Professor Diane Donovan received her PhD from The University of Queensland in 1987 and has been an integral member of the Discipline of Mathematics and assoicated Schools since that time.
She has two main research streams.
1) The application of polynomial chaos expansions for the modeling of physical problems involving uncertain parameters. We are developing methods to accurately and efficiently explore subsurface geometry. The current work is focussed on problems related to groundwater levels, gas extraction and storage. This work is joint with the Centre for Coal Seam Gas at the University of Queensland.
2) The study of mathematics structures, both discrete and continuous, and their applications to problems in science and engineering. Of particular interest is the development and testing of methods for robust sampling techniques. This interests is supported by a long history of publishing on experimental design, block designs, latin squares and associated algebraic structures.
Collaborative research with Australian energy companies developing techniques for production forecasting
Collaborative research with Plant geneticists studying environmental effects on plants in agriculture and nature.
Journal Article: Applying hypergraphs to studies in quantitative biology
Barton, Samuel, Coster, Adelle, Donovan, Diane and Lefevre, James (2024). Applying hypergraphs to studies in quantitative biology. LIFE: International Journal of Health and Life-Sciences, 9, 21-33. doi: 10.20319/lijhls.2024.9.2133
Journal Article: Hypergraphs and centrality measures identifying key features in gene expression data
Barton, Samuel, Broad, Zoe, Ortiz-Barrientos, Daniel, Donovan, Diane and Lefevre, James (2023). Hypergraphs and centrality measures identifying key features in gene expression data. Mathematical Biosciences, 366 109089, 109089. doi: 10.1016/j.mbs.2023.109089
Journal Article: On maximal partial Latin hypercubes
Donovan, Diane M., Grannell, Mike J. and Yazıcı, Emine Şule (2023). On maximal partial Latin hypercubes. Designs, Codes and Cryptography, 92 (2), 419-433. doi: 10.1007/s10623-023-01314-5
ARC Centre of Excellence for Plant Success in Nature and Agriculture
(2020–2027) ARC Centres of Excellence
Advanced mathematical modelling for early assessment of fracced wells' production performance
(2019–2020) Origin Energy Limited
Uncertainty modelling with polynomial chaos expansion
(2015–2017) QGC Pty Limited
Pure and Applied Applications of Combinatorial Mathematics
Doctor Philosophy
Modelling Biological Systems using Mathematical Networks
Doctor Philosophy
Latin Squares and Related Structures
(2016) Doctor Philosophy
Topics in Combinatorics
Modelling and simulation problems for water/gas reservoir estimation
Experimental design for problems in geosciences and petroleum engineering
The study of orthogonal designs for enhanced computer experiments, with particular the study of quasigroups, orthogonal latin squares and orthogonal arrays
The study of trades and their use in establishing existence results for discrete structures
The studey of networks in plant genetics
Dawson, Ed and Donovan, Diane (1993). Shamir's scheme says it all. Publ by Elsevier Science Publishers B.V..
Defining sets in combinatorics: a survey
Donovan, D. M., Mahmoodian, E., Ramsay, C. and Street, A. P. (2003). Defining sets in combinatorics: a survey. Surveys in Combinatorics 2003. (pp. 115-174) edited by C.D. Wensley. UK: Cambridge University Press.
On minimal defining sets in AG( D, 3)
Donovan, D. M., Khodkar, A. and Street, A. P. (2003). On minimal defining sets in AG( D, 3). Designs 2002: Further Computational and Constructive Design Theory. (pp. 103-131) edited by W.D. Wallis. Massachusetts, USA: Kluwer Academic Press. doi: 10.1007/978-1-4613-0245-2_6
Applying hypergraphs to studies in quantitative biology
Barton, Samuel, Coster, Adelle, Donovan, Diane and Lefevre, James (2024). Applying hypergraphs to studies in quantitative biology. LIFE: International Journal of Health and Life-Sciences, 9, 21-33. doi: 10.20319/lijhls.2024.9.2133
Hypergraphs and centrality measures identifying key features in gene expression data
Barton, Samuel, Broad, Zoe, Ortiz-Barrientos, Daniel, Donovan, Diane and Lefevre, James (2023). Hypergraphs and centrality measures identifying key features in gene expression data. Mathematical Biosciences, 366 109089, 109089. doi: 10.1016/j.mbs.2023.109089
On maximal partial Latin hypercubes
Donovan, Diane M., Grannell, Mike J. and Yazıcı, Emine Şule (2023). On maximal partial Latin hypercubes. Designs, Codes and Cryptography, 92 (2), 419-433. doi: 10.1007/s10623-023-01314-5
