 2005), V. S. Sunderam, G. D. van Albada, P. M. A. Sloot, and  J. J. Dongarra (eds.), Lecture Notes in Computer Science, 3516: 760-765 (Part 3). (May 2005, Atlanta, GA)  This paper presents preliminary results for a new method for evaluating internal boundary conditions that arise in molecular electrostatics computations.  The methods were developed to work in concert with existing Monte Carlo methods for solving the entire PDE system, and are a significant improvement on a finite-difference based method previously developed.  Not only is performance enhanced by an order of magnitude, but a bias from the finite-difference based method is eliminated.
8. H. Chi, P. Beerli, D. W. Evans and M. Mascagni (2005), "On the Scrambled Soboĺ Sequence," Proceedings of the Fifth International Conference on Computational Science (ICCS 2005), V. S. Sunderam, G. D. van Albada, P. M. A. Sloot, and  J. J. Dongarra (eds.), Lecture Notes in Computer Science, 3516: 775-782 (Part 3). (May 2005, Atlanta, GA  This paper presents an optimal linear scrambling of the Soboĺ sequence with techniques similar to those previously developed by Chi and Mascagni for the Faure and Halton sequences.  This sequences is shown to be of good quality in comparison to others based on the evaluation of a high-dimensional geometrical Asian option.
9. N. A. Simonov and M. Mascagni (2004), "Random Walk Algorithms for Estimating Electrostatic Properties of Large Molecules," Proceedings of The International Conference on Computational Mathematics (ICCM-2004), Novosibirsk, Russia, G. A. Mikhailov, V. P. Il'in, and Y. M. Laevsky, eds., ICM&G Publisher, Novosibirsk, Russia, Part I: 352-358.  This paper describes a new Monte Carlo algorithm for solving the coupled Poisson/Poisson-Boltzmann system related to the electrostatics of large molecules in a continuum model of solvent.
10. M. Mascagni, A. Karaivanova, C.-O. Hwang (2004), "Quasi-Monte Carlo Methods for Elliptic  Boundary Value Problems," Proceedings of Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing (MCQMC) 2002, H. Niederreiter (ed.), Springer Verlag: Berlin, pp. 345-356.  This paper gives a brief overview of quasi-Monte Carlo methods for solving elliptic boundary value problems using walk-on-spheres variants.
11. Y. Li and M. Mascagni (2004), "E-Science Workflow on the Grid," Proceedings of the International Association for the Development of the Information Society (IADIS) International Conference: e-Society 2004, P. Isaías, P. Komers, M. McPherson (eds.),  pp. 1041-1046.  This paper describes how one can use workflow techniques to implement e-science-based grid computations.  Specifically, it describes how one maps agent operations from workflow onto grid services using XML as the communications intermediary.
12. Y. Li and M. Mascagni (2004), "E-Science on the Grid: Toward a Dynamic E-Science Automation with XML and Workflow Techniques," accepted to the Proceedings of the 8th World Multiconference on Systemics, Cybernetics and Informatics (SCI 2004), Orlando, Florida, 7 pages.  This paper describes how one can use workflow techniques to implement e-science-based grid computations.  Specifically, it describes how one maps agent operations from workflow onto grid services using XML as the communications intermediary.
13. M. Mascagni and H. Chi (2004), "Optimal Quasi-Monte Carlo Valuation of Derivative Securities," Computational Finance and Its Applications, M. Costantino and C. A. Brebbia (eds.), WIT Press, pp. 177-185.  This paper finds an optimal scrambling of the Faure sequence within the i-binomial family.  Then, this derandomized generalized Faure (GFaure) sequence is used to evaluate a high-dimensional derivative security, an European call option on the geometric mean of several assets.  The numerical results show improvement over the plain Faure sequence.
14. M. Mascagni and Y. Li (2004), "Computational Infrastructure for Parallel, Distributed, and Grid-based Monte Carlo Computations," Proceedings of the Fourth International Conference on Large-Scale Scientific Computations (LSSC'03), Sozopol, Bulgaria, I. Lirkov, S. Margenov, J. Wasniewski, P. Yalamov eds., Lecture Notes in Computer Sciences, 2907: 39-52.  This paper provides an overview of computational infrastructure for parallel, distributed, and Grid-based Monte Carlo computations.  The starting point is the Scalable Parallel Random Number Generators (SPRNG) Library, and its uses for parallel and distributed Monte Carlo, and the discussion ends with a description of our Grid-Computing Infrastructure for Monte Carlo Applications (GCIMCA).
