**Publications:**
Ancient preprints | Back
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**Preprints:**

- Andrew Francis, Daniele Marchei, Mike Steel, Phylogenetic network classes through the lens of expanding covers.
- Andrew Francis, "Normal" Phylogenetic Networks Emerge as the Leading Class.
- Andrew Francis, Yi Guo, Paul Hurley, Oliver Obst, Laurence A. F. Park, Mark Tanaka, Russell Thomson, Rosalind Wang, Projected ICU and Mortuary load due to COVID-19 in Sydney (March 2020).
- This was a quick and intense study we did to try to estimate the demand on mortuary beds in Sydney as Covid began to threaten.

**Published:**

- Chad Clark, Julius Jonušas, James D. Mitchell, Andrew Francis, An algebraic model for inversion and deletion in bacterial genome rearrangement,
*Journal of Mathematical Biology*, 87:34 (2023). arXiv version. - Mareike Fischer, Andrew Francis, Kristina Wicke, Phylogenetic Diversity Rankings in the Face of Extinctions: the Robustness of the Fair Proportion Index,
*Systematic Biology*, Vol. 72(3), May 2023, p606-615. arXiv version. - Andrew Francis and Mike Steel, Labellable phylogenetic networks,
*Bulletin of Mathematical Biology*, 85:46 (2023). bioRxiv version. - Andrew Francis, Katharina T. Huber, Vincent Moulton, Taoyang Wu, Encoding and ordering X-cactuses,
*Advances in Applied Mathematics*, 2023, 142, 102414. arXiv version. - Andrew Francis and Peter D Jarvis, Brauer and partition diagram models for phylogenetic trees and forests,
*Proceedings of the Royal Society A*, 2022, 478: 20220044. arXiv version. - Joan Carles Pons, Tomás M. Coronado, Michael Hendriksen, Andrew Francis, A polynomial invariant for a new class of phylogenetic networks,
*PLoS ONE*, 17(5): e0268181. arXiv version. - Andrew Francis, Daniel H. Huson, Mike Steel, Normalising phylogenetic networks,
*Molecular Phylogenetics and Evolution*, Vol. 163, (2021), 107215. arXiv version. - Péter L Erdős, Andrew Francis, Tamás Róbert Mezei, Rooted NNI moves on tree-based phylogenetic networks,
*Discrete Applied Mathematics*, Vol. 294, (2021), p 205-213. arXiv version. - Sangeeta Bhatia, Attila Egri-Nagy, Stuart Serdoz, Cheryl Praeger, Volker Gebhardt, Andrew Francis, A flexible framework for determining weighted genome rearrangement distance,
*Frontiers in Genetics*11:1035, special topic on Algebraic and Geometric Phylogenetics, (2020). - Andrew Francis and Henry Wynn, A mean first passage time genome rearrangement distance,
*Journal of Mathematical Biology*, vol 80 (6), p 1971-1992 (2020). arXiv version. - Mareike Fischer and Andrew Francis, The space of tree-based phylogenetic networks,
*Bulletin of Mathematical Biology*, vol 82:70, 4th June (2020). arXiv version - Mareike Fischer and Andrew Francis, How tree-based is my network? Proximity measures for unrooted phylogenetic networks,
*Discrete Applied Mathematics*, vol 283, p 98-114, 15 September 2020. arXiv version. - Michael Hendriksen and Andrew Francis, A partial order and cluster-similarity metric on rooted phylogenetic trees,
*Journal of Mathematical Biology*, 80 (5), p 1265-1290, April 2020. arXiv version. - R. Zach Aandahl, Sangeeta Bhatia, Natalia Vaudagnotto, Arthur G. Street, Andrew R. Francis, Mark M. Tanaka, MERCAT: computational tools for analysing and visualising molecular data from bacterial isolates,
*Infection, Genetics and Evolution*, Volume 77, January 2020, 104043. - Michael Hendriksen and Andrew Francis, Tree-metrizable HGT networks,
*Mathematical Biosciences*, Volume 318, December 2019, 108283. arXiv version. - Chad Clark, Attila Egri-Nagy, Andrew R. Francis, Volker Gebhardt, Bacterial phylogeny in the Cayley graph,
*Discrete Mathematics, Algorithms and Applications*, Vol. 11, No. 05, 1950059 (2019). arXiv version. - Sangeeta Bhatia, Pedro Feijão, Andrew R. Francis, Position and content paradigms in genome rearrangements: the wild and crazy world of permutations in genomics,
*Bulletin of Mathematical Biology*, December 2018, 80(12), 3227-3246. arXiv version. - Guilherme S. Rodrigues, Andrew R. Francis, Scott A. Sisson, Mark M. Tanaka, Inferences on the acquisition of multidrug resistance in
*Mycobacterium tuberculosis*using molecular epidemiological data, in*Handbook of Approximate Bayesian Computation*, Chapman & Hall, 24 August 2018. - Andrew Francis and Vincent Moulton, Identifiability of tree-child phylogenetic networks under a probabilistic recombination-mutation model of evolution,
*Journal of Theoretical Biology*, Vol. 446, 7 June 2018, 160-167. arXiv version. - Andrew Francis, Katharina Huber, Vincent Moulton, Taoyang Wu, Bounds for phylogenetic network space metrics,
*Journal of Mathematical Biology*, April 2018, Vol. 76 (5), 1229-1248. arXiv version. - Andrew Francis, Katharina Huber, Vincent Moulton, Tree-based unrooted phylogenetic networks,
*Bulletin of Mathematical Biology*, February 2018, Vol. 80 (2), 404-416. arXiv version. A correction to an example in this paper is published here,*Bull. Math. Biol.*, 2019, 81(3), 936--937. - Andrew Francis, Charles Semple, Mike Steel, New characterisations of tree-based networks and proximity measures,
