Refereed Chapters in Edited Volumes:

1. C.-O. Hwang, M. Mascagni and N. A. Simonov (2003), "Monte Carlo Methods for the Linearized Poisson-Boltzmann Equation," to appear in 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.
2. 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.
3. 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.
4. C.-O. Hwang, J. A. Given, and M. Mascagni (2002), "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, 22 pages, in press.  This invited review paper summarizes first- and last-passage methods developed by our research group for solving problems in electrostatics, material science, and biochemistry.
5. 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.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. 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. M. Mascagni and N. A. Simonov (2003), " The Random Walk on the Boundary Method for Calculating Capacitance," to appear in Journal of Computational Physics, 15 pages. 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.
2. C.-O. Hwang and M. Mascagni (2003), " Analysis and Comparison of Green's Function First-Passage Algorithms with "Walk on Spheres" Algorithms," to appear in Mathematics and Computers in Simulation, 14 pages.  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.
3. 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.
4. M. Mascagni and C.-O. Hwang (2003), "e-Shell Error Analysis of Walk on Spheres Algorithms," accepted for publication in Mathematics and Computers in Simulation, 16 pages.  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.
5. Y. Li and M. Mascagni (2003), "Analysis of Large-scale Grid-based Monte Carlo Applications," accepted for a special issue of the International Journal of High Performance Computing Applications (IJHPCA).  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.
6. 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.
7. C.-O. Hwang, M. Mascagni and J. A. Given (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.
8. 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.
9. 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.
10. 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. 
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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
19. 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.
20. 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.
21. 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.
22. 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.
23. 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.
24. 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.
25. 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. 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.
2. 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 Application, to provide services for high-performance and trustworthy grid-based Monte Carlo computations.
3. 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.
4. Y. Li and M. Mascagni (2003), "Improving Performance via Computational Replication on a Large-Scale Computational Grid," accepted to the IEEE/ACM International Symposium on Cluster Computing and the Grid (IEEE/ACM CCGRID2003), Tokyo, 2003, 6 pages.  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.
5. 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," accepted to the First International Workshop on Biomedical Computations on the Grid (BioGrid'03), Tokyo, 2003.  This paper describes the application of our Grid-based Monte Carlo technology to problems in protein biophysics.
6. 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.
7. 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.
8. 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.
9. 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: 12 pages, in press.  (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.
10. 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.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. 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.
17. 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.
18. 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.
19. 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.
20. 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.
21. 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.
22. 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. C.-O. Hwang and M. Mascagni (2003), "Electrical Capacitance of the Unit Cube," submitted for publication in Journal of Applied Physics, 15 pages.  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.
2.  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.
3. M. Mascagni and H. Chi (2003), "Parallel Linear Congruential Generators with Sophie-Germain Moduli," submitted for publication in Parallel Computing, 17 pages.  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.
4. A. Karaivanova and M. Mascagni (2003), "Quasi-Monte Carlo Methods for Some Linear Algebra Problems.  Complexity and Convergence,"  submitted the Journal of Complexity, 16 pages.  This paper reviews several Monte Carlo and quasi-Monte Carlo methods for solving linear systems, matrix inversion, and finding a small number of eigenvalues.  In addition, we consider the complexity of these methods, and provide this information in a timely review.
5. M. Mascagni and N. A. Simonov (2003), "Monte Carlo Methods for Calculating Some Physical Properties of Large Molecules," submitted to the SIAM Journal on Scientific Computing, 16 pages.  This paper describes new Monte Carlo methods for computing the reaction rate in Solc-Stockmayer systems.  In addition, new Monte Carlo methods for computing the electrostatic free energy of a molecule surrounded by a dielectric solvent is treated.
6. E. I Atanassov and M. Mascagni (2003), "Efficient Generation of Low-discrepancy Sequences," submitted the 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.
7. M. Mascagni and N. A. Simonov (2002), "The Random Walk on the Boundary Method for Calculating Capacitance," submitted for publication in the Journal of Computational Physics, 13 pages. 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.
8. M. Mascagni and A. Karaivanova (2002), "A Monte Carlo Approach for Finding More Than One Eigenpair," submitted for publication in the Proceedings of Fifth International Conference on Numerical Methods and Applications, 8 pages.  This paper extends previous results on Monte Carlo methods for spectral linear algebra calculations.
9. M. Mascagni and A. Srinivasan (2002), "Parameterizing Parallel Multiplicative Lagged-Fibonacci Generators," submitted for publication in Parallel Computing, 14 pages.  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.
10. C.-O. Hwang and M. Mascagni (2002), "Analysis and Comparison of Green's Function First-Passage Algorithms with "Walk on Spheres" Algorithms," submitted for publication in Mathematics and Computers in Simulation, 14 pages.  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.
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. 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. 

Software:

1. M. Mascagni, A. Srinivasan, D. M. Ceperley, and F. Saied (1995), "Scalable Parallel Random Number Generators (SPRNG) Library."  This package has become the standard for parallel and distributed random number generation and was originally developed under DARPA Contract Number DABT63-95-C-0123 for ITO: Scalable Systems and Software, entitled A Scalable Pseudorandom Number Generation Library for Parallel Monte Carlo Computations at the University of Illinois at Champaign Urbana's National Center for Supercomputing Applications, the Institute for Defense Analyses' Center for Computing Sciences, and the University of Southern Mississippi's Doctoral Program in Scientific Computing.