15. A. Karaivanova, M. Mascagni and N. Simonov (2004), "Solving Boundary Value Problems Using Quasirandom Walks on the Boundary," Proceedings of the Fourth International Conference on Large-Scale Scientific Computations (LSSC'03), Sozopol, Bulgaria, I. Lirkov, S. Margenov, J. Wasniewski, P. Yalamov eds., Lecture Notes in Computer Sciences, 2907: 162-169.  This paper studies the us of quasirandom numbers in the solution problems using the "random walk on the boundary" Monte Carlo algorithm.  The analysis and numerical results show that a small but significant improvement in convergence rate is seen over traditional Monte Carlo on this algorithm.
16. A. Karaivanova and M. Mascagni (2003), "Quasi-Monte Carlo Methods for Some Problems in Linear Algebra," Proceedings of the 7th Joint Conference on Information Sciences (JCIS 2003), pp. 1754-1757.  This paper presents Monte Carlo and quasi-Monte Carlo methods for the solution of various problems in numerical linear algebra.  The paper begins with an analysis of matrix-vector products, then solutions via Neumann series, and finally the eigenvalue problems including stochastic versions of the power method and the resolvent method.
17. M. Mascagni and A. Karaivanova (2002), "A Monte Carlo Approach for Finding More Than One Eigenpair," Proceedings of Fifth International Conference on Numerical Methods and Applications, I. Dimov, L. Lirkov, S. Margenov, and Z. Zlatev (eds.),  Lecture Notes in Computer Science, 2542: 123-131.  This paper extends previous results on Monte Carlo methods for spectral linear algebra calculations.
18. Y. Li, M. Mascagni and R. van Engelen (2003), "GCIMCA: A Globus and SPRNG Implementation of a Grid-Computing Infrastructure for Monte Carlo Applications," accepted to the The 2003 International Conference on Parallel and Distributed Processing Techniques and Applications, (PDPTA'03), Las Vegas, Nevada,  5 pages.  Taking advantage of the grid facilities of the Globus toolkit and the large-scale random number streams generated by the SPRNG library, this paper discusses the implementation of GCIMCA, the Grid-Computing Infrastructure for Monte Carlo Applications, to provide services for high-performance and trustworthy grid-based Monte Carlo computations.
19. M. Mascagni and N. A. Simonov (2003), "Monte Carlo Methods for Calculating the Electrostatic Energy of a Molecule," Proceedings of the 2003 International Conference on Computational Science (ICCS 2003), P. M. A. Sloot, D. Abramson, A. V. Bogdanov, J. J. Dongarra, A. Y. Zomaya, and Y. E. Gorbachev (eds.), Lecture Notes in Computer Science, 2330: 598-608 (Part 2). (June 2003, Melbourne, Australia and Saint Petersburg, Russia)  This paper presents a new Monte Carlo algorithm for computing an electrostatic form of the internal energy of a large protein molecule.  The algorithm is also analyzed.
20. Y. Li and M. Mascagni (2003), "Improving Performance via Computational Replication on a Large-Scale Computational Grid," Proceedings of the IEEE/ACM International Symposium on Cluster Computing and the Grid (IEEE/ACM CCGRID2003), pp. 442-448.  This paper describes and analyze the computational replication method to improve performance of a generic application on a computational grid.  The computational replication method is extended to an N-out-of-M schedule technique to improve the wall clock time of Grid-based Monte Carlo computations.
21. Y. Li, M. Mascagni and M. H. Peters (2003), "Grid-based Nonequilibrium Multiple-Time Scale Molecular Dynamics/Brownian Dynamics Simulations of Ligand-Receptor Interactions in Structured Protein Systems," Proceedings of the First International Workshop on Biomedical Computations on the Grid (BioGrid'03) in Proceedings of the IEEE/ACM International Symposium on Cluster Computing and the Grid (IEEE/ACM CCGRID2003), pp. 568-573.  This paper describes the application of our Grid-based Monte Carlo technology to problems in protein biophysics.
22. M. Mascagni and N. A. Simonov (2002), "Random Walk Algorithms on The Boundary Methods for Computing Reaction Rate and Capacitance," Proceedings of the The International Conference on Computational Mathematics, G. A. Mikhailov, V. P. Il'in, Y. M. Laevsky (eds.), ICM & MG Publishers, Novosibirsk, Russia, pp. 238-242.  This paper presents "walk on the boundary" methods for solving some boundary-value problems formulated as integral equations.  Specifically, it deals with computing the capacitance of a convex object and diffusion-limited reaction rates.
