Areas of expertise

• Approximation Theory And Asymptotic Methods 010201
• Concurrent Programming 080304
• Health Informatics 080702
• Knowledge Representation And Machine Learning 170203
• Partial Differential Equations 010110
• Conceptual Modelling 080603
• Analysis Of Algorithms And Complexity 080201
• Decision Support And Group Support Systems 080605
• Plasma Physics; Fusion Plasmas; Electrical Discharges 020204
• Operations Research 010206
• Stochastic Analysis And Modelling 010406
• Pattern Recognition And Data Mining 080109
• Stellar Astronomy And Planetary Systems 020110
• Numerical Analysis 010301
• Statistical Theory 010405
• Biological Mathematics 010202
• Numerical Computation 080205
• Numerical Solution Of Differential And Integral Equations 010302
• Neural, Evolutionary And Fuzzy Computation 080108
• Simulation And Modelling 080110
• Numerical And Computational Mathematics 0103
• Artificial Intelligence And Image Processing 0801
• Computer Software 0803
• Genetics 0604

Publications

• Ali, M, Strazdins, P, Harding, B et al. 2016, 'Complex scientific applications made fault-tolerant with the sparse grid combination technique', International Journal of High Performance Computing Applications, vol. 30, no. 3, pp. 335-359.
• Hegland, M & Khakhutskyy, V 2016, 'Spatially-dimension-adaptive sparse grids for online learning', Workshop on Sparse Grids and Applications, SGA 2014, ed. Pfluger D. and Garcke J., Springer, Switzerland, pp. 133-162pp.
• Hegland, M, Harding, B, Kowitz, C et al. 2016, 'Recent developments in the theory and application of the sparse grid combination technique', International Conference on Software for Exascale Computing, SPPEXA 2015, ed. Nagel W.E.,Bungartz H.-J.,Neumann P., Springer Verlag, Switzerland, pp. 143-163pp.
• Hinojosa, A, Harding, B, Hegland, M et al. 2016, 'Handling silent data corruption with the sparse grid combination technique', International Conference on Software for Exascale Computing, SPPEXA 2015, ed. Nagel W.E.,Bungartz H.-J.,Neumann P., Springer Verlag, Switzerland, pp. 165-186pp.
• Harding, B, Hegland, M, Larson, J et al. 2015, 'Fault Tolerant Computation with the Sparse Grid Combination Technique', SIAM Journal on Scientific Computing, vol. 37, no. 3, pp. C331-C353.
• Flemming, J & Hegland, M 2015, 'Convergence rates in l(1)-regularization when the basis is not smooth enough', Applicable Analysis, vol. 94, no. 3, pp. 464-476.
• Hegland, M, Jin, Q & Wang, W 2015, 'Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces', Applicable Analysis, vol. 94, no. 3, pp. 524-547.
• Hegland, M & Leopardi, P 2015, 'Sparse grid quadrature on products of spheres', Numerical Algorithms, vol. 70, no. 3, pp. 485-517pp.
• Ali, M, Strazdins, P, Harding, B et al. 2015, 'A Fault-Tolerant Gyrokinetic Plasma Application using the Sparse Grid Combination Technique', 2015 International Conference on High Performance Computing & Simulation (HPCS), ed. Ljkovic V, Smari WW, IEEE, USA, pp. 499-507.
• Wong, M & Hegland, M 2014, 'Opticom and the iterative combination technique for convex minimisation', in Jochen Garcke and Dirk Pfluger (ed.), Sparse Grids and Applications - Munich 2012, Springer, Switzerland, pp. 317-336.
• Kowitz, C & Hegland, M 2014, 'An Opticom Method for Computing Eigenpairs', in Jochen Garcke and Dirk Pfluger (ed.), Sparse Grids and Applications - Munich 2012, Springer, Switzerland, pp. 239-253.
• Hupp, P, Jacob, R, Heene, M et al. 2014, 'Global Communication Schemes for the Sparse Grid Combination Technique', Advances in Parallel Computing, vol. 25, pp. 564-573.
• Harding, B & Hegland, M 2014, 'A Parallel Fault Tolerant Combination Technique', Advances in Parallel Computing, vol. 25, pp. 584-592.
• Larson, J, Strazdins, P, Hegland, M et al. 2014, 'Managing complexity in the Parallel Sparse Grid Combination Technique', Parallel Computing, vol. 25, pp. 593-602.
• Hegland, M & Khakhutskyy, V 2014, 'Parallel Fitting of Additive Models for Regression', Lecture Notes in Computer Science (LNCS), vol. 8736, pp. 243-254.
