Dr Mark Lukas
BSc(Hons) UWA, PhD ANU

Senior Lecturer

About me

I have been teaching and doing research in mathematics for over 30 years. After growing up in Perth and doing my undergraduate studies at UWA, I moved to Canberra to do my PhD at ANU. From there I had academic positions in Colorado, USA, and in Sydney, before joining Murdoch University in 1985.

Teaching area

I have taught several units over the years at Murdoch University at all levels from first year to Honours, in the areas of calculus, discrete mathematics, operations research, differential equations, modelling and simulation, numerical analysis, optimization and optimal control. The units I have taught most recently are:

Semester 2, 2011

MAS167 Computational Mathematics

MAS375 Modelling and Simulation

 

Semester 1, 2012

MAS182 Applied Mathematics

Research areas

My research interests are in the areas of inverse problems, spline smoothing and numerical analysis. In particular, I am interested in the methodology of regularization methods for solving ill-posed problems and the effective choice of the regularization parameter. The framework and analysis may be either deterministic or stochastic. I am also interested in the smoothing of noisy data by splines and the selection of the smoothing parameter.

Doctoral and masters supervisions

1997 M. Shi PhD

Thesis title: Constrained Regularization with the L1 Norm for Ill-Posed Problems

Publications

Chapters

  • Bauer, F., Gutting, M., Lukas, M., (2015),Evaluation of Parameter Choice Methods for Regularization of Ill-Posed Problems in Geomathematics,In: Handbook of Geomathematics, Springer-Verlag Berlin Heidelberg, pages 1713 to 1774.

Journals

  • Lukas, M., de Hoog, F., Anderssen, R., (2016), Practical use of robust GCV and modified GCVfor spline smoothing, Computational Statistics, 31, 1, pages 269 - 289.
  • Lukas, M., (2014), Performance criteria and discrimination of extreme undersmoothing in nonparametric regression, Journal of Statistical Planning and Inference, 153, , pages 56 - 74.
  • Lukas, M., De Hoog, F., Anderssen, R., (2012), Performance of Robust GCV and Modified GCV for Spline Smoothing, Scandinavian Journal of Statistics: theory and applications, 39, 1, pages 97 - 115.
  • De Hoog, F., Anderssen, R., Lukas, M., (2011), Differentiation of matrix functionals using triangular factorization, Mathematics of Computation, 80, 275, pages 1585 - 1600.
  • Bauer, F., Lukas, M., (2011), Comparing parameter choice methods for regularization of ill-posed problems, Mathematics and Computers in Simulation, 81, 9, pages 1795 - 1841.
  • Lukas, M., (2010), Robust GCV choice of the regularization parameter for correlated data, Journal of Integral Equations and Applications, 22, 3, pages 519 - 547.
  • Lukas, M., de Hoog, F., Anderssen, R., (2010), Efficient algorithms for robust generalized cross-validation splinesmoothing, Journal of Computational and Applied Mathematics, 235, 1, pages 102 - 107.
  • Lukas, M., (2008), Strong robust generalized cross-validation for choosing the regularization parameter, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 24, 3, pages 1 - 16.
  • Lukas, M., (2006), Robust generalized cross-validation for choosing the regularization parameter, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 22, , pages 1883 - 1902.
  • Lukas, M., Shi, M., (2006), Sensitivity analysis of constrained linear L1 regression: Perturbations to constraints, addition and deletion of observations, Computational Statistics & Data Analysis, 51, , pages 1213 - 1231.
  • Shi, M., Lukas, M., (2005), Sensitivity analysis of constrained linear L1 regression: perturbations to response and predictor variables, Computational Statistics & Data Analysis, 48, , pages 779 - 802.
  • Shi, M., Lukas, M., (2002), An L1 estimation algorithm with degeneracy and linear constraints, Computational Statistics & Data Analysis, 39, , pages 35 - 55.
  • Abo-Hashema, K., Cake, M., Lukas, M., Knudsen, J., (2001), The interaction of acyl-CoA with acyl-CoA binding protein and carnitine palmitoyltransferase I, International Journal of Biochemistry & Cell Biology, 33, , pages 807 - 815.
  • Abo-Hashema, K., Cake, M., Lukas, M., Knudsen, J., (1999), Evaluation of the Affinity and Turnover Number of Both Hepatic Mitochondrial and Microsomal Carnitine Acyltransferases: Relevance to Intracellular Partitioning of Acyl-CoAs, Biochemistry, 38, 48, pages 15840 - 15847.
  • Lukas, M., (1998), Asymptotic behaviour of the minimum bound method for choosing the regularization parameter, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 14, , pages 149 - 159.
  • Lukas, M., (1998), Comparisons of parameter choice methods for regularization with discrete noisy data, Inverse Problems: inverse problems, inverse methods and computerized inversion of data, 14, , pages 161 - 184.

Conference

  • Shi, M., Lukas, M., (2005),L1 Optimization for Robust Signal Processing,In: 18th National Conference of the Australian Society for Operations Research (ASOR) & 11th Australian Optimisation Day (2005).