23. Y. Li and M. Mascagni (2002), "Grid-based Monte Carlo Application," Proceedings of Grid Computing-GRID 2002, Manish Parashar (ed.), Lecture Notes in Computer Science, 2536: 13-24.  This paper examines the suitability of Monte Carlo applications for the grid.  In addition, the M-out-of-N strategy is examined to speed Grid Monte Carlo computations in a faulty environment and in using the random number generator to provide the ability to validate a volunteered Monte Carlo computation.
24. M. Mascagni and A. Karaivanova (2002), "A Parallel Quasi-Monte Carlo Method for Solving Systems of Linear Equations,"  Proceedings of the 2002 International Conference on Computational Science, Peter M. A. Sloot, C. J. Kenneth Tan, Jack J. Dongarra, Alfons G. Hoekstra (eds.), Lecture Notes in Computer Science, 2330: 598-608 (Part 2).  (April 2002, Amsterdam, Netherlands)  This paper presents and analyzes a quasi-Monte Carlo approach to solving systems of linear systems.  In addition, the parallel efficiency of this method is shown to be extremely good and consistent with the ordinary Monte Carlo approach to this problem.
25. A. Srinivasan and M. Mascagni (2002), "Monte Carlo Techniques for Estimating the Fiedler Vector in Graph Applications," Proceedings of the 2002 International Conference on Computational Science (ICCS 2002), Peter M.A. Sloot, C. J. Kenneth Tan, Jack J. Dongarra, Alfons G. Hoekstra (eds.), Lecture Notes in Computer Science, 2330: 635-645 (Part 2).   (April 2002, Amsterdam, Netherlands)  This paper shows how to use Monte Carlo techniques, based on Markov chains and the probabilistic computations of matrix-vector products, to estimate the Fiedler vector.  This problem has significance in graph partitioning problems related to domain decomposition.
26. M. Mascagni and A. Karaivanova (2001), "A Parallel Quasi-Monte Carlo Method for Computing Extremal Eigenvalues," Proceedings of Monte Carlo and Quasi-Monte Carlo Methods 2000, K.-T. Fang, H. F. J. Hickernell, and H. Niederreiter, eds., Springer-Verlag: Berlin: pp. 369-380.  (December 2000, Honk Kong, China)  This paper provides an error bound for the use of quasi-Monte Carlo methods for computing extremal eigenvalues of sparse matrices via methods related to the power method.  In addition, it is shown that the parallel efficiency expected of Monte Carlo methods extends to these Markov chain-based quasi-Monte Carlo methods.
27. J. A. Given, C.-O. Hwang and M. Mascagni (2001), "Continuous Path Brownian Trajectories for Diffusion Monte Carlo Via First- and Last-Passage Distributions," Proceedings of the Third International Conference on Large-Scale Scientific Computations, 12 pages, in press. (June 2001, Sozopol, Bulgaria)  This paper presents an overview of the application of the Green's function first-passage and simulation tabulation methods to problems arising in porous media, composite materials, and biochemistry.
28. C.-O. Hwang, J. A. Given, and M. Mascagni (2001), "A Feynman-Kac Path-Integral Implementation for Poisson's Equation," in the Proceedings of the 2001 International Conference on Computational Science, part I, pp. 1282-1288. (May 2001, San Francisco, CA)  This paper presents a new method to evaluate path integrals arising from the Feynman-Kac solution of the Poisson equation when only first-passage information is known about the path trajectories.  This has applications for the use of the Green's function first-passage method for Poisson's equation.
29. M. Mascagni (2000), "Theory and Software for Parallel Random Number Generation," Proceedings of The Fourth International Conference on Supercomputing in Nuclear Applications (SNA 2000), CD-ROM: 14 pages. (September 2000, Tokyo, Japan). This paper presents an overview of parallel random number generation aimed at the Nuclear Engineering community.  Mathematical background and the use of SPRNG is presented.
30. M. Zhou and M. Mascagni (2000), "The Cycle Server: A Web Platform for Running Parallel Monte Carlo Applications on a Heterogeneous Condor Pool of Workstations," Proceedings of the 2000 International Conference on Parallel Processing Workshops on Scalable Web Services, pp. 111-118. (August 2000, Toronto, Canada)  This paper presents a distributed computing tool that permits users to submit and retrieve parallel Monte Carlo jobs to a Condor cluster.  Most importantly, this tool provides a distributed compilation service that, given application source, produces executables for many different operating system/architecture combinations.