QC-LDPC codes from difference matrices and difference covering arrays
Donovan, Diane M., Rao, Asha, Üsküplü, Elif and Yazici, E. Şule (2023). QC-LDPC codes from difference matrices and difference covering arrays. IEEE Access, 11, 52141-52157. doi: 10.1109/access.2023.3279327
Probabilistic mathematical modelling to predict the red cell phenotyped donor panel size
Best, Denisse, Burrage, Kevin, Burrage, Pamela, Donovan, Diane, Ginige, Shamila, Powley, Tanya, Thompson, Bevan and Daly, James (2022). Probabilistic mathematical modelling to predict the red cell phenotyped donor panel size. PLoS One, 17 (11) e0276780, 1-15. doi: 10.1371/journal.pone.0276780
Donovan, Diane, Azadi, Mohsen, Ganpule, Sameer, Nuralishahi, Turaj, Smith, Andrew, Josserand, Sylvain, Thompson, Bevan, Reay, Thomas, Gay, Laura, Burrage, Kevin, Burrage, Pamela, Lawson, Brodie and Yazıcı, Emine (2022). Improved learning cycle assessment of stimulated wells’ performance through advanced mathematical modeling. SPE Journal, 27 (3), 1729-1743. doi: 10.2118/209222-PA
High-rate LDPC codes from partially balanced incomplete block designs
Donovan, Diane, Price, Aiden, Rao, Asha, Üsküplü, Elif and ŞYazıcı, Emine (2022). High-rate LDPC codes from partially balanced incomplete block designs. Journal of Algebraic Combinatorics, 55 (1), 259-275. doi: 10.1007/s10801-021-01111-0
Anti‐Pasch optimal coverings with triples
Demirkale, Fatih, Donovan, Diane and Grannell, Mike (2021). Anti‐Pasch optimal coverings with triples. Journal of Combinatorial Designs, 29 (2), 84-113. doi: 10.1002/jcd.21758
Biembeddings of cycle systems using integer Heffter arrays
Cavenagh, Nicholas J., Donovan, Diane M. and Yazıcı, Emine Ş. (2020). Biembeddings of cycle systems using integer Heffter arrays. Journal of Combinatorial Designs, 28 (12), 900-922. doi: 10.1002/jcd.21753
Embedding partial Latin squares in Latin squares with many mutually orthogonal mates
Donovan, Diane, Grannell, Mike and Yazıcı, Emine Şule (2020). Embedding partial Latin squares in Latin squares with many mutually orthogonal mates. Discrete Mathematics, 343 (6) 111835, 111835. doi: 10.1016/j.disc.2020.111835
Globally simple Heffter arrays H(n;k) when k≡0,3(mod4)
Burrage, Kevin, Donovan, Diane M., Cavenagh, Nicholas J. and Yazıcı, Emine Ş. (2020). Globally simple Heffter arrays H(n;k) when k≡0,3(mod4). Discrete Mathematics, 343 (5) 111787, 111787. doi: 10.1016/j.disc.2019.111787
Maximum partial triple systems on 16 and 17 points
Demirkale, Fatih, Donovan, Diane and Grannell, Mike (2020). Maximum partial triple systems on 16 and 17 points. Utilitas Mathematica, 114, 255-276.
Anti-Pasch optimal packings with triples
Demirkale, Fatih, Donovan, Diane and Grannell, Mike (2019). Anti-Pasch optimal packings with triples. Journal of Combinatorial Designs, 27 (6), 353-368. doi: 10.1002/jcd.21646
Chip-firing on a graph for modelling complex geological architecture in CO2 injection and storage
McCourt, Thomas A., Zhou, Fengde, Bianchi, Valeria, Pike, David and Donovan, Diane (2019). Chip-firing on a graph for modelling complex geological architecture in CO2 injection and storage. Transport in Porous Media, 129 (1), 281-294. doi: 10.1007/s11242-019-01287-x
The enumeration of cyclic mutually nearly orthogonal Latin squares
Demirkale, Fatih, Donovan, Diane M., Kokkala, Janne I. and Marbach, Trent G. (2019). The enumeration of cyclic mutually nearly orthogonal Latin squares. Journal of Combinatorial Designs, 27 (5), 265-276. doi: 10.1002/jcd.21647
McCourt, Thomas A., Blackmore, Ryan, Rodger, Iain, Hurter, Suzanne, Thompson, Bevan, Reilly, Mark and Donovan, Diane (2019). Proxy modelling for multi-well simulations: enabling identification of major input variables and reduced computation time over Monte Carlo sampling. The APPEA Journal, 59 (1), 444-456. doi: 10.1071/aj18065
The existence of square non-integer Heffter arrays
Cavenagh, Nicholas J., Dinitz, Jeff, Donovan, Diane M. and Yazic, Emine Sule (2019). The existence of square non-integer Heffter arrays. Ars Mathematica Contemporanea, 17 (2), 369-395. doi: 10.26493/1855-3974.1817.b97
Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal Array-based sampling
Donovan, D., Burrage, K., Burrage, P., McCourt, T. A., Thompson, B. and Yazici, E. S. (2018). Estimates of the coverage of parameter space by Latin Hypercube and Orthogonal Array-based sampling. Applied Mathematical Modelling, 57, 553-564. doi: 10.1016/j.apm.2017.11.036
On the number of additive permutations and Skolem-type sequences
Donovan, Diane M. and Grannell, Michael J. (2018). On the number of additive permutations and Skolem-type sequences. Ars Mathematica Contemporanea, 14 (2), 415-432.
