Publications, Conference Paricipation and Seminars


THESES

1977 Problems in Functional Analysis, DPhil thesis, University of Oxford, supervised by H Priestley
1974 Matrix Measures, MSc thesis, University of Oxford, supervised by D Sears and H Priestley

    REFEREED CHAPTERS IN BOOKS
     
  1. BRAZIL, M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F., and WORMALD, N.C.– ‘Optimisation in the design of underground mine access’ in Uncertainty and Risk Management in Orebody Modelling and Strategic Mine Planning, Edited by Roussos Dimitrakopoulos: AusIMM Spectrum Series, Vol 14,pp.121-124, (2005).
  2. THOMAS, D.A., WENG, J. F.– ‘Polynomial time algorithms for the rectilinear Steiner tree problem’, in Steiner Trees in Industry, Dordrecht/Boston/London: Kluwer Academic Publishers, pp 405-426, (2001). Invited Book Chapter.
  3. BOOTH, R.S., THOMAS, D.A., and WENG, J.F.– ‘Shortest networks for one line and two points in space’, in Advances in Steiner Trees, eds. D.Z. Du, J.M. Smith and J.H. Rubinstein, Kluwer Academic Publishers, Boston, pp. 15-26, (2000). Invited Book Chapter.
  4. BRAZIL, M., THOMAS, D.A., WENG, J.F. – ‘Rectilinear Steiner minimal trees on parallel lines,’ in Advances in Steiner Trees, eds. D.Z. Du, J.M. Smith and J.H. Rubinstein, Kluwer Academic Publishers, Boston, pp. 27-38, (2000). Invited Book Chapter.

    5. PAPERS SUBMITTED TO INTERNATIONAL JOURNALS AND UNDER REVIEW
     
  5. THOMAS, D.A. and WENG, J.F. - 'Gradient-constrained minimum networks: An algorithm for computing Steiner points', Journal of Discrete Optimization, (Submitted, June 2006).
  6. BRAZIL, M., THOMAS, D.A. and WENG, J.F.- 'Gradient-constrained minimum networks II, Labelled or Locally Minimal Steiner Points', J. Global Optimization, (Submitted, September 2005).
  7. SMITH J. M., BRAZIL, M., WENG, J.F. and THOMAS, D. - 'Equivalence, indicators, quasi-indicators and optimal Steiner topologies on four points in space', Fundamenta Informaticae (Submitted August 2006).
  8. PRENDERGAST, K., THOMAS, D. and WENG, J.F. - 'Optimum Steiner ratio for gradient-constrained networks connecting three points in 3-space', Networks (Submitted August 2006).
  9. BRAZIL, M., NIELSEN, B.K. THOMAS, D.A., WINTER, P. and ZACHARIASEN, M.- 'Novel Approach to Phylogenetic Trees: d-Dimensional Geometric Steiner Trees', Networks (Submitted September 2006).