31. M. Mascagni and S. Rahimi (2000), "Parallel Inversive Congruential Generators:  Software and Field-Programmable Gate Array Implementations," in Proceedings of the International Conference on Monte Carlo Simulation, G. I. Schuëller and P. D. Spanos, eds., pp. 35-40. (June 2000, Monte Carlo, Monaco)  This paper presents a hardware design for modular integer inversion and implements and benchmarks the design on a field-programmable gate array device.  This problem is motivated by the desire to accelerate the generation of inversive congruential pseudorandom numbers.
32. A. Karaivanova and M. Mascagni (2000), "Are Quasirandom Numbers Good for Anything Besides Integration?"  Proceedings of Advances in Reactor Physics and Mathematics and Computation into the Next Millennium (PHYSOR2000),  CD-ROM: 15 pages. (May 2000, Pittsburgh, PA)  This paper presents quasi-Monte Carlo methods for Markov-chain based problems arising from numerical linear algebra.  It contrasts these applications of quasirandom numbers to the more classical application of numerical integration.
33. M. Mascagni (1999), "SPRNG: A Scalable Library for Pseudorandom Number Generation,"  in Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, CD-ROM: 10 pages.  (March 1999, San Antonio, TX)  This paper presents an overview of parallel pseudorandom number generation via parameterization and discuss particulars of the SPRNG library.
34. M. Hydari, D. M. Ceperley, A. Srinivasan, and M. Mascagni (1999), "A Fast High-Quality Pseudo Random Number Library for Java," in Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, CD-ROM: 17 pages. (March 1999, San Antonio, TX)  This paper presents a Java extension to the SPRNG library.
35. M. Mascagni (1999), "SPRNG: A Scalable Library for Pseudorandom Number Generation," Recent Advances in Numerical Methods and Applications II,  O. Iliev, B. Sendov, M. Kaschiev, S. Margenov, P. Vassilevski, editors, World Scientific, pp. 284-295. (August 1998, Sofia, Bulgaria)  This paper presents an overview of parallel pseudorandom number generation via parameterization and discuss particulars of the SPRNG library.
36. J.-L. Larriba-Pey, M. Mascagni, A. Jorba and J. J. Navarro (1995), "An Analysis of the Parallel Computation of Arbitrarily Branched Cable Neuron Models'', in Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, pp. 373-378. (March 1995, San Francisco, CA)  This paper provides an analysis of parallel finite-difference methods for solving nerve equations based on new results for parallel tridiagonal linear system solvers.
37. S. A. Cuccaro, M. Mascagni and D. V. Pryor (1995) "Techniques for Testing the Quality of Parallel Pseudorandom Number Generators'', Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, pp. 279-284. (March 1995, San Francisco, CA)  This paper presents a mathematical framework for the testing of parallel random number generators based on the parallel modification of serials tests and on the use of exponential sum tests.
38. D. V. Pryor, S. A. Cuccaro, M. Mascagni and M. L. Robinson (1994) "Implementation and Usage of a Portable and Reproducible Parallel Pseudorandom Number Generator'', Proceedings of Supercomputing '94, pp. 311-319. (November 1994, Washington, D.C.)  This paper discusses the parallel computational aspects that permit the dynamic spawning of distinct parallel random number generators without the need for interprocessor communication.  The method utilizes parameterized generators mapped to the binary tree and the manipulations that are simplified with this mapping.
39. M. Mascagni, S. A. Cuccaro, D. V. Pryor and M. L. Robinson (1993) "Recent Developments in Parallel Pseudorandom Number Generation'', Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, pp. 524-529. (March 1993, Norfolk, VA)  This paper presents results on the parameterization of additive lagged-Fibonacci generators for use in parallel.

International Conference Proceedings Edited:

1. D. H. Bailey, P. E. Bjørstad, J. R. Gilbert, M. V. Mascagni, R. S. Schreiber, H. D. Simon, V. J. Torczon and L. T. Watson, editors (1995) Proceedings of the Seventh SIAM Conference on Parallel Processing for Scientific Computing, SIAM, Philadelphia.