• Harding, B & Hegland, M 2014, 'Robust solutions to PDEs with multiple grids', in Jochen Garcke and Dirk Pfluger (ed.), Sparse Grids and Applications - Munich 2012, Springer, Switzerland, pp. 171-193.
• Barnsley, M, Hegland, M & Massopust, P 2014, 'Numerics and Fractals', Bulletin of the Institute of Mathematics, Academia Sinica (New Series), vol. 9, no. 3, pp. 389-430.
• Khakhutskyy, V, Pfluger, D & Hegland, M 2014, 'Scalability and fault tolerance of the alternating direction method of multipliers for sparse grids', Advances in Parallel Computing, vol. 25, pp. 603-612.
• Lamichhane, B, Roberts, S & Hegland, M 2014, 'A new multivariate spline based on mixed partial derivatives and its finite element approximation', Applied Mathematics Letters, vol. 35, pp. 82-85.
• Harding, B & Hegland, M 2013, 'A Robust Combination Technique', ANZIAM Journal, vol. 54, pp. 394-411.
• Lamichhane, B & Hegland, M 2013, 'A Stabilised Mixed Finite Element Method for Thin Plate Splines Based on Biorthogonal Systems', ANZIAM Journal, vol. 54, pp. 72-87.
• Wong, M & Hegland, M 2013, 'Maximum a posteriori density estimation and the sparse grid combination technique', ANZIAM Journal, vol. 54, pp. 508-522pp.
• Kowitz, C, Pflueger, D, Jenko, F et al. 2013, 'The combination technique for the initial value problem in linear gyrokinetics', Lecture Notes in Computer Science (LNCS), vol. 88, pp. 205-222.
• Larson, J, Hegland, M, Harding, B et al. 2013, 'Fault-Tolerant Grid-Based Solvers: Combining Concepts from Sparse Grids and MapReduce', International Conference on Computational Science, ICCS 2013, Elsevier B.V., The Netherlands, pp. 130-139.
• Kowitz, C & Hegland, M 2013, 'The sparse grid combination technique for computing eigenvalues in linear gyrokinetics', International Conference on Computational Science, ICCS 2013, Elsevier B.V., The Netherlands, pp. 449-458.
• Hegland, M & Wasilkowski, G 2013, 'On tractability of approximation in special function spaces', Journal of Complexity, vol. 29, no. 1, pp. 76-91.
• Hegland, M & Leopardi, P 2011, 'The rate of convergence of sparse grid quadrature on the torus', ANZIAM Journal, vol. 52, pp. C500-C517.
• Strazdins, P & Hegland, M 2011, 'Performance Analysis of a Cardiac Simulation Code Using IPM', Scalable algorithms for large-scale systems workshop 2011, ed. Jack Dongarra, Association for Computing Machinery Inc (ACM), New York USA, pp. 29-32.
• Anderssen, S, Hegland, M & Wesley, I 2011, 'Resolution enhancement for infrared spectroscopy data', 19th International Congress on Modelling and Simulation, MODSIM 2011, ed. Felix Chan, Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 371-377.
• Hegland, M & Anderssen, R 2011, 'Dilational interpolatory inequalities', Mathematics of Computation, vol. 80, no. 274, pp. 1019-1036.
• Sunkara, V & Hegland, M 2011, 'Parallelising the finite state projection method', ANZIAM Journal, vol. 52, pp. 853-865.
• Arad, A, Madadi, M, Christy, A et al. 2011, 'Wavelet based solution of flow and diffusion problems in digital materials', Australian and New Zealand Industrial and Applied Mathematics Journal, vol. 52, pp. C678-C695.
• Anderssen, R.S., Hegland, M. and Wesley, I.J. (2011). Resolution enhancement for infrared spectroscopy data. In Chan, F., Marinova, D. and Anderssen, R.S. (eds) MODSIM2011, 19th International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand, December 2011, pp. 371-377. ISBN: 978-0-9872143-1-7. www.mssanz.org.au/modsim2011/A4/anderssen3.pdf
• Hegland, M & Roberts, D 2011, 'Solving variational inequalities using wavelet methods', ANZIAM Journal, vol. 52, pp. C949-C966.
• Hegland, M & Hofmann, B 2011, 'Errors of regularisation under range inclusions using variable Hilbert scales', Inverse Problems and Imaging, vol. 5, no. 3, pp. 619-643.
• Griebel, M & Hegland, M 2010, 'A finite element method for densityestimation with Gaussian process priors', SIAM Journal of Numerical Analysis, vol. 47, no. 6, pp. 4759-4792.