Types of directed triple systems
Donovan, Diane M., McCourt, Thomas A., Griggs, Terry S. and Kozlik, Andrew R. (2018). Types of directed triple systems. Australasian Journal of Combinatorics, 71 (3), 485-500.
On the number of additive permutations and Skolem-type sequences
Donovan, Diane M. and Grannell, Michael J. (2017). On the number of additive permutations and Skolem-type sequences. Ars Mathematica Contemporanea, 14 (2), 415-432. doi: 10.26493/1855-3974.1098.ca0
On the number of transversals in a class of Latin squares
Donovan, Diane M. and Grannell, Mike J. (2017). On the number of transversals in a class of Latin squares. Discrete Applied Mathematics, 235, 202-205. doi: 10.1016/j.dam.2017.08.021
Uncertainty quantification of coal seam gas production prediction using Polynomial Chaos
McCourt, Thomas A., Hurter, Suzanne, Lawson, Brodie, Zhou, Fengde, Thompson, Bevan, Tyson, Stephen and Donovan, Diane (2017). Uncertainty quantification of coal seam gas production prediction using Polynomial Chaos. Journal of Petroleum Science and Engineering, 157, 1148-1159. doi: 10.1016/j.petrol.2017.08.012
Orthogonal trades in complete sets of MOLS
Cavenagh, Nicholas J., Donovan, Diane M. and Demirkale, Fatih (2017). Orthogonal trades in complete sets of MOLS. Electronic Journal of Combinatorics, 24 (3) #P3.15, 1-15. doi: 10.37236/6338
Difference covering arrays and pseudo-orthogonal latin squares
Demirkale, Fatih, Donovan, Diane, Hall, Joanne, Khodkar, Abdollah and Rao, Asha (2016). Difference covering arrays and pseudo-orthogonal latin squares. Graphs and Combinatorics, 32 (4), 1353-1374. doi: 10.1007/s00373-015-1649-8
Distributive and anti-distributive Mendelsohn triple systems
Donovan, Diane M., Griggs, Terry S., McCourt, Thomas A., Oprsal, Jakub and Stanovsky, David (2016). Distributive and anti-distributive Mendelsohn triple systems. Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 59 (1), 36-49. doi: 10.4153/CMB-2015-053-2
Permanents and determinants of latin squares
Donovan, Diane, Johnson, Kenneth and Wanless, Ian M. (2016). Permanents and determinants of latin squares. Journal of Combinatorial Designs, 24 (3), 132-148. doi: 10.1002/jcd.21418
A simple approach to constructing quasi-Sudoku-based sliced space-filling designs
Donovan, Diane, Haaland, Benjamin and Nott, David J. (2016). A simple approach to constructing quasi-Sudoku-based sliced space-filling designs. Annals of the Institute of Statistical Mathematics, 69 (4), 1-14. doi: 10.1007/s10463-016-0565-x
Orthogonal trades and the intersection problem for orthogonal arrays
Demirkale, Fatih, Donovan, Diane M., Küçükçifçi, Selda and Yazici, Emine Şule (2015). Orthogonal trades and the intersection problem for orthogonal arrays. Graphs and Combinatorics, 32 (3), 1-10. doi: 10.1007/s00373-015-1638-y
Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares
Demirkale, Faith, Donovan, Diane and Khodkar, Abdollah (2015). Direct constructions for general families of cyclic mutually nearly orthogonal Latin squares. Journal of Combinatorial Designs, 23 (5), 195-203. doi: 10.1002/jcd.21394
Intersection problem for simple 2-fold (3n, n, 3) group divisible designs
Demirkale, Fatih, Donovan, Diane and Lindner, C. C. (2015). Intersection problem for simple 2-fold (3n, n, 3) group divisible designs. Graphs and Combinatorics, 31 (3), 537-545. doi: 10.1007/s00373-013-1397-6
Further biembeddings of twofold triple systems
Donovan, Diane M., Griggs, Terry S., Lefevre, James G. and McCourt, Thomas A. (2015). Further biembeddings of twofold triple systems. Ars Mathematica Contemporanea, 8 (2), 267-273. doi: 10.26493/1855-3974.415.ecd
Square integer Heffter arrays with empty cells
Archdeacon, D. S., Dinitz, J. H., Donovan, D. M. and Yazici, E. S. (2015). Square integer Heffter arrays with empty cells. Designs, Codes, and Cryptography, 77 (2-3), 409-426. doi: 10.1007/s10623-015-0076-4
A polynomial embedding of pairs of orthogonal partial Latin squares
Donovan, Diane M. and Sule Yazici, Emine (2014). A polynomial embedding of pairs of orthogonal partial Latin squares. Journal of Combinatorial Theory. Series A, 126 (1), 24-34. doi: 10.1016/j.jcta.2014.04.003
On the number of transversal designs
Donovan, D. M. and Grannell, M. J. (2013). On the number of transversal designs. Journal of Combinatorial Theory Series A, 120 (7), 1562-1574. doi: 10.1016/j.jcta.2013.05.004
Constructing D-optimal symmetric stated preference discrete choice experiments
Demirkale, Fatih, Donovan, Diane and Street, Deborah J. (2013). Constructing D-optimal symmetric stated preference discrete choice experiments. Journal of Statistical Planning and Inference, 143 (8), 1380-1391. doi: 10.1016/j.jspi.2013.02.004
Simple 2-fold (3n, n, 3) group divisible designs having a prescribed number of triples in common
