# Conrad Burden

## Contacts

Conrad Burden is an Honorary Associate Professor in the Mathematical Sciences Institute at the Australian National University. His current research interests are in mathematical population genetics. Previous research interests include aligment-free sequence comparison, the analysis of high-throughput sequencing data, and the physico-chemical modelling of microarrays.

Before making the move into bioinformatics in 2003 he spent 20 years as a theoretical physicist followed by a short stint working in the IT industry:

He graduated from the University of Queensland with 1st class honours in Applied Mathematics in 1979 and The Australian National University with a PhD in Theoretical Physics in 1983.

Between 1983 and 1988 he held postdoctoral fellowships in theoretical physics at the Weizmann Institute of Science, Glasgow University, The Australian National University and Flinders University.

Between 1988 and 1999 he held a research position in the Department of Theoretical Physics, Australian National University, working mainly in quantum field theory and subatomic particle physics.

Between 1999 and 2002 I was a programmer/developer in the IT industry.

Between 2003 and 2020 I held positions as Research Fellow, Fellow and Associate Professor in the Mathematical Sciences Institute, Australian National University.

Conrad is a Fellow of the Australian Institute of Physics.

Read more about Conrad's biography and research interests.

### Research interests

Currently interested in Mathematical Population Genetics.

Previous research interests since 2003 include physico-chemical modelling of microarrays, pairwise word-match counts in random sequences, and the analysis of high-throughput genomic sequencing data.

Research interests up to 1999 were in quantum field theory and subatomic particle physics.