    10. INTERNATIONAL REFEREED JOURNAL PUBLICATIONS
     
  10. THOMAS, D.A., BRAZIL, M., LEE, D. and WORMALD, N.C. - 'Network modelling of underground mine layout: Two case studies', International Transactions in Operational Research, (Accepted, October 2006).
  11. BRAZIL, M., THOMAS, D.A. and WENG, J.F.- 'Locally minimal uniformly oriented Steiner trees", Discrete Applied Mathematics, (Accepted April 2006).
  12. THOMAS, D.A. and WENG, J.F.- 'Minimum cost flow-dependent communication networks', Networks, 48(1): pp. 39-46, (2006).
  13. BRAZIL, M., THOMAS, D.A.,- 'Network optimization for the design of underground mines', Networks, 49: pp. 40-50 (2007).
  14. BRAZIL, M., THOMAS, D.A., WENG, J.F. and ZACHARIASEN, M. - 'Canonical forms and algorithms for Steiner trees in uniform orientation metrics', Algorithmica, Vol 44, no. 4, pp. 281-300, ( 2006).
  15. BRAZIL, M., THOMAS, D.A., WENG, J.F., RUBINSTEIN, J.H., LEE, D.H.  – ‘Cost optimisation for underground mining networks’, Optimisation and Engineering, 6, pp.241-256, (2005).
  16. BRAZIL, M., THOMAS, D.A. and WENG, J.F.  – ‘Upper and Lower Bounds for the Lengths of Steiner Trees in 3-Space’, , 109, pp. 107-119 (2004).
  17. BOOTH, R.S., THOMAS, D.A. and WENG, J.F.  – ‘Exactly solvable and unsolvable shortest network problems in 3D space’, Contributions to Geometriae DedicataAlgebra and Geometry, 45 (2): pp. 649-663, (2004).
  18. BRAZIL, M., LEE D., RUBINSTEIN, J.H., THOMAS, D.A. and WORMALD, N.C.  – ‘Optimising declines in underground mines’, Mining Technology: Transactions of the Institution of Mining and Metallurgy, Section A, 112 (3): pp. 164-170, (2003).
  19. BRAZIL, M., THOMAS, D.A. and WENG, J.F.  – ‘Forbidden subpaths for Steiner minimum networks in uniform orientation metrics’, Networks, 39 (4): pp.186-202, (2002).
  20. BRAZIL, M., LEE, D.H., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C. – ‘A network model to optimise cost in underground mine design’, Transactions of the South African Institute of Electrical Engineers, Vol.93, No.2, pp. 97-103, (2002).
  21. *RUBINSTEIN, J.H., THOMAS, D.A. and WENG, J.F.  – ‘Minimum networks for four points in space’, Geometriae Dedicata, 93: pp.57-70, (2002).
  22. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Gradient-constrained minimum networks. I. Fundamentals’, J. Global Optimization, Vol. 21, pp. 139-155, (2001).
  23. RUBINSTEIN, J.H., THOMAS, D.A and WORMALD, N.C.  – ‘A polynomial algorithm for a constrained travelling salesman problem’, Networks, 38 (2): pp.1-8, (2001).
  24. BRAZIL, M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Network optimisation of underground mine design’, The Australasian Institute for Mining and Metallurgy Proc, 305, pp. 57-65 (2000).
  25. BRAZIL, M., THOMAS, D.A. and WENG, J.F. – ‘On the complexity of the Steiner problem’, J. Combinatorial Optimization, 4: pp.187-195, (2000).
  26. BRAZIL, M., THOMAS, D.A. and WENG, J.F. – ‘Minimum networks in uniform orientation metrics’, SIAM Journal on Computing, 30, pp. 1579-1593,  (2000).
  27. BRAZIL, M., THOMAS, D.A. and WENG, J.F   – ‘A polynomial time algorithm for rectilinear Steiner trees with terminals constrained to curves’, Networks, 33: pp. 145-155, (1999).
  28. COVINGTON, J. and THOMAS, D.A.  – ‘A homogenizable fishy structure’, J. Algebra, 211: pp. 625-639, (1999).
  29. BRAZIL, M., THOMAS, D.A. and WENG, J.F.  – ‘Gradient-constrained Minimal Steiner trees’, Network Design: Connectivity and Facilities Location, (DIMACS series in discrete mathematics and theoretical computer science), 40: pp. 23-28, (1998).
  30. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Shortest Networks on Spheres’, Network Design: Connectivity and Facilities Location, (DIMACS series in discrete mathematics and theoretical computer science), 40: pp. 453-461, (1998).
  31. RUBINSTEIN, J.H., THOMAS, D.A. and WORMALD, N.C.  – ‘Steiner trees for terminals constrained to curves’, Siam Journal of Discrete Mathematics, 10: pp. 1-17, (1997).
  32. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C. – ‘Minimal Steiner trees for rectangular arrays of lattice points’, J. Combinatorial Theory Series A, 79: pp. 181-208, (1997).
  33. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C. – ‘Full minimal Steiner trees on lattice sets’, J. Combinatorial Theory Series A, 78: pp. 51-91, (1997).
  34. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.   – ‘Minimal Steiner Trees for 2K x2K square lattices’, J. Combinatorial Theory Series A, 73: pp. 91-110, (1996).
  35. THOMAS, D.A.  – ‘Critical points for the Steiner ratio conjecture’, Australasian Journal of Combinatorics, 13: pp.259-282, (1996).
  36. COLE T., RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘The Steiner minimal network for convex configurations’, J. Discrete and Computational Geometry, 9: pp. 323-333, (1993).
  37. RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘Graham's problem on shortest networks for points on a circle’, Algorithmica, 7: pp. 193-218, (1992).
  38. RUBINSTEIN, J.H., THOMAS, D.A. and WENG, J.F.  – ‘Degree five Steiner points cannot reduce network costs for planar sets’, Networks, 22: pp. 531-537, (1992).
  39. RUBINSTEIN, J.H. and THOMAS, D.A. – ‘The Steiner ratio conjecture for cocircular points’, J. Discrete and Computational Geometry, 7: pp. 77-86, (1992).
  40. RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘The Steiner ratio conjecture for six points’, J. Combinatorial Theory Series A, 58: pp. 54-77, (1991).
  41. RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘A variational approach to the Steiner network problem’, Annals of Operations Research, 33: pp. 481-499, (1991).
  42. THOMAS, D.A.  – ‘On general matrix measures’, Quart. J. Math. Oxford, 27: pp.95-104, (1976).