National Conference Papers:

1. M. Zhou and M. Mascagni (1999), "Parallel Monte Carlo in a Distributed Environment: SPRNG and CONDOR," in Proceedings of the First Southern Symposium on Computing, CD-ROM: 5 pages. (December, 1998, Hattiesburg, MS)  This paper briefly reviews a distributed computing tool that permits users to submit and retrieve parallel Monte Carlo jobs to a Condor cluster.  Most importantly, this tool provides a distributed compilation service that, given application source, produces executables for many different operating system/architecture combinations.
2. C.-O. Hwang, J. A. Given and M. Mascagni (1999), "A New Fluid Permeability Estimation,"  in Proceedings of the First Southern Symposium on Computing, CD-ROM: 7 pages. (December, 1998, Hattiesburg, MS)  This paper briefly presents Green's function first-passage Monte Carlo method to compute the permeability of porous media models and provides preliminary numerical results.  

Preprints:

1. Y. Li, M. Mascagni and A. Gorin (2008), "A Decentralized Parallel Implementation for Parallel Tempering Algorithm," submitted to Parallel Computing in March, 2008.  This paper discusses parallel Tempering (PT), also known as Replica Exchange, which is a powerful Markov Chain Monte Carlo sampling approach which aims at reducing the relaxation time in simulations of physical systems. In this paper, we present a novel implementation of PT, so-called decentralized replica exchange PT, using MPI and the Scalable Parallel Random Number Generators (SPRNG) libraries. By adjusting the replica exchange operations in the original PT algorithm, and taking advantage of the characteristics of pseudorandom number generators, this implementation minimizes the overhead caused by interprocessor communication in replica exchange in PT. This enables one to efficiently apply PT to large-scale massively parallel systems. The efficiency of this implementation has been demonstrated in the context of various benchmark energy functions.
2. Y. Li, W. Mirugi and M. Mascagni (2005), "Test the Rule 30 Cellular Automata Random Number Generator," submitted for publication in Mathematics and Computers in Simulation, 8 pages.  This paper looks at the "Rule 30" cellular automata as a random number generator.  This cellular automata was first proposed as a random number generator by Wolfram, and is still used in Mathematica.  Empirical tests showed the generator similar in quality to other common generators, but overall it is unsuitable as the generation time is 1000 times slower.
3. A. Rasulov, G. Raimova and M. Mascagni (2005), "Quasirandom Sequences in Branching Random Walks," submitted for publication in Mathematics and Computers in Simulation, 9 pages.  This paper presents strong numerical evidence that using quasirandom number in the generation of uniform directions, as part of a Markov chain-based algorithm for solving partial differential equations is very effective.
4. N. Simonov and M. Mascagni (2005), "Random Walk Algorithms for Solving Some Boundary-Value Problems in Biomolecular Electrostatics," submitted for publication in Mathematics and Computers in Simulation, 14 pages.  This paper presents new results based on using a tangent plane approximation to remove a negative term that arose in an integral equation-based method for enforcing certain boundary conditions.  These boundary conditions are part of an electrostatics system involving molecular geometry and the Poisson and Poisson-Boltzmann equations.
5. H. Chi, R. Jones, and M. Mascagni (2005), "Generating Parameterized Parallel Random Number Streams via LCGs with Differing Moduli," submitted for publication in Mathematics and Computers in Simulation, 12 pages.  This paper presents a new parameterization of linear congruential generators (LGCs) of the kind already used in the SPRNG library.  Using spectral test methods based on combined LCGs, we create a new criterion to assess the parallel quality of LCGs which have different moduli.  The approach is explained, justified theoretically, and a small numerical example is carried out.
6. A. Rasulov, G. Raimova and M. Mascagni (2005), "Monte Carlo Solution of Some Nonlinear Parabolic Initial-Value Problems," submitted for publication in Mathematics and Computers in Simulation, 9 pages.  This paper presents a Markov chain-based algorithm for solving the pure initial-value problem for a class of nonlinear parabolic equations.  The nonlinearity is dealt with with a branching Markov chain, and numerical results are presented as further evidence of efficacy.
7. Y. Li and M. Mascagni (2005), "Optimizing Dynamic Grid-based Resources for Large-Scale Monte Carlo Applications," submitted for publication in Mathematics and Computers in Simulation, 14 pages.  In this paper we present a novel, bio-inspired method for optimizing the organization of dynamic computational resources on a Grid for carrying out large-scale Monte Carlo applications. The kernel of the scheduling mechanism is a swarm intelligence algorithm.  We tested the algorithm on a simulated computational Grid and compared it with static scheduling algorithms. Our results showed good performance, adaptability, and robustness on a dynamic computational Grid with respect to its competitors. 
