% --------------------------------------------------------------------------
%
% BIBLIOGRAPHY FOR ADJOINTS AND IMPORTANCE
% Part 1: Background Material
%
% Compiled by Per H. Christensen
% per.christensen (at) acm.org
%
% March 9, 2004
%
% This annotated bibliography contains references to mathematics texts on
% adjoints in general and articles and books about the use of importance
% in nuclear physics (where it is an adjoint of neutron density). The
% entries are sorted chronologically within each category.
%
% Many thanks to Philippe Bekaert who pointed out some of these references.
%
% Note that importance is also known as "visual importance", "potential",
% "visual potential", "value", or "potential value".
%
% I have been unable to find and read a few of the references; those are
% marked with "(*)".
%
% --------------------------------------------------------------------------
%
% MATHEMATICS
%
@BOOK{OED89,
editor = "J. A. Simpson and Edmund S. Weiner",
title = "The Oxford English Dictionary",
edition = "2nd",
publisher = "Oxford University Press",
year = 1989,
keywords = {mathematics, adjoints},
comments = "Adjoint equation. Lagrange used the term équation adjointe.
In 1889, T. Craig wrote in Treat. Linear Differential Equations:
`When Chapter I was written ... I had not seen Forsyth's memoir,
and had not been able to find an adopted English term for
Lagrange's équation adjointé, so I used the word adjunct,
suggested by the German adjungirte, and not unlike the French
adjointe. It seems better now, however, to employ the word
associate, or, when speaking simply of Lagrange's équation
adjointé, the word adjoint.'"
}
% Full name is Erik Ivar Fredholm, but he skipped Erik in his papers
@ARTICLE{Fredholm03,
author = "Ivar Fredholm",
title = "Sur une classe d'\'equations fonctionelles",
journal = "Acta Mathematica",
volume = 27,
pages = "365--390",
month = Mar,
year = 1903,
keywords = {mathematics, integral equations, adjoints},
comments = "On page 384, Fredholm uses adjoint equations and operators
(although he didn't use those terms) to study the solvability
of 2nd kind Fredholm equations."
}
@BOOK{Hammersley64,
author = "John M. Hammersley and David C. Handscomb",
title = "Monte Carlo Methods",
publisher = "Methuen \& Co.",
year = 1964,
keywords = {mathematics, Monte Carlo, adjoints},
comments = "Excellent introduction to Monte Carlo methods.
Chapter 7 is about the solution of linear operator equations.
It presents adjoint/dual systems and Haltons sequential
Monte Carlo method for linear systems."
}
@BOOK{Ermakow75,
author = "S. M. Ermakow",
title = "Die Monte-Carlo-Methode und verwandte Fragen",
publisher = "Deutscher Verlag der Wissenschaften",
year = 1975,
keywords = {mathematics, Monte Carlo, adjoints},
comments = "Description of Monte Carlo methods and adjoint equations."
}
@BOOK{Rubinstein81,
author = "Reuven Y. Rubinstein",
title = "Simulation and the Monte Carlo method",
publisher = "John Wiley \& Sons",
year = 1981,
keywords = {mathematics, Monte Carlo, Markov chains, integral equations,
adjoints},
comments = "Chapter 5 talks about adjoints and integral equations.
Does not talk about importance."
}
@BOOK{Colton83,
author = "David Colton and Rainer Kress",
title = "Integral Equation Methods in Scattering Theory",
publisher = "John Wiley \& Sons",
year = 1983,
keywords = {mathematics, nuclear physics, integral equations, adjoints},
comments = "Section 1.3 talks about adjoint operators and Fredholms
use of them."
}
@BOOK{Lang84,
author = "Serge Lang",
title = "Algebra",
publisher = "Addison-Wesley",
year = 1984,
edition = "2nd",
keywords = {mathematics, operators, adjoints},
comments = "Proves that an adjoint operator is unique."