• Anderssen, R & Hegland, M 2010, 'Derivative spectroscopy-An enhanced role for numerical differentiation', Journal of Integral Equations and Applications, vol. 22, no. 3, pp. 355-367.
• Hegland, M 2010, 'Error bounds for spectral enhancement which are based on variable Hilbert scale inequalities', Journal of Integral Equations and Applications, vol. 22, no. 2, pp. 285-312.
• Hegland, M & Garcke, J 2010, 'On the numerical solution of the chemical master equation with sums of rank one tensors', Australian and New Zealand Industrial and Applied Mathematics Journal, vol. 52, pp. C628-C643.
• Sunkara, V & Hegland, M 2010, 'An Optimal Final State Projection Method', Procedia Computer Science, vol. 1, no. 1, pp. 1573-1580.
• Booth, H, Burden, C, Hegland, M et al. 2007, 'A Stochastic Model of Gene Regulation Using the Chemical Master Equation', in Andreas Deutsch, Lutz Brusch, Helen Byrne, Gerda de Vries and (ed.), Mathematical modeling of biological systems, Birkhauser Verlag, Boston, US, pp. 73-84.
• Garcke, J & Hegland, M 2009, 'Fitting multidimensional data using gradient penalties and the sparse grid combination technique', Computing, vol. 84, no. 1-2, pp. 1-25.
• Hegland, M 2009, 'Solving the Chemical Master Equation with the Aggregation-Disaggregation Method', 18th World IMACS Congress and International Congress on Modelling and Simulation: Interfacing Modelling and Simulation with Mathematical and Computational Sciences, MODSIM 2009, ed. R S Anderssen, R D Braddock & L T H Newham , Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 691 - 696.
• Detering PhD, F, Blackwell, B, Hegland, M et al. 2008, 'Reduction of magnetic confinement fusion data for data mining', Computational Techniques and Applications Conference (CTAC 2008), ed. Conference Program Committee, Australia and New Zealand Industrial and Applied Mathematics (ANZIAM), Canberra, pp. C729-C743.
• Garcke, J & Hegland, M 2008, 'Fitting Multidimensional Data Using Gradient Penalties and Combination Techniques', International Conference on High Performance Scientific Computing (HPSC 2006), ed. Hans Georg Bock, Ekaterina Kostina, Hoang Xuan Phy, Rolf Rannacher, Springer, Berlin, Germany, pp. 235-248.
• Khoo, C & Hegland, M 2008, 'The total quasi-steady state assumption: its justification by singular perturbation theory and its application to the chemical master equation', ANZIAM Journal, vol. 50, pp. C429-C443.
• Hegland, M 2008, 'Approximating the solution of the chemical master equation by aggregation', ANZIAM Journal, vol. 50, no. SUPPL., pp. C371-C384.
• Hegland, M, Hellander, A & Lotstedt, P 2008, 'Sparse grids and hybrid methods for the chemical master equation', BIT: Numerical mathematics (Lisse), vol. 48, no. 2, pp. 265-283.
• Hegland, M, Burden, C & Santoso, L 2008, 'Modelling Gene Regulatory Networks Using Galerkin Techniques Based on State Space Aggregation and Sparse Grids', International Conference on High Performance Scientific Computing (HPSC 2006), ed. Hans Georg Bock, Ekaterina Kostina, Hoang Xuan Phy, Rolf Rannacher, Springer, Berlin, Germany, pp. 259-272.
• Blackwell, B, Pretty, D, Howard, J et al. 2008, 'Configurational Effects on Stability and Confinement in the H-1NF Heliac', International Atomic Energy Agency Fusion Energy Conference (FEC 2008), International Atomic Energy Agency (IAEA), Geneva.
• Hegland, M & Griebel, M 2007, 'Variational problems in machine learning and their solution with finite elements', ANZIAM Journal, vol. 48, pp. 381-396.
• Hegland, M, Burden, C, Santoso, L et al. 2007, 'A Solver for the Stochastic Master Equation Applied to Gene Regulatory Networks', Journal of Computational and Applied Mathematics, vol. 205, pp. 708-724.
• Hegland, M, Garcke, J & Challis, V 2007, 'The combination technique and some generalisations', Linear Algebra and its Applications, vol. 420, pp. 249-275.
• Burrage, K, Hegland, M, MacNamara, S et al. 2006, 'A Krylov-based Finite State Projection algorithm for solving the chemical master equation arising in the discrete modelling of biological systems', in Langville, Stewart (ed.), Markov Anniversary Meeting An International Conference to celebrate the 150th Anniversary of the birth of A. A. Markov, Boson Books, USA, pp. 21-38.