Demirkale, Fatih, Donovan, Diane and Lindner, C. C. (2013). Simple 2-fold (3n, n, 3) group divisible designs having a prescribed number of triples in common. Electronic Notes in Discrete Mathematics, 40, 107-111. doi: 10.1016/j.endm.2013.05.020
Donovan, Diane and Loch, Birgit (2013). Closing the feedback loop: engaging students in large first-year mathematics test revision sessions using pen-enabled screens. International Journal of Mathematical Education in Science and Technology, 44 (1), 1-13. doi: 10.1080/0020739X.2012.678898
Cyclic Biembeddings of Twofold Triple Systems
Donovan, Diane M., Griggs, Terry S., Lefevre, James G. and McCourt, Thomas A. (2013). Cyclic Biembeddings of Twofold Triple Systems. Annals of Combinatorics, 18 (1), 57-74. doi: 10.1007/s00026-013-0211-8
On biembedding an idempotent latin square with its transpose
Donovan D.M., Griggs T.S. and Psomas C. (2013). On biembedding an idempotent latin square with its transpose. Acta Mathematica Universitatis Comenianae, 82 (1), 11-20.
On the existence of 3-way k-homogeneous Latin trades
Gh, Behrooz Bagheri, Donovan, Diane and Mahmoodian, E. S. (2012). On the existence of 3-way k-homogeneous Latin trades. Discrete Mathematics, 312 (24), 3473-3481. doi: 10.1016/j.disc.2012.08.020
Defining Sets of Full Designs with Block Size Three II
Donovan, Diane, Lefevre, James, Waterhouse, Mary and Yazici, Emine Sule (2012). Defining Sets of Full Designs with Block Size Three II. Annals of Combinatorics, 16 (3), 507-515. doi: 10.1007/s00026-012-0143-8
On the number of designs with affine parameters
Donovan, D. M. and Grannell, M. J. (2012). On the number of designs with affine parameters. Designs Codes and Cryptography, 63 (1), 15-27. doi: 10.1007/s10623-011-9528-7
Distinct equilateral triangle dissections of convex regions
Donovan, Diane M., Lefevre, James G., McCourt, Thomas A. and Cavenagh, Nicholas J. (2012). Distinct equilateral triangle dissections of convex regions. Commentationes Mathematicae Universitatis Carolinae, 53 (2), 189-210.
Identifying flaws in the security of critical sets in latin squares via triangulations
Donovan, Diane M., Lefevre, James G., McCourt, Thomas A., Cavenagh, Nicholas J. and Khodkar, Abdollah (2012). Identifying flaws in the security of critical sets in latin squares via triangulations. Australasian Journal of Combinatorics, 52, 243-268.
The triangle intersection problem for nested Steiner triple systems
Billington, Elizabeth J., Donovan, Diane, Lefevre, James, McCourt, Thomas and Lindner, C. C. (2011). The triangle intersection problem for nested Steiner triple systems. Australasian Journal of Combinatorics, 51, 221-233.
Designs having the parameters of projective and affine spaces
Donovan, D. M. and Grannell, M. J. (2011). Designs having the parameters of projective and affine spaces. Designs, Codes and Cryptography, 60 (3), 225-240. doi: 10.1007/s10623-010-9429-1
Self-embeddings of cyclic and projective Steiner quasigroups
Donovan, Diane M., Grannell, Mike J., Griggs, Terry S., Lefevre, James G. and McCourt, Thomas (2011). Self-embeddings of cyclic and projective Steiner quasigroups. Journal of Combinatorial Designs, 19 (1), 16-27. doi: 10.1002/jcd.20258
Rao, Asha, Donovan, Diane and Hall, Joanne L. (2010). Mutually orthogonal Latin squares and mutually unbiased bases in dimensions of odd prime power: MOLS and MUBs in odd prime power dimensions. Cryptography and Communications, 2 (2), 221-231. doi: 10.1007/s12095-010-0027-x
On parity vectors of Latin squares
Donovan, D. M., Grannell, M. J., Griggs, T. S. and Lefevre, J. G. (2010). On parity vectors of Latin squares. Graphs and Combinatorics, 26 (5), 673-684. doi: 10.1007/s00373-010-0942-9
Third-regular bi-embeddings of Latin squares
Donovan, D. M., Grannell, M. J. and Griggs, T. S. (2010). Third-regular bi-embeddings of Latin squares. Glasgow Mathematical Journal, 52 (3), 497-503. doi: 10.1017/S0017089510000376
Quarter-regular biembeddings of Latin squares
Donovan, D. M., Drápal, A., Grannell, M. J., Griggs, T. S. and Lefevre, J. G. (2010). Quarter-regular biembeddings of Latin squares. Discrete Mathematics, 310 (4), 692-699. doi: 10.1016/j.disc.2009.08.020
On defining sets of full designs with block size three
Donovan, D., Lefevre, J., Waterhouse, M. and Yazici, E. S. (2009). On defining sets of full designs with block size three. Graphs and Combinatorics, 25 (6), 825-839. doi: 10.1007/s00373-010-0882-4
A constraint on the biembedding of Latin squares
Lefevre, J. G., Donovan, D. M., Grannell, M. J. and Griggs, T. S. (2009). A constraint on the biembedding of Latin squares. European Journal of Combinatorics, 30 (2), 380-386. doi: 10.1016/j.ejc.2008.05.007
Minimal Defining Sets of 1-Factorizations of Complete Graphs
Cavenagh, N. J., Donovan, D. and Khodkar, A. (2008). Minimal Defining Sets of 1-Factorizations of Complete Graphs. Utilitas Mathematica, 76, 191-211.
