Dr. Michael
Mascagni 
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postscript version of paper when available)
Refereed Chapters in Edited Volumes:
 C.O. Hwang, M. Mascagni and N. A. Simonov
(2003), "Monte Carlo Methods for the
Linearized PoissonBoltzmann 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
PoissonBoltzmann 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 PoissonBoltzmann
equation is becoming more important in applications where biomolecules are
studied in solution.
 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. 644649. 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.
 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. 249258. This invited review of
parallel quasiMonte 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.
 C.O. Hwang, J. A. Given, and M. Mascagni (2002), "First and LastPassage
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
lastpassage methods developed by our research group for solving problems in
electrostatics, material science, and biochemistry.
 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. 1336. 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.
 M. Mascagni (1999), "Serial and Parallel Random
Number Generation," in Quantum Monte Carlo in Physics and Chemistry, P.
Nightingale and C. Umrigar, editors, SpringerVerlag: New York, Berlin, pp.
277288. 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.
 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. 277288. 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.
 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. 569606. This invited review is a second
edition update of the review done in 1989 that is listed below.
 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.
 M. Mascagni (1996), "Random Number Generation,"
in CRC Standard Mathematical Tables and Formulae 30th Edition, D.
Zwillinger, editor, pp. 593598. 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.
 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.
439484. This invited chapter reviews numerical methods for the solution
of problems that arise in the quantitative simulation of the nervous
system. It presents finitedifference 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:
 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.
 C.O. Hwang and M. Mascagni (2003), " Analysis and Comparison of Green's
Function FirstPassage Algorithms with "Walk on Spheres" Algorithms,"
to appear in Mathematics and Computers in Simulation,
14 pages. This paper shows that the Green's function firstpassage (GFFP)
algorithm is always more efficient that the "walk on spheres"
algorithm for solving elliptic PDEs. In addition, the complexity of
GFFP is analyzed.
 C.O. Hwang, M. Mascagni and J. A. Given (2003),
"A FeynmanKac
PathIntegral Implementation for Poisson's Equation Using an hconditioned
Green's Function," Mathematics and Computers in Simulation, 62:
347355. This paper presents a new random walk method for solving the
Poisson equation using the FeynmanKac formula using only a small number of
points in a Brownian trajectory.
 M. Mascagni and C.O. Hwang (2003), "eShell
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
eshell used in Walk on Spheres algorithms is
linear in e. This result motivates the
preferential usage of the Green's function firstpassage method over Walk
on Spheres when both are applicable.
 Y. Li and M. Mascagni (2003), "Analysis of Largescale Gridbased 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 MoutofN technique for Gridbased
Monte Carlo. Also, methods for producing trustworthy Monte Carlo
computations are presented.
 A. Srinivasan, M. Mascagni, and D. Ceperley (2003),
"Testing
Parallel Random Number Generators," Parallel Computing,
29: 6994. 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 laggedFibonacci generators, candidates for SPRNG,
are presented.
 C.O. Hwang, M. Mascagni and J. A. Given (2002),
"First and lastpassage
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
"lastpassage" diffusion. These methods are compared with each other and
with the best firstpassage algorithm for computing the charge density on a
circular disk held at unit potential.
 C.O. Hwang, J. A. Given, and M. Mascagni (2001),
"The SimulationTabulation Method for Classical Diffusion Monte Carlo," Journal
of Computational Physics, 174: 925946. This
paper shows how simulated Green's functions, simulationtabulation, can be
used to augment our Green's function firstpassage Monte Carlo method.
The utility of simulationtabulation is verified by solving problems from
materials science and biochemistry.
 M. Mascagni, A. Karaivanova, and Y. Li (2001),
"A QuasiMonte Carlo Method for Elliptic Partial Differential Equations,"
Monte Carlo Methods and Applications, 7: 283294. This
paper presents new bounds on errors associated with the use of quasirandom
numbers in Markov chainbased methods for the solution of elliptic partial
differential equations.