• Hegland, M 2006, 'An Approximate Maximum a Posteriori Method with Gaussian Process Priors', in Bron, Liu, Sharma (ed.), Contributions to Probability and Statistics: Applications and Challenges. Proceedings of the International Statistics Workshop, World Scientific Publishing Company, Singapore, pp. 261-275.
• Garcke, J, Hegland, M & Nielsen, O 2006, 'Parallelisation of sparse grids for large scale data analysis', ANZIAM Journal, vol. 48, pp. 11-22.
• Blackwell, B, Pretty, D, Harris, J et al. 2006, 'Observations of Alfvenic MHD Activity in the H-1 Heliac', International Atomic Energy Agency Fusion Energy Conference (FEC 2006), Conference Organising Committee, Website, p. 8.
• Booth, H, Burden, C, Hegland, M et al. 2005, 'Markov process modelling of gene regulation', Australian Mathematical Society Gazette, vol. 32, no. 1, pp. 31-41.
• Hegland, M & Anderssen, R 2005, 'Resolution enhancement of spectra using differentiation', Inverse Problems, vol. 21, pp. 915-934.
• Laffan, S, Nielsen, O, Silcock, H et al. 2005, 'Sparse grids: a new predictive modelling method for the analysis of geographic data', International Journal of Geographical Information Science, vol. 19, no. 3, pp. 267-292.
• Hegland, M & Pestov, V 2005, 'Additive models in high dimensions', ANZIAM Journal, vol. 46, pp. C1205-C1221.
• Hegland, M & Pozzi, P 2005, 'Concentration of measure and the approximation of functions of many variables', Mathematical Methods for Curves and Surfaces, ed. Conference Program Committee, Nashboro Press Inc, USA, pp. 199-212.
• Santoso, L, Booth, H, Burden, C et al. 2005, 'A stochastic model of gene switches', ANZIAM Journal, vol. 46, pp. C530-543.
• Hegland, M, Nielsen, O & Shen, Z 2004, 'Multidimensional smoothing using hyperbolic interpolatory wavelets', Electronic Transactions on Numerical Analysis, vol. 17, pp. 168-180.
• Semenova, T, Hegland, M, Graco, W et al. 2004, 'Conceptual mining of large administrative health data', Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD 2004), ed. Honghua Dai, Ramakrishnan Srikant & Chengqi Zhang, Springer, Germany, pp. 659-669.
• Christen, P, Churches, T & Hegland, M 2004, 'Febrl - A Parallel Open Source Data Linkage System', Pacific Asia Conference on Knowledge Discovery and Data Mining (PAKDD 2004), ed. Honghua Dai, Ramakrishnan Srikant & Chengqi Zhang, Springer, Germany, pp. 638-647.
• Hegland, M & Laffan, S 2003, 'Mining geographical data with sparse grids', Australasian Data Mining Conference (AusDM 2003), ed. Simeon J. Simoff, Graham J. Williams and Markus Hegland, Unknown, Sydney, Australia, pp. 163-180.
• Hegland, M, Nielsen, O & Garcke, J 2003, 'Parallelisation of sparse grids for large scale data analysis', International Conference on Computational Science (ICCS 2003), ed. P.M.A. Sloot, D. Abramson, A.V. Bogdanov, J.J. Dongarra, A.Y. Zomaya, Y.E. Gorba, Springer, Berlin, pp. 683-692.
• Boskovitz, A, Gore, R & Hegland, M 2003, 'A Logical Formalisation of the Fellegi-Holt Method of Data Cleaning', International Symposium on Intelligent Data Analysis (IDA 2003), ed. Berthold, Lenz, Bradley, Kruse, Borgelt, Springer, Berlin, pp. 554-565.
• Roberts, S, Hegland, M & Altas, I 2003, 'Approximation of a Thin Plate Spline Smoother using Continuous Piecewise Polynomial Functions', SIAM Journal of Numerical Analysis, vol. 41, no. 1, pp. 208-234.
• Hegland, M 2003, 'Adaptive sparse grids', ANZIAM Journal, vol. 44, no. E, pp. C335-C353.
• Hegland, M & Kahn, M 2003, 'Predictive modelling with sparse grids', APAC Conference and Exhibition on Advanced Computing, Grid Applications and eResearch, ed. Joseph Young and Rajesh Chhabra, Australian Partnership for Advanced Computing, Australia, p. 13.
• Hegland, M 2003, 'Additive sparse grid fitting', International Conference on Curves and Surfaces 2002, ed. Albert Cohen, Jean-Louis Merrien and Larry L. Schumaker, Nashboro Press Inc, TN, USA, pp. 209-218.