    43. REFEREED CONFERENCE PUBLICATIONS
     
  43. PRENDERGAST, K., THOMAS, D. and WENG, J.F. - 'Optimum gradient-constrained networks with a single Steiner point in 3-space', International Network Optimisation Conference (Submitted October 2006).
  44. SMITH J. M., BRAZIL, M., WENG, J.F. and THOMAS, D.- 'Quasi-indicators and optimal Steiner topologies on four points in space', 17th Australian Workshop on Combinatorial Algorithms, Alice Springs, pp. 54-66, (2006).
  45. THOMAS, D. and WENG, J.  – ‘A note on Distance-based Geographic Location in Sensor Networks’, Proceedings of International Symposium on Communications and Information Technologies, Beijing, IEEE Catalog Number: 05EX1224, pp. 681-684, (2005).
  46. BOOTH, R.S., WENG, J.F. and THOMAS, D.  – ‘Steiner trees for four points in space’, The 6th International Conference on Optimization: Techniques and Applications ICOTA6, Ballarat, 2004.
  47. WENG, J. and THOMAS, D. – ‘An Algorithm for Finding Steiner Points in Gradient-Constrained Minimum Networks’, International Congress of Chinese Mathematicians, China, (2004).
  48. BRAZIL, M., THOMAS, D.A., WENG, J.F., WINTER, P. and ZACHARIASEN, M.  – ‘The structure and flexibility of Steiner trees in uniform orientation metrics’, Proceedings of 6th International Conference on Optimization: Techniques and Applications ICOTA6, Ballarat, 11 pages, (2004).
  49. BRAZIL, M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F., and WORMALD, N.C.  – ‘Optimisation in the design of underground mine access’ The International Symposium on “Orebody Modelling and Strategic Mine Planning: Uncertainty and Risk Management”, Proc Aus. Inst Min Metall. 305: pp 57-65, Perth, (2004).
  50. THOMAS, D.A. and WENG, J.F.  – ‘Contructing minimum cost flow-dependent networks, Network Design and management’, Qian Mao, Shoa-Kai Liu, Kwok-wai Cheung, Editors, Proceedings of SPIE Vol. 4909, pp.239-247, (2002).
  51. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A. and WENG, J.F.  – ‘Modelling and Optimisation of a Weighted Network in an Underground Mine Design’, Proceedings of the 3rd International Conference on Control Theory and Applications, Pretoria, South Africa, pp. 564-568 (2001).
  52. THOMAS, D.A. – ‘A homogenizable fishy poorset’, Victorian Algebra Conference, 13, pp. 11, (1995).
  53. RUBINSTEIN, J.H., THOMAS, D.A. and WORMALD, N.C. – ‘Algorithms for constrained shortest networks’, Proceedings of the Fifth Australian Workshop on Combinatorial Algorithms, Geometric Algorithms Laboratory, University of Newcastle, 8 pages, (1992).
  54. RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘Polynomial time algorithms for constrained shortest networks’, Proceedings of the Sixth Australian Teletraffic Seminar, Wollongong, 8 pages, (1991).
  55. RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘Minimal cost networks in the plane’, Proceedings of the Fourth Australian Teletraffic Seminar, Brisbane, 8 pages, (1989).
  56. RUBINSTEIN, J.H. and THOMAS, D.A. – ‘The Steiner problem of shortest networks’, Proceedings of the Third Australian Teletraffic Seminar, Clayton, 14 pages, (1988).
  57. RUBINSTEIN, J.H. and THOMAS, D.A.  – ‘A variational approach to the Steiner problem’, Proceedings of the Second Australian Teletraffic Seminar, Adelaide, 8 pages, (1987).