 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:
213222. This paper uses our Green's function firstpassage Monte
Carlo method to compute the permeability of a wide class of porous media
models considerably extending our previous results.
 C.O. Hwang and M. Mascagni (2001),
"Efficient Modified Walk on Spheres Algorithm for the Linearized
PoissonBoltzmann Equation," Applied Physics Letters, 76:
787789. This paper presents an improved method for using the
FeynmanKac formula as the basis for a Monte Carlo algorithm to solve the
linearized PoissonBoltzmann equation. This is accomplished with a new
probability that is used to terminate random walks in the linearized
PoissonBoltzmann case.
 M. Mascagni and A. Karaivanova (2000), "Matrix Computations Using
Quasirandom Sequences," Springer Verlag
Lecture Notes in Computer Science, 1988: 552559. This paper
presents new methods and error bounds for using quasiMonte Carlo methods for
computing eigenvalues of large, sparse matrices.
 M. Mascagni and A. Srinivasan (2000),
"Algorithm 806: SPRNG: A Scalable Library for Pseudorandom Number Generation,"
ACM Transactions on Mathematical Software, 26: 436461.
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.
 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: 16991709. This paper derives our Green's function firstpassage 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.
 M. Mascagni (1998),
"Parallel Linear Congruential Generators with Prime Moduli," Parallel Computing,
24: 923936. 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.
 M. Mascagni, M. L. Robinson, D. V. Pryor and S.
A. Cuccaro (1995), "Parallel Pseudorandom Number Generation Using Additive
LaggedFibonacci Recursions'', Springer Verlag Lecture Notes in
Statistics, 106: 263277. This paper proves bounds on
exponential sum bounds used to estimate the crosscorrelation between
different random number streams produced using our parallelization of additive
laggedFibonacci generators.
 M. Mascagni, S. A. Cuccaro, D. V. Pryor and M.
L. Robinson (1995), "A Fast, High Quality, and Reproducible Parallel
LaggedFibonacci Pseudorandom Number Generator'', Journal of Computational
Physics, 119: 211219. This paper presents a novel
parameterization of additive laggedFibonacci 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.
 A. Sherman and M. Mascagni (1994),
"A Gradient
Random Walk Method for TwoDimensional ReactionDiffusion Equations'', SIAM
Journal on Scientific Computing, 15: 12801293. This paper
presents and analyzes a Monte Carlo method for solving twodimensional
reactiondiffusion equations. The method is related to the random vortex
method for the twodimensional incompressible NavierStokes equations, and the
paper also presents numerical evidence of it's
 M. Mascagni (1991),
"A Parallelizing Algorithm
for Computing Solutions to Arbitrarily Branched Neuron Models," Journal of
Neuroscience Methods, 36: 105114. This paper presents a
parallel algorithm for solving coupled, branching, onedimensional nonlinear
reactiondiffusion equations based on finitedifference methods. These
kinds of equations arise in the realistic modeling of the nervous
system.
 M. Mascagni (1991),
"HighDimensional Numerical
Integration and Massively Parallel Computing,"
Contemporary Mathematics, 115: 5373. This paper presents parallel
dataparallel methods for doing deterministic and Monte Carlo highdimensional
numerical integration using parallel prefix methods. In addition,
dataparallel techniques for Monte Carlo solution of partial differential
equations based on random walks is presented along with numerical examples
performed on the CM2 massively parallel computer.
 M. Mascagni (1990),
"The Backward Euler Method
for Numerical Solution of the HodgkinHuxley Equations of Nerve Conduction,"
SIAM Journal on Numerical Analysis, 27: 941962. This
method analyzed the convergence of the backward Euler method for the
finitedifference solution of the Neumann initialboundary value problem for
the HodgkinHuxley equations of nerve conduction. Convergence is proved
with the help of derived a priori bounds for solutions to the nonlinear
difference equations.