}
@BOOK{Delves85,
author = "L. M. Delves and J. L. Mohamed",
title = "Computational Methods for Integral Equations",
publisher = "Cambridge University Press",
year = 1985,
keywords = {mathematics, integral equations, adjoints, quadrature},
comments = "Very thorough textbook on many types of integral equations.
Talks about adjoint operators and equations in chapter 3.
Does not talk about importance."
}
@BOOK{Kress89,
author = "Rainer Kress",
title = "Linear Integral Equations",
publisher = "Springer-Verlag",
year = 1989,
keywords = {mathematics, integral equations, adjoints, quadrature},
comments = "Thorough book on many types of integral equations.
Chapter 4 describes Fredholm theory and adjoints.
According to this book, [Fredholm03] used adjoint equations
in order to study the solvability of 2nd kind Fredholm
equations. Does not talk about importance."
}
@BOOK{Mikhailov92,
author = "Gennadii A. Mikhailov",
title = "Optimization of Weighted Monte Carlo Methods",
publisher = "Springer-Verlag",
year = 1992,
keywords = {mathematics, Monte Carlo, adjoints, importance,
integral equations, splitting, Russian roulette},
comments = "Section 1.3 and chapters 2 and 3 discuss the use of the
adjoint solution for importance sampling."
}
%
% NUCLEAR PHYSICS
%
@TECHREPORT{Wigner45,
author = "Eugene P. Wigner",
title = "The Effect of Small Perturbations on Pile Period",
number = "CP-3048",
institution = "Metallurgical Laboratory (now Argonne National Laboratory)",
address = "Lemont, Illinois",
year = 1945,
keywords = {nuclear physics, neutron transport, perturbation theory,
adjoints},
comments = "According to [Lewins65], this tech report introduced
perturbation theory and non-self adjoint methods to
reactor physics",
note = "(*)"
}
@TECHREPORT{Hurwitz48,
author = "H. {Hurwitz, Jr.}",
title = "A Note on the Theory of Danger Coefficients",
number = "KAPL-48",
institution = "Knolls Atomic Power Laboratory",
address = "Schenectady, New York",
year = 1948,
keywords = {nuclear physics, neutron transport, adjoints},
comments = "According to [Lewins65], Hurwitz independently used a
physical interpretation of the adjoint function. He used a
normalized adjoint function to mean the iterated fission
probability.",
note = "(*)"
}
@TECHREPORT{Goertzel49,
author = "Gerald Goertzel",
title = "Quota Sampling and Importance Functions in Stochastic Solution
of Particle Problems",
number = 434,
institution = "Oak Ridge National Laboratory",
address = "Oak Ridge, Tennessee",
month = jun,
year = 1949,
keywords = {nuclear physics, Monte Carlo, importance sampling, adjoints,
importance},
comments = "The first demonstration of a zero variance estimator: if
we knew the exact importance, we wouldn't have to simulate
the primary quantity (neutron density, radiance).
The adjoint function is the optimal importance function for
importance sampling. In other words, if we knew the
optimal importance sampling function, one sample would be
enough. It is also suggested to solve the primary and the
dual problem in parallel, using each one to improve the
solution of the other.
Of historical interest: ``many of the thoughts herein arose
during conferences between Mr. Kahn and me during the days
June 15--17.''
According to [Kahn49a], Goertzel introduced the term
`importance sampling'. However, in this tech report he
uses the older term `quota sampling' (which is a little
misleading since it is different from the quota sampling
used in statistics)."
}
@TECHREPORT{Kahn49a,
author = "Herman Kahn",
title = "Modifications of the {Monte Carlo} method",
number = "P-132",
institution = "Rand Corporation",
month = nov,
year = 1949,
keywords = {nuclear physics, Monte Carlo, splitting, Russian roulette,
importance sampling, adjoints, importance},
comments = "Describes importance sampling and adjoint equations.