• Hegland, M, Laffan, S, Nielsen, O et al. 2003, 'Sparse Grids: A New Tool for Analysing Geographic Data', International Conference on GeoComputation 2003, ed. D Martin, GeoComputation, UK, pp. 2 total.
• Laffan, S, Silcock, H, Nielsen, O et al. 2003, 'A new approach to analysing spatial data using sparse grids', International Congress on Modelling and Simulation (MODSIM 2003), ed. David A. Post, Modelling and Simulation Society of Australia and New Zealand Inc., UWA UniPrint, pp. 708-712.
• Hegland, M 2003, 'Algorithms for Association Rules', in Shahar Mendelson and Alexander J. Smola (ed.), Advanced Lectures on Machine Learning, Springer, Germany, pp. 226-234.
• Nielsen, O, Christen, P, Hegland, M et al. 2001, 'A Toolbox Approach to Flexible and Efficient Data Mining', in D. Cheung, G. Williams, Li Q (ed.), Advances in Knowledge Discovery and Data Mining (2001), Springer, Berlin, pp. 124-135.
• Hawkins, S, Williams, G, Baxter, R et al. 2001, 'Data Mining of Administrative Claims Data of Pathology Services', Hawaii International Conference on System Sciences 2001, ed. Ralph H Sprague, Institute of Electrical and Electronics Engineers (IEEE Inc), online http://www.computer.org/proceedings/hicss/0981/0981toc.html.
• Hegland, M, Clarke, W & Kahn, M 2001, 'Mining the MACHO dataset', Computer Physics Communications, vol. 142, no. 1-3, pp. 22-28.
• Nielsen, O, Christen, P, Hegland, M et al. 2001, 'Data Mining with Python', 9th International Python Conference, ed. van Rossum, Foretec Seminars, Restn, USA, pp. 225-232.
• Christen, P, Nielsen, O, Hegland, M et al. 2001, 'Parallel Data Mining on a Beowulf Cluster', International Conference and Exhibition on High Performance Computing in the Asia-Pacific Region HPC Asia 2001, ed. Joseph Young, Australian Partnership for Advanced Computing, Australia.
• Christen, P, Nielsen, O & Hegland, M 2001, 'DMtools - Open Source Software for Database Mining', PKDD-Workshop on Database Support for KDD 2001, ed. Gunter Saake, Kai-Uwe Sattler, Springer, Germany, pp. 27-38.
• Hegland, M 2001, 'Data mining techniques', in Iserles, A (ed.), Acta Numerica, Cambridge University Press, Cambridge, United Kingdom, pp. 313-355.
• Christen, P, Hegland, M, Nielsen, O et al. 2001, 'Scalable parallel algorithms for surface fitting and data mining', Parallel Computing, vol. 27, pp. 941-961.
• Hegland, M, Osborne, M & Sun, J 2001, 'Parallel Interior Point Schemes for Solving Multistage Convex Programming', Annals of Operations Research, vol. 108, no. 1-4, pp. 75-85.
• Christen, P, Hegland, M, Nielsen, O et al. 2001, 'Towards a Parallel Data Mining Toolbox', International Workshop on Parallel and Distributed Data Mining in conjunction with International Parallel and Distributed Processing Symposium (IPDPS 2001), ed. Pradip Srimani, Institute of Electrical and Electronics Engineers (IEEE Inc), Piscataway, USA.
• Hegland, M, Hooker, G & Roberts, S 2000, 'Finite Element Thin Plate Splines in Density Estimation', ANZIAM Journal, vol. 42, pp. C712-C734.
• Bakin, S, Hegland, M & Williams, G 2000, 'Mining Taxation Data with Parallel BMARS1', Parallel Algorithms and Applications, vol. 15, pp. 37-55.
• Christen, P, Hegland, M, Nielsen, O et al. 2000, 'Algorithms for Predictive Modelling', IEEE International Conference on Data Mining (ICDM 2000), ed. Ebecken, N and Brebbia, CA, WIT Press, Southampton, UK, pp. 423-434.
• Hegland, M, McIntosh, I & Turlach, B 1999, 'A Parallel Solver for Generalised Additive Models', Computational Statistics and Data Analysis, vol. 31, pp. 377-396.

Projects and Grants

Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.

• Solving inverse problems with Iterative regularisation and convex penalties (Secondary Investigator)
• Theory and Applications of Three Dimensional Fractal Transformations (Secondary Investigator)
• Robust numerical solution of partial differential equations on petascale computer systems with applications to tsunami modelling and plasma physics (Primary Investigator)
• Hybrid and heterogeneous computing models in computational science (Primary Investigator)
• Australian Centre of Excellent in Bioinformatics (Primary Investigator)