 M. Mascagni (1990),
"In InitialBoundary Value
Problem of Physiological Importance for Equations of Nerve Conduction," Communications on Pure and Applied Mathematics, 42:
213227. The paper proves well posedness in the sense of Hadamard for
the Neumann initialboundary value problem for the HodgkinHuxley equations of
nerve conduction. In addition, a priori bounds on the solution of
this nonlinear system of partial differential equations.
 M. Mascagni (1989),
"Animation's Role in Mathematically Modeling the Nervous System," Iris Universe,
Winter
1989: 618. This paper presents computational results obtained in
the numerical modeling of a ring of HodgkinHuxley 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.
 M. Mascagni and W. L. Miranker (1985),
"Arithmetically Improved Algorithmic Performance," Computing,
35: 153175. This paper presents theoretical and numerical
evidence that numerical algorithms sensitive to numerical accuracy can be
significantly improved by using augmented floatingpoint arithmetic to exactly
compute inner products. This augmented arithmetic was implemented in
hardware in IBM 370 series mainframe with the ACRITH product.
 W. L. Miranker, M. Mascagni, and S. Rump
(1985), "Case Studies for Augmented FloatingPoint Arithmetic," Lecture
Notes in Computer Science, 235: 86118. This paper provides
numerical examples from poorly posed problems arising from finitedifference
solutions of ordinary and partial differential equations, and numerical linear
algebra to motivate the use of augmented floatingpoint arithmetic to
exactly compute inner products.
Invited International Publications:
 M. Mascagni (1999), "Parallel Pseudorandom Number Generation," SIAM
News, August, pp. 1,810. 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.
 M. Mascagni (1998), "HighPerformance Monte Carlo Tools," IEEE
Computational Science and Engineering, 5(2): 9798. This
article summarizes the results of a workshop on HighPerformance Monte
Carlo Tools.
 M. Mascagni (1990), "Parallel Wiener Integral
Methods for Elliptic Boundary Value Problems: A Tale of Two Architectures,"
SIAM News, July, pp. 2733. 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:
 A. Karaivanova and M. Mascagni (2003), "
"QuasiMonte Carlo Methods for
Some Problems in Linear Algebra"," Proceedings of the 7th Joint
Conference on Information Sciences (JCIS 2003), pp. 17541757.
This paper presents Monte Carlo and quasiMonte Carlo methods for the solution
of various problems in numerical linear algebra. The paper begins with an
analysis of matrixvector products, then solutions via Neumann series,
and finally the eigenvalue problems including stochastic versions of the power
method and the resolvent method.
 Y. Li, M. Mascagni and R. van Engelen (2003),
"GCIMCA: A Globus and SPRNG
Implementation of a GridComputing 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 largescale random number
streams generated by the SPRNG library, this paper discusses the
implementation of GCIMCA, the GridComputing Infrastructure for Monte Carlo
Application, to provide services for highperformance and trustworthy
gridbased Monte Carlo computations.
 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:
598608 (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.
 Y. Li and M. Mascagni (2003), "Improving Performance via Computational
Replication on a LargeScale 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 NoutofM schedule technique to improve the wall
clock time of Gridbased Monte Carlo computations.
 Y. Li, M. Mascagni and M. H. Peters (2003),
"Gridbased Nonequilibrium
MultipleTime Scale Molecular Dynamics/Brownian Dynamics Simulations of
LigandReceptor 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 Gridbased Monte Carlo technology to problems in protein biophysics.
 Y. Li and M. Mascagni (2002), "Gridbased Monte Carlo Application,"
Proceedings of Grid ComputingGRID 2002, Manish Parashar (ed.),
Lecture Notes in Computer Science, 2536: 1324. This paper
examines the suitability of Monte Carlo applications for the grid. In
addition, the MoutofN 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.
 M. Mascagni and A. Karaivanova (2002), "A Parallel QuasiMonte 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: 598608 (Part
2). (April 2002, Amsterdam, Netherlands) This paper
presents and analyzes a quasiMonte 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.