ORCiD: 0000-0003-0015-319X

ResearcherID: D-5556-2016

### Groups

- Retired Fellow, Bioinformation science

### Projects

- Researcher, Mathematical aspects of population genetics

- Vogl, C, Mikula, L & Burden, C 2020, 'Maximum likelihood estimators for scaled mutation rates in an equilibrium mutation-drift model', Theoretical Population Biology, vol. 134, no. -, pp. 106-118.
- Burden, C & Griffiths, R 2018, 'Stationary distribution of a 2-island 2-allele Wright-Fisher diffusion model with slow mutation and migration rates', Theoretical Population Biology, vol. 124, pp. 70-80pp.
- Burden, C & Wei, Y 2018, 'Mutation in populations governed by a Galton-Watson branching process', Theoretical Population Biology, vol. 120, pp. 52-61pp.
- Burden, C & Tang, Y 2017, 'Rate matrix estimation from site frequency data', Theoretical Population Biology, vol. 113, pp. 23-33pp.
- Burden, C & Tang, Y 2016, 'An approximate stationary solution for multi-allele neutral diffusion with low mutation rates', Theoretical Population Biology, vol. 112, pp. 22-32.
- Burden, C & Simon, H 2016, 'Genetic drift in populations governed by a Galton-Watson branching process', Theoretical Population Biology, vol. 109, pp. 63-74.
- Lin, P, Foret, S, Wilson, S et al 2015, 'Estimation of the methylation pattern distribution from deep sequencing data', BMC Bioinformatics, vol. 16, no. 145, pp. 145-145.
- Burden, C 2015, 'Can evolutionary rate matrices be estimated from allele frequencies?',
*6th International Conference on Bioinformatics Models, Methods and Algorithms, BIOINFORMATICS 2015*, ed. oa H.Fred A.Elias D., SciTePress, TBC, pp. 183-188. - Burden, C, Qureshi, S & Wilson, S 2014, 'Error estimates for the analysis of differential expression from RNA-seq count data', PeerJ, vol. 2, no. 1, pp. e576-e576.
- Burden, C, Leopardi, P & Foret, S 2014, 'Word match counts between markovian biological sequences', Communications in Computer and Information Science, pp. 147-161.
- Burden, C, Leopardi, P & Foret, S 2014, 'The distribution of word matches between markovian sequences with periodic boundary conditions', Journal of Computational Biology, vol. 21, no. 1, pp. 41-63.
- Burden, C, Leopardi, P & Foret, S 2013, 'The distribution of short word match counts between Markovian sequences',
*International Conference on Bioinformatics Models, Methods and Algorithms 2013*, SciTePress, Barcelona Spain, pp. 25-33. - Harrison, A, Binder, H, Buhot, A et al 2013, 'Physico-chemical foundations underpinning microarray and next-generation sequencing experiments', Nucleic Acids Research, vol. 41, no. 5, pp. 2779-2796.
- Burden, C, Qureshi, S & Wilson, S 2013, 'Controlling false discovery rates in RNA-sequencing data',
*ISI World Statistics Conference*, International Statistical Institute, The Hague, The Netherlands, pp. 1339-1344pp. - Burden, C, Jing, J & Wilson, S 2012, 'Alignment-free Sequence Comparison for Biologically Realistic Sequences of Moderate Length', Statistical Applications in Genetics and Molecular Biology, vol. 11, no. 1, p. 29.
- Burden, C, Jing, J, Foret, S et al 2012, 'Application of k-word match statistics to the clustering of proteins with repeated domains',
*International Conference on Computational Statistics (COMPSTAT 2012)*, ed. Ana Colubi, Konstantinos Fokianos, Erricos John Kontoghiorghes, Gil Gonzalez-Ro, The International Association for Statistical Computing (IASC), Unknown, pp. 131-142. - Robles, J, Qureshi, S, Stephen, S et al 2012, 'Efficient experimental design and analysis strategies for the detection of differential expression using RNA-Sequencing', BMC Genomics, vol. 13, no. 1, pp. 1-14.
- Jing, J, Wilson, S & Burden, C 2011, 'Weighted k-word matches: a sequence comparison tool for proteins', ANZIAM Journal, vol. 52, pp. C172-C189.
- Subhani, N, Rueda, L, Ngom, A et al 2011, 'Alignment-Based Clustering of Gene Expression Time-Series Data', in Sumeet Dua & Rajendra Acharya U. (ed.),
*Data Mining in Biomedical Imaging, Signaling, and Systems*, CRC Press, -, pp. 227-261pp. - Subhani, N, Rueda, L, Ngom, A et al 2010, 'New approaches to clustering microarray time-series data using multiple expression profile alignment',
*2010 IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology, CIBCB 2010*, IEEE, Montreal, QC, pp. 170-176. - Subhani, N, Rueda, L, Ngom, A et al 2010, 'Multiple gene expression profile alignment for microarray time-series data clustering', Bioinformatics, vol. 26, no. 18, pp. 2281-2288.
- Jing, J, Burden, C, Foret, S et al 2010, 'Statistical considerations underpinning an alignment-free sequence comparison method', Journal of the Korean statistical society, vol. 39, no. 3, pp. 325-335.
- Binder, H, Krohn, K & Burden, C 2010, 'Washing scaling of GeneChip microarray expression', BMC Bioinformatics, vol. 11, p. 30.
- Burden, C & Binder, H 2010, 'Reply to 'linking probe thermodynamics to microarray quantification'', Physical Biology, vol. 7, no. 4.
- Burden, C & Binder, H 2010, 'Physico-chemical modelling of target depletion during hybridization on oligonulceotide microarrays', Physical Biology, vol. 7, no. 1, pp. 16004-16004.
- Subhani, N, Rueda, L, Ngom, A et al 2009, 'Clustering microarray time-series data using expectation maximization and multiple profile alignment',
*2009 IEEE International Conference on Bioinformatics and Biomedicine Workshops, BIBMW 2009*, IEEE, Washington, DC, pp. 2-7. - Numanul, S, Ngom, A, Rueda, L et al 2009, 'Microarray Time-Series Data Clustering via Multiple Alignment of Gene Expression Profiles', in V. Kadirkamanathan (ed.),
