University of North Carolina at Chapel Hill

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- B.A. 1953 (Cambridge)
- M.A. 1957 (Cambridge)
- D.Phil. 1960 (Oxford)
- Sc.D. 2008 (Cambridge)

- Fellow, Cambridge Philosophical Society (F.C.P.S.), 1954.
- Fellow, Institute of Mathematics and Its Applications (F.I.M.A.), 1964.
- Fellow, British Computer Society (F.B.C.S.), 1980.
- Senior Member, Institute of Electrical and Electronic Engineers (S.M.I.E.E.E.), 1984.
- Chartered Engineer (C.Eng.), British Engineering Council, 1990.
- Chartered Mathematician (C.Math.), Institute of Mathematics Council, 1992.
- Chartered Scientist (C.Sci.), British Science Council, 2006.

*Monte Carlo method. *All aspects of the method are
studied---including the design and analysis of quasi-random sequences
and sets; pseudo-random and quasi-random trees for parallel and
branching computations; sampling in multi-dimensional spaces, with
generalized probabilities; efficient variance-reduction techniques;
generalized antithetic transformations; solution of large linear and
nonlinear systems; sequential sampling techniques; parallel- and
multi-processing; smooth approximation; optimization; and all kinds of
applications.

*Combinatorial, probabilistic, geometric, and parallel algorithms*.
These are designed and analyzed for a variety of problems, such as the
Traveling Salesman Problem, application of tree structure to
computation, bin-packing, triangulation, and the Shoelace Problem.

*Decision-making in applied science and engineering*.
Mathematical, statistical, and scientific methods are employed.

*Mathematics and numerical analysis*. Various problems
relating to combinatorics, graphs, algebra, analysis, asymptotics, and
geometry are investigated.

*Absolute and probabilistic bounds on performance of complex
systems*. These include multicomputer algorithms, questions of
scale, networking and communication paradigms, control schemes,
debugging strategies, fault-tolerance and error-correction, distributed
operating systems, and parallel languages.

*PC boards and VLSI chips*. The design of efficient layouts,
and the efficient process of design of such circuits, are studied and
analyzed.

The shortest path through many points. *Proceedings of the
Cambridge Philosophical Society*, 55 (1959) pp. 299–327 (with J. E.
BEARDWOOD and J. M. HAMMERSLEY)

On the efficiency of certain quasi-random sequences of points in
evaluating multi-dimensional integrals.* Numerische Mathematik*,
2 (1960) pp. 84–90.

The extreme and L2 discrepancies of some plane sets. *Monatshefte
für Mathematik*, 73 (1969) pp. 316–328 (with S. K. ZAREMBA)

A retrospective and prospective survey of the Monte Carlo method. *Society
for Industrial and Applied Mathematics (SIAM) Review*, 12 (1970)
pp. 1–63.

A fast algorithm for the Euclidean Traveling Salesman Problem,
optimal with probability one. *SIAM Journal on Computing*, 11
(1982) pp. 28–46 (with R. TERADA)

On the efficiency of generalized antithetic transformations for
Monte Carlo integration.* Nuclear Science and Engineering*, 98
(1988) pp. 299–316.

Pseudo-random trees—multiple independent sequence generators for
parallel and branching computations.* Journal of Computational
Physics*, 84 (1989) pp. 1–56.

The properties of random trees.* Information Sciences*, 47
(1989) pp. 95–133.

On the thickness of graphs of given degree. *Information Sciences*,
54 (1991) pp. 219–238.

Sequential Monte Carlo techniques for the solution of linear systems.*
Journal of Scientific Computing*, 9 (1994) pp. 213–257.

Quasi-probability—why quasi-Monte-Carlo methods are statistically
valid and how their errors can be estimated statistically. *Monte
Carlo Methods & Applications*, 11 (2005) pp. 203–350.

Sequential Monte Carlo techniques for solving non-linear systems. *Monte
Carlo Methods & Applications*, 12 (2006) pp. 113–141.

Sequential Monte Carlo for linear systems—a practical summary. *Monte
Carlo Methods & Applications*, 14 (2008) pp. 1–27.

Sigma-algebra theorems. Monte
Carlo Methods & Applications, 14 (2008) pp. 171–189.

Click here for a full list of publications.

*John H. Halton (halton at
cs.unc.edu)
Last updated 12 December 2008 *

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