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Elizabeth S. Allman, Sonja Petrović, John A. Rhodes, Seth Sullivant, "Identifiability of TwoTree Mixtures for GroupBased Models," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 3, pp. 710722, May/June, 2011.  
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@article{ 10.1109/TCBB.2010.79, author = {Elizabeth S. Allman and Sonja Petrović and John A. Rhodes and Seth Sullivant}, title = {Identifiability of TwoTree Mixtures for GroupBased Models}, journal ={IEEE/ACM Transactions on Computational Biology and Bioinformatics}, volume = {8}, number = {3}, issn = {15455963}, year = {2011}, pages = {710722}, doi = {http://doi.ieeecomputersociety.org/10.1109/TCBB.2010.79}, 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  Identifiability of TwoTree Mixtures for GroupBased Models IS  3 SN  15455963 SP710 EP722 EPD  710722 A1  Elizabeth S. Allman, A1  Sonja Petrović, A1  John A. Rhodes, A1  Seth Sullivant, PY  2011 KW  Phylogenetic mixture KW  groupbased model KW  identifiability of phylogenetic models. VL  8 JA  IEEE/ACM Transactions on Computational Biology and Bioinformatics ER   
[1] E.S. Allman, C. Ané, and J.A. Rhodes, "Identifiability of a Markovian Model of Molecular Evolution with GammaDistributed Rates," Advances in Applied Probability, vol. 40, pp. 229249, arXiv:0709.0531, 2008.
[2] E.S. Allman, C. Matias, and J.A. Rhodes, "Identifiability of Parameters in Latent Structure Models with Many Observed Variables," Annals of Statistics, vol. 37, no. 6A, pp. 30993132, 2009.
[3] E.S. Allman, S. Petrović, J.A. Rhodes, and S. Sullivant, "Supplementary Material," http://www4.ncsu.edu~smsulli2/Pubs/TwoTreesWebsite twotrees.html, 2009.
[4] E.S. Allman and J.A. Rhodes, "Phylogenetic Invariants for the General Markov Model of Sequence Mutation," Math. Bioscience, vol. 186, no. 2, pp. 113144, 2003.
[5] E.S. Allman and J.A. Rhodes, "The Identifiability of Tree Topology for Phylogenetic Models, Including Covarion and Mixture Models," J. Computational Biology, vol. 13, no. 5, pp. 11011113, 2006.
[6] E.S. Allman and J.A. Rhodes, "Phylogenetic Ideals and Varieties for the General Markov Model," Advances in Applied Math., vol. 40, no. 2, pp. 127148, 2008.
[7] E.S. Allman and J.A. Rhodes, "The Identifiability of Covarion Models in Phylogenetics," IEEE/ACM Trans. Computational Biology and Bioinformatics, vol. 6, no. 1, pp. 7688, Jan.Mar. 2009.
[8] J.A. Cavender and J. Felsenstein, "Invariants of Phylogenies in a Simple Case with Discrete States," J. Classification, vol. 4, pp. 5771, 1987.
[9] J.T. Chang, "Full Reconstruction of Markov Models on Evolutionary Trees: Identifiability and Consistency," Math. Bioscience, vol. 137, no. 1, pp. 5173, 1996.
[10] D. Cox, J. Little, and D. O'Shea, Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, second ed. SpringerVerlag, 1997.
[11] J. Draisma, "A Tropical Approach to Secant Dimensions," J. Pure and Applied Algebra, vol. 212, no. 2, pp. 349363, 2008.
[12] M. Drton, B. Sturmfels, and S. Sullivant, "Lectures on Algebraic Statistics," Oberwolfach Seminars, vol. 39, Birkhäuser Basel, 2008.
[13] S.N. Evans and T.P. Speed, "Invariants of Some Probability Models Used in Phylogenetic Inference," Annals of Statistics, vol. 21, no. 1, pp. 355377, 1993.
[14] W. Fulton, "The William H. Roever Lectures in Geometry," Introduction to Toric Varieties, Princeton Univ. Press, 1993.