    58. REFEREED CONFERENCE PUBLICATIONS ON ENGINEERING EDUCATION
     
  58. THOMAS, D.A. and SONDERGAARD, H. –“Providing effective feedback to small and large classes”, Proceedings of the 2004 ASEE/IEEE Frontiers in Education Conference, pages F1E-9 - F1E-14. Savannah GA, USA, 2004
  59. THOMAS, D.A., and SEATON, KA.  – ‘The round table discussion on teaching engineers subjects other than their specialty’, Proceedings of the Second Australasian Women in Engineering Forum, 1995.
  60. THOMAS, D.A. and SCHMID, R.  – ‘"Mathematics for engineers" at the University of Melbourne: a success’, Proceedings of the Seventh Annual Convention and Conference of the Australian Association for Engineering Education, (December 1995).

    61. REFEREED CONFERENCE PUBLICATIONS ON DIVERSITY IN ENGINEERING
     
  61. THOMAS, D.A. and JAYASURIYA, K  –“Establishing women-only positions in engineering to increase gender diversity - the process and its implications”, ASEE Conference: Frontiers in Education, New Orleans, October 2004.
  62. JAYASURIYA, K. and THOMAS D.A.  – ‘Enhancing diversity in engineering as part of an action plan – work in progress’, Proceedings of the 14th Annual Conference of the Australasian Association for Engineering Education, pp.563-572, Melbourne, September 2003.
  63. BROWN, D. and THOMAS D.A.  – ‘Engineering the benefits of staff diversity’, Proceedings of the 13th Annual Conference of the Australasian Association for Engineering Education, pp.401-404, Canberra, September 2002.
  64. BROWN, D., and THOMAS, D.A. – ‘Strategies for attracting women engineers into academia’, Proceedings of the Australasian Association for Engineering Education 12th Annual Conference, (September 2001).

    65. INVITED PUBLICATIONS ON WOMEN IN MATHEMATICS
     
  65. THOMAS D., A – Short article in “Voices from Six Continents”, Complexities, Women in Mathematics eds. B.A.Case and A.M. Leggett, Princeton University Press, Princeton, pp. 140-141, (2005).
  66. IRVINE, S., LANDMAN, K., MANGELSDORF, C. and THOMAS, D.A. – ‘Women in mathematics, Part 3’, Association for Women in Mathematics newsletter, 27, No 4,pp. 13-15, (1997). (Invited)
  67. IRVINE, S., LANDMAN, K., MANGELSDORF, C. and THOMAS, D.A. – ‘Women in mathematics, Part 2’, Association for Women in Mathematics newsletter, 26, No 6, pp. 18-21, (1996). (Invited)
  68. IRVINE, S., LANDMAN, K., MANGELSDORF, C. and THOMAS, D.A.  – ‘Women in mathematics, Part 1’, Association for Women in Mathematics newsletter, 26, No 4, pp. 22 24, (1996). (Invited)

    69. COMMISSIONED PROJECT ON TEACHING
     
  69. THOMAS, D.A. – ‘Reflections on University teaching’, 1995 CAUT (Committee for Advanced University Teaching) commissioned project, a report, (1995).

    70. CONFERENCE ABSTRACTS - INVITED PAPERS
     
  70. THOMAS, D.A. – ‘Optimal design of a navigable decline’ INFORMS, Pittsburgh, Pennsylvania (USA) (2006).
  71. THOMAS, D.A. - 'Modelling and software design for optimal declines in underground mine development, ISMP, Rio de Janeiro, (2006).
  72. THOMAS, D.A. – ‘Optimal declines in underground mine development including barrier avoidance’, Euro/IFORS Conference, Iceland, (2006).
  73. BRAZIL M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A.  – ‘Network modeling of underground mines’, IFORS Operations Research Conference, Hawaii, July 2005.
  74. BRAZIL, M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F., and WORMALD, N.C.  – A model of an underground mine layout as a weighted network - an application of gradient-constrained minimum network theory’, Optimisation 2004, Lisbon.
  75. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F., and WORMALD, N.C.  – Three-dimensional gradient constrained networks, Optimisation 2004, Lisbon.
  76. BRAZIL, M., THOMAS, D.A., WENG, J.F. and ZACHARIASEN, M.  – ‘Flexibility of Steiner minimum trees in uniform orientation metrics’, 18th International Symposium on Mathematical Programming (ISMP), Technical  University of Denmark, Denmark (2003)
  77. THOMAS, D.A. – ‘A model of an underground mine layout as a weighted network - an application of gradient-constrained minimum network theory’, Workshop on Geometric Network Design, University of Copenhagen, Copenhagen, (2003).
  78. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Minimum Steiner trees on spheres’, 3rd International Conference on Combinatorial Mathematics and Combinatorial Computing, The University of Melbourne, (1997).
  79. THOMAS, D.A. – ‘Gradient constrained networks’, DIMACS Workshop on Network Design: Connectivity and Facility Location, Princeton, (1997).
  80. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Shortest networks on spheres’, DIMACS Workshop on Network Design: Connectivity and Facility Location, Princeton, (1997).
  81. THOMAS, D.A. – ‘Rectilinear Steiner trees with terminals constrained to smooth curves’, 16th International Symposium on Mathematical Programming, pp. 265, Lausanne, (1997).
  82. THOMAS, D.A. – ‘Minimal Steiner trees on configurations of integer lattice points’, Optimisation Days, Montreal, (1996).
  83. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Minimal Steiner trees on lattice sets’, 21st Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, Deakin University, (1995).
  84. THOMAS, D.A. – ‘A variational approach to the Steiner ratio conjecture for six points’, Proceedings of the NATO Advanced Research Workshop "Topological Network Design: Analysis and Synthesis", Copenhagen, (1989).