Contains the following interesting footnote: `It was during
some conversations at the Oak Ridge National Laboratory
during the summer of 1949 that it was decided that finding
the optimum importance function was probably always equivalent
to solving the adjoint problem. Present at these conversations
were H. Feshbach, F. Friedman, G. Goertzel, and H. Kahn.'.
(Can be ordered from Rand Corp. (www.rand.org) for 4 US
dollars.)"
}
@INPROCEEDINGS{Kahn49b,
author = "Herman Kahn and T. E. Harris",
title = "Estimation of Particle Transmission by Random Sampling",
booktitle = "Monte Carlo Method",
series = "Applied Mathematics Series",
volume = 12,
pages = "27--30",
publisher = "National Bureau of Standards",
year = 1949,
keywords = {nuclear physics, Monte Carlo, splitting, Russian roulette,
adjoints, importance},
comments = "Introduces a) Russian roulette and splitting (credits John
von Neumann with inventing them), b) analytical integration
(the use of expected values, similar to next event estimation)
and c) importance sampling (both straightforward and using
the adjoint equation).
Suggests sequentially alternating propagation of neutron
flux and importance."
}
@INCOLLECTION{Soodak49,
author = "Harry Soodak",
title = "Pile Kinetics",
editor = "Clark Goodman",
booktitle = "The Science and Engineering of Nuclear Power",
volume = 2,
chapter = 8,
pages = "89--102",
organization = "United Nations Atomic Energy Commission",
publisher = "Addison-Wesley Press",
year = "1949",
keywords = {nuclear physics, neutron transport, adjoints, importance},
comments = "This article is where the term ``importance function'' was
introduced. Uses a particle count as importance, ie. the
importance of a neutron is the total number of neutrons
resulting from that neutron (its progeny)."
}
% Is it Ehrlich and Hurwitz?
@ARTICLE{Hurwitz54,
author = "H. {Hurwitz, Jr.} and R. Ehrlich",
title = "Multi-Group Methods for Neutron Diffusion Problems",
journal = "Nucleonics",
volume = 12,
number = 2,
pages = "23--30",
year = 1954,
comments = "Supposedly more readable than [Hurwitz48].",
note = "(*)"
}
@INPROCEEDINGS{Kahn56,
author = "Herman Kahn",
title = "Use of Different Monte Carlo Sampling Techniques",
editor = "Herbert A. Meyer",
booktitle = "Symposium on Monte Carlo Methods",
publisher = "John Wiley \& Sons",
year = 1956,
keywords = {nuclear physics, Monte Carlo, splitting, Russian roulette,
adjoints?, importance?},
comment = "Elaborates on the topics in [Kahn49a,b].",
note = "(*) QA273.F67"
}
@BOOK{Davison57,
author = "B. Davison and J. B. Sykes",
title = "Neutron Transport Theory",
publisher = "Oxford University Press",
year = 1957,
keywords = {nuclear physics, neutron transport, variational methods,
perturbation methods, iteration methods, adjoints, importance},
note = "(*)"
}
@ARTICLE{Goertzel58,
author = "Gerald Goertzel and Malvin H. Kalos",
title = "Monte Carlo Methods in Transport Problems",
journal = "Progress in Nuclear Energy, Series I",
volume = 2,
pages = "315--369",
publisher = "Pergamon Press",
year = 1958,
keywords = {nuclear physics, adjoints, importance, zero variance},
comments = "It is shown here that importance (the function satisfying
the adjoint equation) permits the answer to the primary
equation to be obtained exactly -- ie. with zero variance.
(This was also shown in [Goertzel49].)"
}
@BOOK{Weinberg58,
author = "Alvin M. Weinberg and Eugene P. Wigner",
title = "The Physical Theory of Neutron Chain Reactors",
publisher = "University of Chicago Press",
year = 1958,
keywords = {nuclear physics, neutron transport, adjoints, importance},
comments = "Defines the importance of a photon to be the number of
progeny it produces."