*Advances in Applied Mathematics*, February 2018, vol. 93, p93-107. arXiv version. - Jeremy G Sumner, Peter D Jarvis, Andrew R Francis, A representation-theoretic approach to the calculation of evolutionary distance in bacteria,
*Journal of Physics A: Mathematical and Theoretical*, vol 50 (33), August 2017. arXiv version. - David Bryant, Andrew Francis, Mike Steel, Can we 'future-proof' consensus trees?,
*Systematic Biology*, 2017, 66 (4): 611-619. arXiv version. - Andrew R. Francis, Milan Stehlik and Henry P. Wynn, "Building" exact confidence nets,
*Bernoulli*, 2017, Vol. 23, No. 4B, 3145-3165. arXiv version. - Stuart Serdoz, Attila Egri-Nagy, Jeremy G. Sumner, Barbara R. Holland, Peter D. Jarvis, Mark M. Tanaka, Andrew R. Francis, Maximum likelihood estimates of pairwise rearrangement distances,
*Journal of Theoretical Biology*, 2017, 423, p31-40. arXiv version. - Andrew R. Francis and Mike Steel, Which phylogenetic networks are merely trees with additional arcs?,
*Systematic Biology*, 2015, - Sangeeta Bhatia, Attila Egri-Nagy, Andrew R. Francis, Algebraic double cut and join -- A group-theoretic approach to the operator on multichromosomal genomes,
*Journal of Mathematical Biology*, 2015, 71 (5): 1149-1178. arXiv version. - Andrew R. Francis and Mike Steel, Tree-like reticulation networks: When do tree-like distances also support reticulate evolution?,
*Mathematical Biosciences,*Volume 259, 2015, p12-19. arXiv version. - Andrew R. Francis, An algebraic view of bacterial genome evolution,
*Journal of Mathematical Biology*, Volume 69, Issue 6, 2014, Pages 1693-1718. arXiv version - Attila Egri-Nagy, Andrew R. Francis and Volker Gebhardt,
__Bacterial genomics and computational group theory: the BIOGAP package for GAP__,*Mathematical Software -- ICMS 2014 4th International Conference, Seoul, South Korea, August 5-9, 2014, Lecture Notes in Computer Science*, Volume 8592, 2014. - Attila Egri-Nagy, Volker Gebhardt, Mark M. Tanaka and Andrew R. Francis, Group-theoretic models of the inversion process in bacterial genomes,
*Journal of Mathematical Biology*, 2014, 69:243-265. arXiv version - Andrew R. Francis and Henry P. Wynn,
__Subgroup majorization__,*Linear Algebra and its Applications*, Volume 444, 1 March 2014, Pages 53-66. - Tadeusz Bak, Dewei Chu, Andrew R Francis, Wenxian Li and Janusz Nowotny, Concentration of electrons at grain boundaries in TiO2 (Rutile): Impact on charge transport and reactivity,
*Catalysis Today*, Volume 224, 1 April 2014, Pages 200-208. - Andrew Francis and Lenny Jones, Multiplicative Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group, Proceedings of the Southeastern Lie Theory Workshop Series, Kailash C. Misra, Daniel Nakano, and Brian Parshall (eds), Proceedings of Symposia in Pure Mathematics, American Mathematical Society, 2012, p159-164.
- Andrew R. Francis and Mark M. Tanaka, Evolution of variation in presence and absence of genes in bacterial pathways, BMC Evolutionary Biology 2012, 12:55 (20 April 2012)
- Andrew Francis and Lenny Jones, Monomial Bases for the Centres of the Group Algebra and Iwahori-Hecke Algebra of the Symmetric Group, Far East Journal of Mathematical Sciences, 2011, 58 (2), p119-143
- Paul G. Stevenson, Mariam Mnatsakanyan, Andrew R. Francis and R. Andrew Shalliker, A discussion on the process of defining two-dimensional separation selectivity, Journal of Separation Science, 2010, 33, 1405-1413.
- Sara Ballouz, Andrew R. Francis, Ruiting Lan and Mark M. Tanaka, Conditions for the evolution of gene clusters in bacterial genomes, PLoS Computational Biology, 2010, 6(2): e1000672
- Fabio Luciani, Scott A. Sisson, Honglin Jiang, Andrew R. Francis and Mark M. Tanaka, The epidemiological fitness cost of drug resistance in Mycobacterium tuberculosis,
*Proceedings of the National Academy of Sciences of the United States of America*, August 25, 2009, 106(34), 14711-14715*.* - Andrew Francis and Lenny Jones, A new integral basis for the centre of the Hecke algebra of type
*A*, Journal of Algebra, 321 (3), 2009, 866-878. - Andrew Francis and Weiqiang Wang, The centers of Iwahori-Hecke algebras are filtered,
*Representation Theory,*29-38, - Chaka Tang, Josephine F. Reyes, Fabio Luciani, Andrew R. Francis and Mark M. Tanaka,
__spolTools: online utilities for analyzing spoligotypes of the Mycobacterium tuberculosis complex__,*Bioinformatics*, 2008, 24 (20), 2414-2415. - Josephine F. Reyes, Andrew R. Francis and Mark M. Tanaka,
__Models of deletion for visualizing bacterial variation: an application to tuberculosis spoligotypes__, BMC Bioinformatics, 2008, 9:496. - Fabio Luciani, Andrew R. Francis and Mark M. Tanaka, Interpreting genotype cluster sizes of
*Mycobacterium tuberculosis*isolates typed with IS*6110*and spoligotyping,*Infection, Genetics and Evolution*, 8 (2), 2008, 182-190.