*Pattern Recognition in Bioinformatics: proceedings of the 4th international workshop on Pattern Recognition in Bioinformatics*, Springer, Germany, pp. 377-390. - Foret, S, Wilson, S & Burden, C 2009, 'Characterizing the D2 Statistic: Word Matches in Biological Sequences', Statistical Applications in Genetics and Molecular Biology, vol. 8, no. 1, pp. Article 43.
- Burden, C 2009, 'Intensity isotherms and distributions on oligonucleotide microarrays',
*Congress on Evolutionary Computation (CEC 2009)*, ed. Hussein Abbass, Mohammad Abido, Ajith Abraham, et all, Institute of Electrical and Electronics Engineers (IEEE Inc), USA, pp. 3095-3102. - Binder, H, Brucker, J & Burden, C 2009, 'Nonspecific Hybridization Scaling of Microarray Expression Estimates: A Physicochemical Approach for Chip-to-Chip Normalization', Journal of Physical Chemistry B, vol. 113, no. 9, pp. 2874-2895.
- Burden, C 2008, 'Understanding the physics of oligonucleotide microarrays: the Affymetrix spike-in data reanalysed', Physical Biology, vol. 5, no. 1, p. 16004.
- Foret, S, Wilson, S & Burden, C 2008, 'Empirical distribution of k-word matches in biological sequences', Pattern Recognition, vol. 42, pp. 539-548.
- Burden, C 2008, 'Comment on "Stationary rotating strings as relativistic particle mechanics"', Physical Review D-Particles, Fields, Gravitation and Cosmology, vol. 78, p. 2.
- Burden, C, Kantorovitz, M & Wilson, S 2008, 'Approximate word matches between two random sequences', Annals of Applied Probability, vol. 18, no. 1, pp. 1-21.
- Burden, C, Foret, S & Wilson, S 2008, 'k-Word Matches: an Alignment-free Sequence Comparison Method',
*International Conference on Pattern Recognition (ICPR 2008)*, ed. Conference Program Committee, IEEE Computer Society, Melbourne, Australia, pp. 235-238. - 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. - Burden, C & Oakley, A 2007, 'Anisotropic atomic motions in high-resolution protein crystallography molecular dynamics simulations', Physical Biology, vol. 4, no. 2, pp. 79-90.
- Kantorovitz, M, Booth, H, Burden, C et al 2007, 'Asymptotic Behaviour of
*k*-Word Matches Between Two Uniformly Distributed Sequences', Journal of Applied Probability, vol. 44, pp. 788-805. - 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.
- Foret, S, Burden, C & Wilson, S 2007, 'Asymptotic behaviour and optimal word size for exact and approximate word matches between random sequences',
*International Congress on Industrial and Applied Mathematics 2007*, ed. Conference Program Committee, Wiley Interscience, Weinheim, Germany, pp. 1121801-1121802. - 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. - Burden, C, Pittelkow, Y & Wilson, S 2007, 'Statistical Analysis and Physical Modelling of Oligonucleotide Microarrays', in Andreas Deutsch, Lutz Brusch, Helen Byrne, Gerda de Vries and (ed.),
*Mathematical modeling of biological systems*, Birkhauser Verlag, Boston, US, pp. 323-336. - Foret, S, Kantorovitz, M & Burden, C 2006, 'Asymptotic behaviour and optimal word size for exact and approximate word matches between random sequences', BMC Bioinformatics, vol. 7, no. Suppl 5, pp. S21.
- Burden, C, Pittelkow, Y & Wilson, S 2006, 'Adsorption models of hybridization and post-hybridization behaviour on oligonucleotide microarrays', Journal of Physics: Condensed Matter, vol. 18, pp. 5545-5565.
- Burden, C, Pittelkow, Y & Wilson, S 2005, 'Oligonucleotide Microarrays and Langmuir Adsorption Theory',
*National Congress Australian Institute of Physics 2005*, ed. Max Colla, Australian Institute of Physics, Canberra, p. 4. - Maindonald, J & Burden, C 2005, 'Selection bias in plots of microarray or other data that have been sampled from a high-dimensional space', ANZIAM Journal, vol. 46, pp. C59-C74.
- Santoso, L, Booth, H, Burden, C et al. 2005, 'A stochastic model of gene switches', ANZIAM Journal, vol. 46, pp. C530-543.
- Booth, H, Burden, C, Maindonald, J et al 2005, 'Discussion of "A Bayesian approach to DNA sequence segmentation"', Biometrics, vol. 61, no. 2, pp. 635-639.
- 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.
- Burden, C, Pittelkow, Y & Wilson, S 2004, 'Statistical analysis of adsorption models for oligonucleotide microarrays', Statistical Applications in Genetics and Molecular Biology, vol. 3, no. 1-27, p. 29.
- Burden, C & Pichowsky, M 2002, 'J
^{PC}-Exotic Mesons from the Bethe-Salpeter Equation', Few-Body Systems, vol. 32, no. 3, pp. 119-126. - Burden, C 1999, 'The Effect of the Ultraviolet Part of the Gluon Propagator on the Heavy Quark Propagator', Physical Review D, vol. 59, no. 3, pp. 1-4.
- Walker, M & Burden, C 1999, 'Chiral Symmetry in Supersymmetric Three Dimensional Quantum Electrodynamics', Physical Review D, vol. 59, no. 12, pp. 1-7.
- Walker, M & Burden, C 1999, 'Nonperturbative Vertices in Supersymmetric Quantum Electrodynamics', Physical Review D, vol. 60, no. 10, pp. 1-10.

Courses previously developed and taught:

MATH3353 and MATH6208 Topics in Bioinformatics (2006, 2007, 2012 to 2021)

MATH2307 and MATH6100 Bioinformatics and Biological Modelling (2010 to 2019)

BIOL2001 Introduction to Quantitative Biology (2017)

BIOL8002 Advanced Topics in Quantitative Biology, module 1: Mathematical and Progamming Background (2018 to 2020)

Special relativity, general relativity, relativistic quantum mechanics and quantum field theory components of various 2nd and 3rd year undergraduate physics courses during the period 1988 to 1999 and in 2003, 2005