[15] D.R. Grayson and M.E. Stillman, "Macaulay2, a Software System for Research in Algebraic Geometry," http://www.math.uiuc. eduMacaulay2/, 2002.
[16] G.M. Greuel, G. Pfister, and H. Schönemann, "Singular 3.1.0 A Computer Algebra System for Polynomial Computations," http:/www.singular.unikl.de, 2009.
[17] J. Harris, Algebraic Geometry: A First Course. SpringerVerlag, 1992.
[18] M.D. Hendy, "The Relationship between Simple Evolutionary Tree Models and Observable Sequence Data," Systematic Zoology, vol. 38, pp. 310321, 1989.
[19] M.D. Hendy and D. Penny, "Spectral Analysis of Phylogenetic Data," J. Classification, vol. 10, pp. 120, 1993.
[20] M.D. Hendy and D. Penny, "Complete Families of Linear Invariants for Some Stochastic Models of Sequence Evolution, with and without the Molecular Clock Assumption," J. Computational Biology, vol. 3, no. 1, pp. 1931, 1996.
[21] S. Hoşten, A. Khetan, and B. Sturmfels, "Solving The Likelihood Equations," Foundations of Computational Math., vol. 5, pp. 389407, arXiv:math.ST/0408270, 2005.
[22] J.A. Lake, "A Rate Independent Technique for Analysis of Nucleic Acid Sequences: Evolutionary Parsimony," Molecular Biology and Evolution, vol. 4, no. 2, pp. 167191, 1987.
[23] F.A. Matsen, E. Mossel, and M. Steel, "MixedUp Trees: The Structure of Phylogenetic Mixtures," Bull. of Math. Biology, vol. 70, no. 4, pp. 11151139, 2008.
[24] F.A. Matsen and M.A. Steel, "Phylogenetic Mixtures on a Single Tree Can Mimic a Tree of Another Topology," Systematic Biology, vol. 56, no. 5, pp. 767775, 2007.
[25] E. Mossel and E. Vigoda, "Phylogenetic MCMC Algorithms Are Misleading on Mixtures of Trees," Science, vol. 309, pp. 22072209, 2005.
[26] S. Rudich, "Complexity Theory: From Gödel to Feynman," Computational Complexity Theory, vol. 10, pp. 587, Am. Math. Soc., 2004.
[27] C. Semple and M. Steel, Phylogenetics, vol. 24. Oxford Univ. Press, 2003.
[28] D. Speyer and B. Sturmfels, "The Tropical Grassmannian," Advances in Geometry, vol. 4, no. 3, pp. 389411, 2004.
[29] M.A. Steel and Y.X. Fu, "Classifying and Counting Linear Phylogenetic Invariants for the JukesCantor Model," J. Computational Biology, vol. 2, no. 1, pp. 3947, 1995.
[30] B. Sturmfels, Gröbner Bases and Convex Polytopes, vol. 8. Am. Math. Soc., 1996.
[31] B. Sturmfels and S. Sullivant, "Toric Ideals of Phylogenetic Invariants," J. Computational Biology, vol. 12, no. 2, pp. 204228, 2005.
[32] L. Székely, P.L. Erdös, M.A. Steel, and D. Penny, "A Fourier Inversion Formula for Evolutionary Trees," Applied Math. Letters, vol. 6, no. 2, pp. 1317, 1993.
[33] L.A. Székely, M.A. Steel, and P.L. Erdös, "Fourier Calculus on Evolutionary Trees," Advances in Applied Math., vol. 14, no. 2, pp. 200210, 1993.
[34] D. Štefankovič and E. Vigoda, "Phylogeny of Mixture Models: Robustness of Maximum Likelihood and NonIdentifiable Distributions," J. Computational Biology, vol. 14, no. 2, pp. 156189, 2007.
[35] J. Chai and E.A. Housworth, "On Rogers's Proof of Identifiability for the GTR + Gamma + I Model," to appear in Systematic Biology.