- Andrew Francis and Lenny Jones, On the square root of the centre of the Hecke algebra of type
*A*,*Journal of the Australian Mathematical Society*, 82, 2007, 209-220 - Andrew Francis and John J Graham, Centres of Hecke algebras: the Dipper-James conjecture,
*Journal of Algebra*. 306 (1), 2006, 244-267. Special Issue in Honour of Gordon Douglas James. - Mark M Tanaka and Andrew R Francis, Detecting emerging strains of tuberculosis by using spoligotypes,
*Proceedings of the National Academy of Sciences of the United States of America*, October 10 2006, 103 (41), 15266-15271. - Mark M Tanaka, Andrew R Francis, Fabio Luciani and Scott Sisson, Using approximate Bayesian computation to estimate tuberculosis transmission parameters from genotype data,
*Genetics*, July 2006, 173 (3) 1511-1520. - Mark M Tanaka, Renault Phong and Andrew R Francis, An evaluation of indices for quantifying tuberculosis transmission using genotypes of pathogen isolates,
*BMC Infectious Diseases*2006, 6:92 - Andrew Francis and Lenny Jones, On bases of centres of Iwahori-Hecke algebras of the symmetric group,
*Journal of Algebra*, 289 (1), 2005, 42-69. - Mark M Tanaka and Andrew R Francis, Methods of quantifying and visualising outbreaks of tuberculosis using genotypic information,
*Infection, Genetics and Evolution*, 5 (1), January 2005, 35-43 - Andrew Francis, Centralizers of Iwahori-Hecke algebras II: the general case,
*Algebra Colloquium*, 10 (1), 2003, 95-100 - Andrew Francis, The Brauer homomorphism and the minimal basis for the centre of an Iwahori-Hecke algebra of type
*A*,*Communications in Algebra*, 2001, 29 (1), 85-97. - Andrew Francis, Centralizers of Iwahori-Hecke algebras,
*Transactions of the American Mathematical Society*, 2001, 353 (7), 2725-2739 - Andrew Francis, The minimal basis for the centre of an Iwahori-Hecke algebra,
*Journal of Algebra*, 1999, 221 (1), 1-28.

- Andrew Francis, Centralizers in the Hecke algebras of complex reflection groups. arxiv 2007

- Andrew Francis, Centres and centralizers of Iwahori-Hecke algebras, PhD thesis, University of New South Wales, 1998.