8. B. Bouta, A. Srinivasan and M. Mascagni (2005), "Exploring Monte Carlo Linear Solver Splittings: A Load-Balancing Example," submitted for publication in Mathematics and Computers in Simulation, 18 pages.  This paper presents new Monte Carlo methods for solving linear systems are studied within the context of the load-balancing problem.  In our take on his problem, the graph Laplacian matrix provides the linear system.  We then study this system with three stat, ionary iterative methods that are used as the basis for providing Monte Carlo methods.  This work represents new results based on using more advantageous splittings to improve the performance of Monte Carlo methods in Linear Algebra.
9. H. Chi and M. Mascagni (2003), "Scrambled Quasirandom Sequences and Their Application," submitted for publication in SIAM Review, 41 pages.  This paper is a review of the state-of-the-art in methods of scrambling quasirandom numbers.  In addition, applications of quasirandom sequences are discussed including automatic error estimation for quasi-Monte Carlo and parallel quasirandom number generation.  Also, the topics of randomized quasirandom numbers and the derandomization of quasirandom numbers is reviewed.
10. E. I. Atanassov and M. Mascagni (2003), "Efficient Generation of Low-discrepancy Sequences," submitted to Journal of Complexity, 18 pages.  This paper presents algorithms and source code examples for the efficient generation of scrambled Halton and Sobol' quasirandom numbers on modern microprocessor architectures.
11. C.-O. Hwang, M. Mascagni and J. A. Given (2001), "A Feynman-Kac Formula Implementation for the Linearized Poisson-Boltzmann Equation," submitted for publication in Mathematics and Computers in Simulation, 10 pages.  This paper presents a new random walk method for solving the linear Poisson-Boltzmann equation and proves mathematically (not implementationally) the same as a previously published method of the authors.

Reports:

1. M. H. Zhou, M. Mascagni, and A. Y. Qiao (1998), "Explicit Finite Difference Schemes for the Advection Equation," Conservation Law Preprint 1998-024.  This report presents a new explicit finite-difference method for solving the advection equation.
2. M. Mascagni (1997), "Polynomial versus Matrix Methods for Leap-Ahead in Shift Register Type Pseudorandom Number Generators," Institute for Mathematics and its Applications (IMA) Reprint 1469.  This paper shows that fast leap-ahead methods applicable to shift-register pseudorandom number generators can be extended to additive lagged-Fibonacci generators.
3. M. Mascagni (1995), "A Deterministic Particle Method for One-Dimensional Reaction-Diffusion Equations'', Research Institute for Advanced Computer Science (RIACS) Technical Report: 95.23, Institute for Defense Analyses Center for Computing Sciences (IDA/CCS) Technical Report: CCS-TR-95-144.  This paper derives a one-dimensional particle method for the solution of nonlinear reaction-diffusion equations.  This method is a level-set analog of Monte Carlo methods previously studied by the author.  Numerical evidence is presented on the efficacy of the method, and error analysis and proof is provided.
4. M. Mascagni and S. A. Cuccaro (1992), "A Comparison of Modular Multiplication Across Parallel Supercomputing Architectures," Institute for Defense Analyses Supercomputing Research Center Technical Report: SRC-TR-92-116.  This paper compares the speed of integer modular multiplication modulo a Mersenne prime across supercomputing and special purpose computing systems.  This paper was classified after initial publication, and is no longer publicly available.

Abstracts:

1. J. Tabak, M. Mascagni and R. Bertram (2007), "Spontaneous Episodic Activity: Why Episode Duration is Correlated with the Length of the Preceding but not Following Interval," Society for Neuroscience Abstracts, 33: 925.7.  This abstract presents results on using a simple stochastic model to replace a homogeneous integrate-and-fire network of excitatory neurons.  The results are based on correlation between of episode duration with the previous but not the following inter-episode interval.  The leads to a diagnostic for synaptic depression versus cellular adaptation.
2. M. Mascagni (1987), "Computer Simulation of Negative Feedback in Neurons," Society for Neuroscience Abstracts, 13: 375.4.  This abstract presents results on the use of a Hodgkin-Huxley axon/dendrite model to study the effect of negative feedback on repetitive firing behavior of neurons.  It is empirically shown that negative feedback increases the input sensitivity of the repetitive firing response.