}
@ARTICLE{Kalos63,
author = "Malvin H. Kalos",
title = "Importance sampling in {Monte Carlo} shielding calculations",
journal = "Nuclear Science and Engineering",
volume = 16,
pages = "227--234",
year = 1963,
keywords = {nuclear physics, neutron transport, adjoints, importance},
comments = "Importance sampling based on the solution of the
adjoint equation."
}
@BOOK{Lewins65,
author = "Jeffery Lewins",
title = "Importance, The Adjoint Function: The Physical Basis of
Variational and Perturbation Theory in Transport and
Diffusion Problems",
publisher = "Pergamon Press",
year = 1965,
keywords = {nuclear physics, neutron transport, variational theory,
perturbation theory, adjoints, importance},
comments = "An entire book dedicated to importance. Describes the
use of importance in simulation of neutron transport.
Importance is defined as an adjoint of neutron density.
Also contains historical information on the origins of
importance."
}
@ARTICLE{Coveyou67,
author = "R. R. Coveyou and V. R. Cain and K. J. Yost",
title = "Adjoint and Importance in {Monte Carlo} Application",
journal = "Nuclear Science and Engineering",
volume = 27,
pages = "219--234",
year = 1967,
keywords = {nuclear physics, neutron transport, Monte Carlo,
variance reduction, adjoints, importance},
comments = "Presents the most useful methods of variance reduction.
Shows that importance (called the `value function'),
the solution of an adjoint integral equation, is a good
choice for sample density biasing (importance sampling)."
}
% volume = "?"
@Article{Kalos68,
author = "Malvin H. Kalos",
title = "{Monte Carlo} Integration of the Adjoint Gamma-Ray Transport
Equation",
journal = "Nuclear Science and Engineering",
year = 1968,
number = 33,
pages = "284--290",
note = "(*)"
}
% volume = "?"
@Article{Levitt69,
author = "L. Levitt and J. Spanier",
title = "A New Non-Multigroup Adjoint {Monte Carlo} Technique",
journal = "Nuclear Science and Engineering",
year = 1969,
number = 37,
pages = "278--287",
note = "(*)"
}
@BOOK{Spanier69,
author = "Jerome Spanier and Ely M. Gelbard",
title = "Monte Carlo Principles and Neutron Transport Problems",
publisher = "Addison-Wesley Publishing Co.",
year = 1969,
keywords = {nuclear physics, neutron transport, Monte Carlo, adjoints,
importance},
comments = "A very comprehensive overview of the Monte Carlo method and
its use for neutron transport problems. Describes
adjoints and importance. Also covers the use of correlated
random numbers for simulation of small pertubations"
}
@ARTICLE{Greenspan76,
author = "E. Greenspan",
title = "Developments in Perturbation Theory",
journal = "Advanced / Advances in Nuclear Science and Technology",
year = 1976,
volume = 9,
pages = "181--??",
keywords = {nuclear physics, neutron transport, perturbation theory,
adjoints, importance},
comments = "According to [Lewis84], the concept of particle importance
is elaborated here for a broad range of neutron transport
problems.",
note = "(*)"
}
@BOOK{Lewis84,
author = "Elmer E. Lewis and W. F. {Miller, Jr.}",
title = "Computational Methods of Neutron Transport",
publisher = "John Wiley \& Sons",
year = 1984,
keywords = {nuclear physics, neutron transport, discrete ordinates,
Monte Carlo, adjoints, importance},
comments = "Describes neutron transport and the adjoint transport
equation. Also describes discrete ordinates and
Monte Carlo methods."
}
@BOOK{Kalos86,
author = "Malvin H. Kalos and Paula A. Whitlock",
title = "Monte Carlo Methods",
publisher = "John Wiley \& Sons",
year = 1986,
keywords = {nuclear physics, neutron transport, Monte Carlo,
random walk, integral equations, adjoints, importance},
comments = "General book on Monte Carlo methods with many examples
from neutron transport. Chapter 7 talks about adjoints
and importance and describes how they can be used for
solution of integral equations (for example for neutron
transport simulation)."
}