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P. Jarvis, J. Sumner, "Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 9, no. 3, pp. 828836, MayJune, 2012.  
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@article{ 10.1109/TCBB.2012.24, author = {P. Jarvis and J. Sumner}, title = {Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels}, journal ={IEEE/ACM Transactions on Computational Biology and Bioinformatics}, volume = {9}, number = {3}, issn = {15455963}, year = {2012}, pages = {828836}, doi = {http://doi.ieeecomputersociety.org/10.1109/TCBB.2012.24}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE/ACM Transactions on Computational Biology and Bioinformatics TI  Markov Invariants for Phylogenetic Rate Matrices Derived from Embedded Submodels IS  3 SN  15455963 SP828 EP836 EPD  828836 A1  P. Jarvis, A1  J. Sumner, PY  2012 KW  statistical analysis KW  embedded systems KW  evolution (biological) KW  genetics KW  Markov processes KW  Mtheory KW  physiological models KW  standard det invariant KW  Markov invariants KW  phylogenetic rate matrices KW  progenitor model KW  general rate matrix model KW  symmetric embedded models KW  statistical properties KW  Markov processes KW  Phylogeny KW  Adaptation models KW  Polynomials KW  Tensile stress KW  Algebra KW  Biological system modeling KW  representation theory. KW  Markov chains VL  9 JA  IEEE/ACM Transactions on Computational Biology and Bioinformatics ER   
[1] H.J. Bandelt and A.W.M. Dress, "Split Decomposition: A New and Useful Approach to Phylogenetic Analysis of Distance Data," Molecular Phylogenetics and Evolution, vol. 1, pp. 242252, 1992.
[2] D. Barry and J.A. Hartigan, "Asynchronous Distance between Homologous DNA Sequences," Biometrics, vol. 43, pp. 261276, 1987.
[3] J.A. Cavender and J. Felsenstein, "Invariants of Phylogenies in a Simple Case with Discrete States," J. Classification, vol. 4, pp. 5771, 1987.
[4] B. Fauser, P.D. Jarvis, R.C. King, and B.G. Wybourne, "New Branching Rules Induced by Plethysm," J. Physics A: Math. General, vol. 39, pp. 26112655, 2006.
[5] I. Gronau, S. Moran, and I. Yavneh, "Towards Optimal Distance Functions for Stoch Astic Substitution Models," J. Theoretical Biology, vol. 260, pp. 294307, 2009.
[6] B. Holland and V. Moulton, "Consensus Networks: A Method for Visualising Incompatibilities in Collections of Trees," Proc. Third Workshop Algorithms in Bioinformatics, pp. 165176, 2004.
[7] J.P. Huelsenbeck, B. Larget, and M.E. Alfaro, "Bayesian Phylogenetic Model Selection Using Reversible Jump Markov Chain Monte Carlo," Molecular Biology Evolution, vol. 21, pp. 11231133, 2004.
[8] A. Isaev, Introduction to Mathematical Methods in Bioinformatics. Springer, 2004.
[9] J.E. Johnson, "MarkovType Lie Groups in $GL(n,{{\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}})$ ," J. Math. Physics, vol. 26, pp. 252257, 1985.
[10] J.A. Lake, "A RateIndependent Technique for Analysis of Nucleic Acid Sequences: Evolutionary Parsimony," Molecular Biology Evolution, vol. 4, pp. 167191, 1987.
[11] D.E. Littlewood, "The Kronecker Product of Symmetric Group Representations," J. London Math. Soc., vol. s131, no. 1, pp. 8993, 1955.
[12] I.G. MacDonald, Symmetric Functions and Hall Polynomials. Clarendon Press, 1979.
[13] B. Mourad, "On a LieTheoretic Approach to Generalised Doubly Stochastic Matrices and Applications," Linear and Multilinear Algebra, vol. 52, pp. 99113, 2004.
[14] M. Pagel and A. Meade, "A Phylogenetic Mixture Model for Detecting PatternHeterogeneity in Gene Sequence or CharacterState Data," Systematic Biology, vol. 53, pp. 571581, 2004.
[15] D. Posada and K.A. Crandall, "Modeltest: Testing the Model of DNA Substitution," Bioinformatics, vol. 14, pp. 817818, 1998.
[16] C. Semple and M. Steel, Phylogenetics. Oxford Press, 2003.
[17] J.G. Sumner, J. FernándezSánchez, and P.D. Jarvis, "Lie Markov Models," J. Theoretical Biology, vol. 298, pp. 1631, 2012.
[18] J.G. Sumner, M.A. Charleston, L.S. Jermiin, and P.D. Jarvis, "Markov Invariants, Plethysms, and Phylogenetics," J. Theoretical Biology,, vol. 253, pp. 601615, 2008.
[19] J.G. Sumner, B.H. Holland, and P.D. Jarvis, "The Algebra of the General Markov Model on Trees and Networks," to appear in Bull. Math. Biology, DOI: 10.1007/s115380119691z, (2011b).
[20] J.G. Sumner and P.D. Jarvis, "Entanglement Invariants and Phylogenetic Branching," J. Math. Biology, vol. 51, pp. 1836, 2005.
[21] J.G. Sumner and P.D. Jarvis, "Using the Tangle: A Consistent Construction of Phylogenetic Distance Matrices," Math. Biosciences, vol. 204, pp. 4967, 2006.
[22] J.G. Sumner and P.D. Jarvis, "Markov Invariants and the Isotropy Subgroup of a Quartet Tree," J. Theoretical Biology, vol. 258, pp. 302310, 2009.
[23] M. Woodhams, J.G. Sumner, and M.A. Charleston, "Mosiac Models for Phylogenetic Estimation," in preparation, 2009.
[24] B.G. Wybourne, "Schur: An Interactive Programme for Calculating Properties of Lie Groups," Version 6.03, http://sourceforge. net/projectsschur, 2004.