 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: 635645 (Part 2).
(April 2002, Amsterdam, Netherlands) This paper shows how to
use Monte Carlo techniques, based on Markov chains and the probabilistic
computations of matrixvector products, to estimate the Fiedler vector.
This problem has significance in graph partitioning problems related to domain
decomposition.
 M. Mascagni and A. Karaivanova (2001), "A Parallel QuasiMonte Carlo
Method for Computing Extremal Eigenvalues," Proceedings of Monte Carlo and
QuasiMonte Carlo Methods 2000, K.T. Fang, H. F. J. Hickernell, and H.
Niederreiter, eds., SpringerVerlag: Berlin: 12 pages, in press.
(December 2000, Honk Kong, China) This paper provides an error bound for
the use of quasiMonte 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 chainbased quasiMonte Carlo methods.
 J. A. Given, C.O. Hwang and M. Mascagni (2001), "Continuous Path Brownian
Trajectories for Diffusion Monte Carlo Via First and LastPassage
Distributions," Proceedings of the Third International Conference on
LargeScale Scientific Computations, 12 pages, in press. (June
2001, Sozopol, Bulgaria) This paper presents an overview of the
application of the Green's function firstpassage and simulation tabulation
methods to problems arising in porous media, composite materials, and
biochemistry.
 C.O. Hwang, J. A. Given, and M. Mascagni (2001), "A FeynmanKac
PathIntegral Implementation for Poisson's Equation," in the Proceedings of
the 2001 International Conference on Computational Science, part I, pp.
12821288. (May 2001, San Francisco, CA) This paper presents a new
method to evaluate path integrals arising from the FeynmanKac solution of the
Poisson equation when only firstpassage information is known about the path
trajectories. This has applications for the use of the Green's function
firstpassage method for Poisson's equation.
 M. Mascagni (2000), "Theory and Software for Parallel Random Number
Generation," Proceedings of The Fourth International Conference on
Supercomputing in Nuclear Applications (SNA 2000), CDROM: 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.
 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. 111118. (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.
 M. Mascagni and S. Rahimi (2000), "Parallel Inversive Congruential
Generators: Software and FieldProgrammable Gate Array Implementations,"
in Proceedings of the International Conference on Monte Carlo Simulation,
G. I. Schuëller and P. D. Spanos, eds. pp. 3540. (June 2000, Monte Carlo,
Monaco) This paper presents a hardware design for modular integer
inversion and implements and benchmarks the design on a fieldprogrammable
gate array device. This problem is motivated by the desire to accelerate
the generation of inversive congruential pseudorandom numbers.
 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), CDROM: 15 pages. (May 2000, Pittsburgh, PA)
This paper presents quasiMonte Carlo methods for Markovchain based problems
arising from numerical linear algebra. It contrasts these applications
of quasirandom numbers to the more classical application of numerical
integration.
 M. Mascagni (1999), "SPRNG: A Scalable Library for Pseudorandom Number
Generation," in Proceedings of the Ninth SIAM Conference on Parallel
Processing for Scientific Computing, CDROM: 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.
 M. Hydari, D. M. Ceperley, A. Srinivasan, and M. Mascagni (1999),
"A Fast
HighQuality Pseudo Random Number Library for Java," in Proceedings of the
Ninth SIAM Conference on Parallel Processing for Scientific Computing,
CDROM: 17 pages. (March 1999, San Antonio, TX) This paper
presents a Java extension to the SPRNG library.
 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. 284295. (August 1998, Sofia, Bulgaria) This paper
presents an overview of parallel pseudorandom number generation via
parameterization and discuss particulars of the SPRNG library.
 J.L. LarribaPey, 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. 373378.
(March 1995, San Francisco, CA) This paper provides an analysis of
parallel finitedifference methods for solving nerve equations based on new
results for parallel tridiagonal linear system solvers.
 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. 279284. (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.