Minimal homogeneous Steiner 2-(v,3) trades
Cavenagh, N. J., Donovan, D. M. and Yazici, E. S. (2008). Minimal homogeneous Steiner 2-(v,3) trades. Discrete Mathematics, 308 (5-6), 741-752. doi: 10.1016/j.disc.2007.07.060
On the spectrum of critical sets in latin squares of order 2n
Donovan, D. M., Lefevre, J. G. and Van Rees, G. H. J. (2008). On the spectrum of critical sets in latin squares of order 2n. Journal of Combinatorial Designs, 16 (1), 25-43. doi: 10.1002/jcd.20144
Packing a complete graph of order 5 (mod 6) with triangles: a new method
Billington, Elizabeth J., Donovan, Diane M. and Smith, Nicole (2008). Packing a complete graph of order 5 (mod 6) with triangles: a new method. Bulletin of the Institute of Combinatorics and its Applications, 53, 77-81.
When is a partial Latin square uniquely completable, but not its completable product?
Cavenagh, N. J., Donovan, D. M., Khodkar, A. and Van Rees, J. (2008). When is a partial Latin square uniquely completable, but not its completable product?. Discrete Mathematics, 308 (13), 2830-2843. doi: 10.1016/j.disc.2006.06.046
Minimal and minimum size latin bitrades of each genus
Lefevre, J. G., Donovan, D. M., Cavenagh, N. and Drapal, A. (2007). Minimal and minimum size latin bitrades of each genus. Commentationes Mathematicae Universitatis Carolinae, 48 (2), 189-203.
On the spectrum of critical sets in back circulant latin squares
Cavenagh, N. J., Donovan, D. M. and Khodkar, A. (2007). On the spectrum of critical sets in back circulant latin squares. Ars Combinatoria, 82, 287-319.
Seeking solutions to Suduko squares
Donovan, D. M., Hamalainen, C. and Street, A. P. (2007). Seeking solutions to Suduko squares. Pi in the Sky, 10, 7-12.
Minimal Homogeneous Latin Trades
Cavenagh, N. J., Donovan, D. M. and Yazici, E. S. (2006). Minimal Homogeneous Latin Trades. Discrete Mathematics, 306 (17), 2047-2055. doi: 10.1016/j.disc.2006.05.006
Cavenagh, N., Donovan, D. M. and Drapal, A. (2005). 3-Homogeneous latin trades. Discrete Mathematics, 300 (1-3), 57-70. doi: 10.1016/j.disc.2005.04.021
Cavenagh, N. J., Donovan, D. M. and Drapal, A. (2005). 4-homogeneous latin trades. Australasian Journal of Combinatorics, 32, 285-303.
A new class of critical sets in Latin squares
Cavenagh, NJ, Donovan, D and Gower, RAH (2005). A new class of critical sets in Latin squares. Utilitas Mathematica, 67 (-), 285-300.
Constructing and Deconstructing Latin Trades
Nicholas Cavenagh, Diane Donovan and Ales Drapal (2004). Constructing and Deconstructing Latin Trades. Discrete Mathematics, 284 (1-3), 97-105. doi: 10.1016/j.disc.2003.11.026
An investigation of 2-critical sets in latin squares
Donovan, Diane, Fu, Chin-Mei and Khodkar, Abdollah (2004). An investigation of 2-critical sets in latin squares. Ars Combinatoria, 72, 223-234.
Labelings of unions of up to four uniform cycles
Donovan, D. M., El-Zanati, S. I., Vanden Eynden, C. and Sutinuntopas, S. (2004). Labelings of unions of up to four uniform cycles. Australasian Journal of Combinatorics, 29, 323-336.
Uniform critical sets in Latin squares
Donovan, D. M. and Khodkar, A. (2004). Uniform critical sets in Latin squares. Journal of Combinatorial Mathematics and Combinatorial Computing, 48, 3-23.
Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems
Donovan, Diane, Khodkar, Abdollah and Street, Anne Penfold (2003). Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems. Graphs and Combinatorics, 19 (1), 65-89. doi: 10.1007/s00373-002-0485-9
Product constructions for critical sets in latin squares
Donovan, D. M. and Khodkar, A. (2003). Product constructions for critical sets in latin squares. Journal of Combinatorial Mathematics and Combinatorial Computing, 46, 227-254.
A note on critical sets in latin squares of order 2n-1
Donovan, D. M., Khodkar, A., Sutinuntopas, S. and Thappia, S. (2002). A note on critical sets in latin squares of order 2n-1. Congressus Numerantium: a conference journal of numerical themes, 79 (12), 215-219.
An algorithm for writing any Latin interchange as a sum of intercalates
Donovan, D. M. and Mahmoodian, E. (2002). An algorithm for writing any Latin interchange as a sum of intercalates. Bulletin of the Institute of Combinatorics and its Applications, 34, 90-98.
Latin interchanges and direct products
Donovan, D, Gower, RAH and Khodkar, A (2002). Latin interchanges and direct products. Ars Combinatoria, 64, 271-287.
Steiner trades that give rise to completely decomposable latin interchanges
Bean, Richard, Donovan, Diane, Khodkar, Abdollah and Street, Anne Penfold (2002). Steiner trades that give rise to completely decomposable latin interchanges. International Journal of Computer Mathematics, 79 (12), 1273-1284. doi: 10.1080/00207160214654
Closing a gap in the spectrum of critical sets
Bean, R. and Donovan, D. M. (2000). Closing a gap in the spectrum of critical sets. Australasian Journal of Combinatorics, 22, 191-200.
The completion of partial latin squares
Donovan, D. M. (2000). The completion of partial latin squares. Australasian Journal of Combinatorics, 22, 247-264.
Towards the spectrum of critical sets
Donovan, D. M. and Howse, A. (2000). Towards the spectrum of critical sets. Australasian Journal of Combinatorics, 21, 107-130.
Critical sets in Latin squares of order less than 11
Donovan, D. M. (1999). Critical sets in Latin squares of order less than 11. Journal of Combinatorial Mathematics and Combinatorial Computing, 29, 223-240.
Critical sets for families of Latin squares
Donovan, D (1998). Critical sets for families of Latin squares. Utilitas Mathematica, 53, 3-16.
On the distance between distinct group Latin squares
Donovan, D, OatesWilliams, S and Praeger, CE (1997). On the distance between distinct group Latin squares. Journal of Combinatorial Designs, 5 (4), 235-248. doi: 10.1002/(SICI)1520-6610(1997)5:4<235::AID-JCD1>3.0.CO;2-G
Quasigroups, isotopisms and authentication schemes
Dawson, Ed, Donovan, Diane and Offer, Alan (1996). Quasigroups, isotopisms and authentication schemes. Australasian Journal of Combinatorics, 13, 75-88.
Critical sets in back circulant latin squares
Donovan, Diane and Cooper, Joan (1996). Critical sets in back circulant latin squares. Aequationes Mathematicae, 52 (1), 157-179. doi: 10.1007/BF01818333
Critical sets in direct products of back circulant Latin squares
Cooper, J, Donovan, D and Gower, RAH (1996). Critical sets in direct products of back circulant Latin squares. Utilitas Mathematica, 50, 127-162.
The breadth of Shamir's secret-sharing scheme
Dawson, Ed and Donovan, Diane (1994). The breadth of Shamir's secret-sharing scheme. Computers and Security, 13 (1), 69-78. doi: 10.1016/0167-4048(94)90097-3
Single laws for sloops and squags
Donovan D. and Oates-Williams S. (1991). Single laws for sloops and squags. Discrete Mathematics, 92 (1-3), 79-83. doi: 10.1016/0012-365X(91)90268-7
Single laws for two subvarieties of squags
Donovan D. (1990). Single laws for two subvarieties of squags. Bulletin of the Australian Mathematical Society, 42 (1), 157-165. doi: 10.1017/S0004972700028276
More balanced ternary designs with block size four
Donovan, Diane (1987). More balanced ternary designs with block size four. Journal of Statistical Planning and Inference, 17 (C), 109-133. doi: 10.1016/0378-3758(87)90105-4
A family of balanced ternary designs with block size four
Donovan D. (1986). A family of balanced ternary designs with block size four. Bulletin of the Australian Mathematical Society, 33 (3), 321-327. doi: 10.1017/S0004972700003889
Donovan, Diane M., Grannell, Mike and Yazici, Emine S. (2020). Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results. International Conference on Loops, Budapest Hungary, Jul 07-13, 2019. Prague: Charles University, Faculty of Mathematics & Physics. doi: 10.14712/1213-7243.2021.003
Impacting factors on horizontal coal seam gas well production and proxy model comparison
Wang, Qian, Donovan, Diane, Thompson, Bevan, Rodger, Iain, Zhou, Fengde, Su, Xianbo and Yazici, Emine Şule (2019). Impacting factors on horizontal coal seam gas well production and proxy model comparison. SPE/AAPG/SEG Asia Pacific Unconventional Resources Technology Conference, Brisbane, QLD Australia, 18-19 November. Brisbane, QLD Australia: Unconventional Resources Technology Conference (URTEC). doi: 10.15530/AP-URTEC-2019-198251
Combinatorial questions: how can graph labelling help?
