Keith Geoffery Bowden BEng(Hons), PhD, MIEEE, MBCS, CEng
Associate Research Fellow Theoretical Physics Research Unit
Tel. 020 7631 6555 e-mail k.bowden@physics.bbk.ac.uk |
My research work has centred around Kron's Method of Tearing, a technique for splitting up physical problems into subproblems, solving each individual subproblem and then recombining to give an exact overall solution. The technique is efficient on sequential computers, but is particularly so on parallel architectures, as I demonstrated in my paper on Transputer arrays. It is peculiar as a decomposition method, in that it involves taking values on the "intersection layer" (the boundary between subsystems) into account. The method has been rediscovered by the parallel processing community recently under the name "Domain Decomposition".
My first two ANPA papers showed that Kron's Method is equivalent to Huygens' Principle (in the form of Maurice Jessel's "Principle of Secondary Sources") and that its computational efficiency is due to a series of holographic transformations which, in a new hierarchical form, are similar to that described by David Bohm and Basil Hiley as the holomovement, but in a discrete space. (Jessel was a doctoral student of Louis de Broglie.) The work can be formulated in continuous space in Jessel's formulation, or over a network, a la Kron; the coefficients can be polynomials over the Laplace transform. Topologically the theory is described by de Rham cohomology and singular homology respectively; the de Rham theorem gives the appropriate isomorphism between the two.
Recent work involves the definition of a new General (Physical) Systems Theory which is based on the ideas of Mesarovic and Takahara in Category Theory and is not only a generalisation of the work of both Kron and Jessel, but also is similar to that of Tom Etter. Etter has recently shown that a statistical formulation of such a theory of decomposition or "linking" can be used seen an interpretation of Quantum Theory. Topology naturally arises out of data and is defined by statistical correlations. A subsystem is called a boundary if fixing its values makes two other subsystems (the interior and the exterior) independent. In potential theory these ideas are referred to as "balayage". In general a boundary is a basis for its interior.
I have also, more recently, (thanks to Stephen Wood) discovered the closely related work of Goguen on sheaves and colimits in Computer Science. I had been independently looking at applying these concepts in the holographic theory and found that Goguen had already solved a number of problems that I had been grappling with, although he does not seem to have recognised the holographic connection. Generally work in Computer Science seems to concentrate on colimits and presheaves, which might explain this oversight. Currently I am also considering how these ideas relate to the Holographic Principle of Quantum Gravity.
1. Bowden K, and Leather C, The Apple II as an Intelligent Interactive Graphics Terminal, Microcomputer Applications, Vol 3, No 3. This paper was presented at the Liverpool University Microprocessor Workshop, Sept 1979.
2. Bowden K, An Introduction to Homological Systems Theory: Topological Analysis of Invariant System Zeros, Matrix and Tensor Quarterly, Dec 1980.
3. Bowden K, On Inverse Suboptimal Control, Matrix and Tensor Quarterly, Sept 1981.
4. Bowden K, A Direct Solution of the Discretised Form of Laplace's Equation, Matrix and Tensor Quarterly, March 1982.
5. Bowden K, A Fast Contouring Algorithm for Potential Arrays, Matrix and Tensor Quarterly, March 1982.
6. Bowden K, The Companion to the Commodore 64, PAN, April 1984. A cool book on programming graphics and sound on one of the best computers ever built!
7. Bowden K, Go Forth and Prosper, Personal Computer World, July 1985. A serious discussion of the computer language Forth.
8. Bowden K, The use of Kron's Lemma to derive an efficient algorithm for fitting data to Multivariable Autoregressive Time Series Models, Matrix and Tensor Quarterly, July 1987.
9. Bowden K, A Direct Solution to the Block Tridiagonal Matrix Inversion Problem, International Journal of General Systems, Vol 15, 1989, pp 185-198.
10. Bowden K, On General Physical Systems Theories, International Journal of General Systems, Vol 18, 1990, pp 61-79. This paper is based on a lecture given to the 11th International ANPA Conference on Discrete Physics at King's College, Cambridge, Sept 1989 and was also published in the Conference Proceedings. An earlier version of this paper was presented at a BCS Machine Group seminar.
11. Bowden K, Kron's Method of Tearing on a Transputer Array, British Computer Society Computer Journal, Vol 33, No 5, 1990, pp 453-459. This paper was originally presented at a seminar at Centre National de Recherche Scientifique in Marseilles, France.
12. Bowden K, Hierarchical Tearing: An Efficient Holographic Algorithm for System Decomposition, International Journal of General Systems, 24(1), pp 23-38. This paper is based on a lecture given to the 12th international ANPA Conference on Discrete Physics at King's College, Cambridge, Sept 1994 and was also published in the Conference Proceedings.
13. Bowden K, Orthogonality and General Systems Theory in Computing and Physics, Proceedings of the 14th ANPA Conference on Discrete Physics, Kings College, Cambridge, Sept 1992.
14. Bowden K, The Spatial Transmission of Information, Proceedings of the 15th ANPA Conference on Discrete Physics, King's College, Cambridge, Sept 1993.
15a. Bowden K, Physical Parallelism and Computation, Proceedings of BCS Symposium on Alternative Approaches to Computation and Parallelism, (chaired by Sir Brian Oakley), University of Greenwich, Feb 1994.
15b. Bowden K, Constructive PostModern Physics, Proceedings of ANPA 16, University of Cambridge, Sept 1994. Based on (15a).
15c. Physical Parallelism and Computation (Constructive PostModern Physics), Proceedings of the Third International Conference on Physics and Computation, PhysComp94 in Dallas, Texas, Nov 1994. The IEEE has given permission to reprint this paper in (20).
16. Bowden K. et al, Obituary for Maurice Jessel, International Journal of General Systems, 23(4), 1994.
17. Bowden K, A View on the Combinatorial Hierarchy, Proceedings of the 8th ANPA West Meeting, Stanford University, Feb 1995.
18. Bowden K, On Eddington's Fundamental Theory, ibid. Reprinted in Aspects II, the Proceedings of ANPA 20, Cambridge 1998.
19. Bowden K, Classical Computation can be Counterfactual, Aspects I, Proceedings of ANPA 19, Cambridge 1997.
20. Bowden K, (ed), Special Double Issue of the International Journal of General Systems on General Physical Systems and the Emergence of Physical Structure, 1998.
21. Bowden K, Huygens Principle, Physics and Computers, ibid. Reprinted in Participations, the Proceedings of ANPA 21, Cambridge, 1999.
22. Bowden K, Some ANPA Prehistory, Implications, Proceedings of ANPA 22, Cambridge, 2000.