 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. 311319. (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.
 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. 524529. (March 1993, Norfolk,
VA) This paper presents results on the parameterization of additive
laggedFibonacci generators for use in parallel.
International Conference Proceedings Edited:
 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:
 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, CDROM: 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.
 C.O. Hwang, J. A. Given and M. Mascagni (1999), "A New Fluid Permeability
Estimation," in Proceedings of the First Southern Symposium on
Computing, CDROM: 7 pages. (December, 1998, Hattiesburg, MS) This
paper briefly presents Green's function firstpassage Monte Carlo method to
compute the permeability of porous media models and provides preliminary
numerical results.
Preprints:
 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 firstpassage variant based on walks on planes. The
computed results are consistent with our previous computations, and has a
slightly smaller set of error bars.
 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 stateoftheart in methods of scrambling
quasirandom numbers. In addition, applications of quasirandom sequences
are discussed including automatic error estimation for quasiMonte Carlo and
parallel quasirandom number generation. Also, the topics of randomized
quasirandom numbers and the derandomization of quasirandom numbers is reviewed.
 M. Mascagni and H. Chi (2003), "Parallel Linear Congruential Generators
with SophieGermain 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
SophieGermain moduli are used.
 A. Karaivanova and M. Mascagni (2003), "QuasiMonte Carlo Methods for Some
Linear Algebra Problems. Complexity and Convergence," submitted
the Journal of Complexity, 16 pages. This paper reviews several
Monte Carlo and quasiMonte 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.
 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 SolcStockmayer
systems. In addition, new Monte Carlo methods for computing the
electrostatic free energy of a molecule surrounded by a dielectric solvent is
treated.
 E. I Atanassov and M. Mascagni (2003), "Efficient Generation of
Lowdiscrepancy 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.
 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.
 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.
 M. Mascagni and A. Srinivasan (2002), "Parameterizing Parallel
Multiplicative LaggedFibonacci Generators," submitted for publication in
Parallel Computing, 14 pages. This paper shows how to
parameterize fullperiod multiplicative laggedFibonacci 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.
 C.O. Hwang and M. Mascagni (2002), "Analysis and Comparison of Green's
Function FirstPassage 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 firstpassage
(GFFP) algorithm is always more efficient that the "walk on spheres" algorithm
for solving elliptic PDEs. In addition, the complexity of GFFP is
analyzed.
 C.O. Hwang, M. Mascagni and J. A. Given (2001), "A FeynmanKac Formula
Implementation for the Linearized PoissonBoltzmann Equation," submitted for
publication in Mathematics and Computers in Simulation, 10 pages.
This paper presents a new random walk method for solving the linear
PoissonBoltzmann equation and proves mathematically (not implementationally)
the same as a previously published method of the authors.
Reports:
 M. H. Zhou, M. Mascagni, and A. Y. Qiao (1998), "Explicit Finite
Difference Schemes for the Advection Equation," Conservation Law Preprint
1998024. This report presents a new explicit finitedifference method
for solving the advection equation.
 M. Mascagni (1997), "Polynomial versus Matrix Methods for LeapAhead in
Shift Register Type Pseudorandom Number Generators," Institute for Mathematics
and its Applications (IMA) Reprint 1469. This paper shows that fast
leapahead methods applicable to shiftregister pseudorandom number generators
can be extended to additive laggedFibonacci generators.
 M. Mascagni (1995), "A Deterministic Particle
Method for OneDimensional ReactionDiffusion Equations'', Research Institute
for Advanced Computer Science (RIACS) Technical Report: 95.23, Institute for
Defense Analyses Center for Computing Sciences (IDA/CCS) Technical Report:
CCSTR95144. This paper derives a onedimensional particle method for
the solution of nonlinear reactiondiffusion equations. This method is a
levelset 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.
 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: SRCTR92116. 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:
 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 HodgkinHuxley 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:
 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 DABT6395C0123 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.