Donovan, Diane and McCourt, Thomas A. (2018). Combinatorial questions: how can graph labelling help?. 28th International Workshop on Combinational Algorithms, IWOCA 2017, Newcastle, NSW, Australia, 17-21 July 2017. Cham, Switzerland: Springer Verlag. doi: 10.1007/978-3-319-78825-8_2
Burrage, Kevin, Burrage, Pamela, Donovan, Diane and Thompson, Bevan (2015). Populations of models, experimental designs and coverage of parameter space by Latin Hypercube and Orthogonal sampling. International Conference On Computational Science, ICCS 2015, Reykjavik, Iceland, 1-3 June 2015. Amsterdam, Netherlands: Elsevier. doi: 10.1016/j.procs.2015.05.383
Estimates on the coverage of parameter space using populations of models
Burrage, Kevin, Burrage, Pamela M., Donovan, Diane, McCourt, Thomas A. and Thompson, Harold B. (2014). Estimates on the coverage of parameter space using populations of models. 5th IASTED International Conference on Modelling and Simulation, AfricaMS 2014, Gaborone,, September 1, 2014-September 3, 2014. ACTA Press. doi: 10.2316/P.2014.813-013
Hall, Joanne L., Rao, Asha and Donovan, Diane (2012). Planar difference functions. ISIT 2012: IEEE International Symposium on Information Theory, Cambridge, MA, USA, 1-6 July, 2012. Piscataway, NJ, United States: Institute of Electrical and Electronics Engineers. doi: 10.1109/ISIT.2012.6283019
Professional development for teaching in higher education
Wood, Leigh N., Vu, Tori, Bower, Matt, Brown, Natalie, Skalicky, Jane, Donovan, Diane, Loch, Birgit, Joshi, Nalini and Bloom, Walter (2011). Professional development for teaching in higher education. Volcanic Delta 2011: The 8th Delta Conference on Teaching and Learning Undergraduate Mathematics and Statistics, Rotorua, New Zealand, 27 November-2 December, 2011. Abingdon, Oxfordshire, United Kingdom: Taylor & Francis. doi: 10.1080/0020739X.2011.608864
Donovan, D. M., Lefevre, J. G. and Simpson, L. (2008). A discussion of constrained binary embeddings with applications to cryptanalysis of irregularly clocked stream ciphers. International Conference on Discrete Mathematics (ICDM 2006), Bangalore, India, 15-18 December 2006. Bangalore, India: Ramanujan Mathematical Society.
Change detection through clustering and spectral analysis.
Donovan, Diane, Loch, Birgit, Thompson, H. B and Thompson, Jayne (2008). Change detection through clustering and spectral analysis.. 18th International Workshop on Combinatorial Algorithms (IWOCA 2007), Newcastle, NSW, Australia, 5-9 November 2007. London, United Kingdom: College Publishing.
Permutation Representation of 3 and 4-Homogenous Latin Bitrades
Lefevre, J. G., Donovan, D. M. and Drapal, A. (2008). Permutation Representation of 3 and 4-Homogenous Latin Bitrades. Netherlands: IOS Press.
Change detection through clustering and spectral analysis
Donovan, D. M., Loch, B., Thompson, H. B. and Thompson, J. (2007). Change detection through clustering and spectral analysis. 18th International Workshop on Combinatorial Algorithms 2007, Lake MacQuarrie, New South Wales, 5-9 November, 2007. Newcastle, New South Wales: Newcastle University.
Donovan, D M, Lefevre, J G and Simpson, L (2006). A discussion of constrained binary embeddings with applications to cryptanalysis of irregularly clocked stream ciphers. International Conference on Discrete Mathematics 2006 (ICDM 2006), Banglaore, India, 15-18 December 2006. Bangalore: Indian Institute of Science.
Vladimirov, I G, Donovan, D M and Thompson, H B (2006). Gibbs equilibrium in interacting particle systems with coordination constrained bonding on Bethe lattices. AWOCA 2006, Uluru & Kings Canyon, Central Austraila, July 13 - 19 2006. Australia: Ballarat University.
Are there three MOLS of Order 10?
Cavenagh, N. J., Donovan, D. M. and Hamalainen, C. (2005). Are there three MOLS of Order 10?. Australasian Workshop on Combinatorial Algorithms, Ballarat, 18 - 21 September 2005. Ballarat, Australia: University of Ballarat.
On greedy critical sets in latin squares
Donovan, D. M., Hamalainen, C. and Khodkar, A. (2004). On greedy critical sets in latin squares. Fifteenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2004), Ballina, N.S.W., Australia, 6-9 July 2004. Alexandria, N.S.W., Australia: National Information and Communications Technology Australia.