    85. TECHNICAL REPORTS
     
  85. BRAZIL, M., LEE D. and THOMAS, D. A.,  Technical report, BHP Billiton, Olympic Dam Operations (July 2005).
  86. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.   – ‘Optimal design of the Callie underground mine’, Technical report, Normandy Mining Ltd., (February 1999).
  87. BRAZIL, M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Vera South optimisation study’, Technical report, Normandy Mining Ltd., (May 1998).
  88. BRAZIL, M., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Optimal design for an underground mine’, Technical report, North Gold (WA) Ltd., (May 1998).
  89. BRAZIL, M., LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., WENG, J.F. and WORMALD, N.C.  – ‘Optimisation of a combined shaft/ ramp haulage system in an underground mine’, Technical report, Western Mining Company, Copper Uranium Division, (May 1997).

    90. AUSTRALIAN PROVISIONAL PATENT AND LICENSED SOFTWARE
     
  90. Global Network Design Tool: non-exclusive license granted to Newmont Australia under an ARC Linkage Grant agreement (2005-2007).
  91. Decline Optimisation Tool: non-exclusive licence granted to Newmont Australia under an ARC Linkage Grant agreement (2004-2006).
  92. Global Network Design Tool: non-exclusive license granted to Normandy Mining Ltd. (formally Normandy Mining Ltd), under an ARC Linkage Grant agreement (2001-2003).
  93. Australian Provisional Patent (1997): ‘Method of determining a haulage system in an underground mine’, Inventors: LEE, D., RUBINSTEIN, J.H., THOMAS, D.A., and WORMALD, N.C.

INVITED SPEAKER AT INTERNATIONAL CONFERENCES AND UNIVERSITY SEMINARS

2006      ISMP Conference, Rio de Janeiro. Invited talk on mining.
2006      Euro/IFORS Conference, Iceland. Invited talk on mining.
2006      INFORMS, Pittsburgh, Pennsylvania (USA). Invited talk on mining.
2006      University of Witwatersrand, Johannesburg. Invited talk on mining.
2005      University of Copenhagen, Denmark.
2005      Thomas D A, 'New approaches to teaching and learning', The University of Melbourne Vice Chancellor's Colloquium on Teaching and Learning, "Learning, Teaching and the Melbourne Experience".
2005      Thomas D A, 'Network Modeling of Underground Mines', IFORS Operations Research. Conference, Hawaii. Invited talk on mining.
2004      M. Brazil and D.A. Thomas, 'Optimising the design of underground mine access using gradient-constrained network theory', The 2nd Australia-China Workshop on Optimization, Ballarat. Invited talk.
2004      M. Brazil and D.A. Thomas, 'The structure and flexibility of Steiner trees in uniform orientation metrics', 6th ICOTA, Ballarat. Invited talk.
2004      Optimisation 2004 Conference, Lisbon. Invited talk on mining.
2003      Thomas D A and Sondergaard H- 'Providing feedback to large classes', The University of Melbourne Vice Chancellor's Colloquium on Teaching and Learning, 'Optimising teaching and learning at Melbourne'.
2003      Workshop on Geometric Network Design, Copenhagen. Invited talk on mining.
2003      University of Cape Town, South Africa.
2001      Third International Conference on Control Theory and Applications, Pretoria.
1998      University of Massachusetts, USA.
1997      DIMACS Workshop on Network Design: Connectivity and Facility Location, Princeton. 16th International Symposium on Mathematical Programming, Lausanne.
1996      Optimisation Days, Montreal.