Donovan, Diane, Pickett, Trevor and Wilson, Richard (2004). Visualising energy data. Australia: Australian Mathematical Society.
An investigation of 2-critical sets in Latin squares
Donovan, D. M., Fu, C.-M. and Khodkar, A. (2002). An investigation of 2-critical sets in Latin squares. AWOCA 2002, Fraser Island, Queensland, 7-10 July, 2002. Brisbane, Queensland: The University of Queensland.
Premature partial Latin squares and critical sets
Donovan, D. M. and Khodkar, A. (2002). Premature partial Latin squares and critical sets. AWOCA 2002, Fraser Island, Queensland, 7-10 July, 2002. Brisbane, Queensland: The University of Queensland.
A discussion of 2-critical sets in Abelian 2-groups
Donovan, D. M., Fu, C.-M. and Khodkar, A. (2001). A discussion of 2-critical sets in Abelian 2-groups. Australasian Workshop on Combinatorial Algorithms, Bandung, Indonesia, 14 July - 17 July 2001. Bandung, Indonesia: Dept. of Mathematics, Institut Teknologi Bandung.
Interactive Discrete Mathematics
Donovan, D. M. (2000). Interactive Discrete Mathematics. 4th Biennial Engineering Mathematics & Applications Conference EMAC 2000, Royal Melbourne Institute of Technology, Melbourne, 10-13th September 2000. Melbourne Australia: Royal Melbourne Institute of Technology University.
Steiner trades that give rise to completely decomposable latin interchanges
Bean, R., Donovan, D. M., Khodkar, A. and Street, A. P. (2000). Steiner trades that give rise to completely decomposable latin interchanges. Eleventh Australasian Workshop on Combinatorial Algorithms, Hunter Valley, NSW, Australia, 20th July - 1st August 2000. Newcastle, Australia: The University of Newcastle.
Methods for sharing cryptographic keys
Dawson E., Donovan D. and Rahilly A. (1992). Methods for sharing cryptographic keys. Conference on Communication Technology, Services and Systems - COMMUNICATIONS '92, Sydney, Aust, October 20, 1992-October 22, 1992.
Topics in balanced ternary designs
Donovan, Diane Margaret (1987). Topics in balanced ternary designs. PhD Thesis, School of Physical Sciences, The University of Queensland. doi: 10.14264/uql.2015.44
ARC Centre of Excellence for Plant Success in Nature and Agriculture
(2020–2027) ARC Centres of Excellence
Advanced mathematical modelling for early assessment of fracced wells' production performance
(2019–2020) Origin Energy Limited
Uncertainty modelling with polynomial chaos expansion
(2015–2017) QGC Pty Limited
(2010–2012) University of Technology Sydney
(2009–2010) ALTC Leadership for Excellence in Learning and Teaching
Security Applications of Combinatorial Puzzles
(2006–2008) ARC Discovery Projects
(2005) University of Queensland Research Development Grants Scheme
The fundamental structure of combinatorial configurations
(2004–2007) ARC Linkage International
2004 Travel Scheme Cat 2_Charles Univ, Prague; 01/01/04 to 23/01/04
(2004) UQ Travel Grants Scheme
Modelling, simulation and risk analysis in the Australian energy markets
(2001–2004) ARC Collaborative Grant (SPIRT)
Enhanced Computer Security, from Inter-relations between Combinatorial Structures
(1999–2001) ARC Australian Research Council (Large grants)
(1999) ARC Australian Research Council (Small grants)
Graph decompositions and their defining sets.
(1995) UQ External Support Enabling Grant
Pure and Applied Applications of Combinatorial Mathematics
Doctor Philosophy — Principal Advisor
Other advisors:
Modelling Biological Systems using Mathematical Networks
Doctor Philosophy — Principal Advisor
Other advisors:
A study of combinatorial problems and their applications
Doctor Philosophy — Associate Advisor
Other advisors:
The evolution of genetic networks during polygenic adaptation
Doctor Philosophy — Associate Advisor
Latin Squares and Related Structures
(2016) Doctor Philosophy — Principal Advisor
Other advisors:
Orthogonal Arrays; Enumeration and Applications
(2013) Doctor Philosophy — Principal Advisor
Other advisors:
(2010) Doctor Philosophy — Principal Advisor
Other advisors:
Latin Bitrades and Related Structures
(2007) Doctor Philosophy — Principal Advisor
Latin trades and critical sets in Latin squares
(2003) Doctor Philosophy — Principal Advisor
SMALL GRAPH DESIGNS AND THEIR VARIOUS PROPERTIES
(2005) Doctor Philosophy — Associate Advisor
Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.
Topics in Combinatorics
Modelling and simulation problems for water/gas reservoir estimation
Experimental design for problems in geosciences and petroleum engineering
The study of orthogonal designs for enhanced computer experiments, with particular the study of quasigroups, orthogonal latin squares and orthogonal arrays
The study of trades and their use in establishing existence results for discrete structures
The studey of networks in plant genetics