Publications and Preprints -- Seth Sullivant

**Books**

- Lectures on Algebraic Statistics (with Mathias Drton and Bernd Sturmfels), Oberwolfach Seminar Series
**39**, Birkhauser, 2009 - Emerging Applications of Algebraic Geometry (edited with Mihai Putinar), IMA Series
**149**, Springer, 2008

**Papers in Preparation**

- Symmetric matrix Schubert varieties and applications to Gaussian graphical models (with Alex Fink and Jenna Rajchgot)
- Statistically consistent k-mer methods for phylogenetic tree reconstruction (with Elizabeth Allman and John Rhodes)

**Submitted Papers and Preprints**

- Unimodular binary hierarchical models (with Daniel I. Bernstein) 1502.06131
- Bounds on the expected size of the maximum agreement subtree (with Daniel I. Bernstein, Lam Ho, Colby Long, Mike Steel, and Katherine St. John) 1411.7338
- Identifiability results for several classes of linear compartment models (with Nicolette Meshkat and Marisa Eisenberg) 1410.8587
- Sequential importance sampling for the Ising model (with Jing Xi) 1410.4217
- The maximum likelihood threshold of a graph (with Elizabeth Gross) 1404.6989
- Lifting Markov bases and higher codimension toric fiber products (with Johannes Rauh) 1404.6392
- The Markov basis of K_3,N (with Johannes Rauh) 1406.5936

**Papers in Press**

- Tying up loose strands: the defining equations of the strand symmetric model (with Colby Long) To appear in
*Journal of Algebraic Statistics.*1410.3344 Supplementary Materials

**Papers in Print**

- Identifiability of Jukes-Cantor 3-tree mixtures (with Colby Long)
*Adv. in Appl. Math.***64**(2015), 89–110. 1406.7256 Supplementary Materials - Distance-based phylogenetic algorithms around a polytomy (with Ruth Davidson)
*IEEE/ACM Transactions in Computational Biology and Bioinformatics***11**(2014) 325-335 1307.5908 Supplementary Materials - Positive margins and primary decomposition. (with Thomas Kahle and Johannes Rauh)
*Journal of Algebraic Combinatorics***39**(2014), 335-3721201.2591 - Structural identifiability of viscoelastic mechanical systems (with Adam Mahdi and Nicolette Meshkat)
*PLOS One***9**(2014): e864111 1308.4950 - Identifiable reparametrizations of linear compartment models (with Nicolette Meshkat)
*Journal of Symbolic Computation***63**(2014), 46–67.1305.5768 - Multigraded commutative algebra of graph decompositions. (with Alexander Engström and Thomas Kahle)
*J. Algebraic Combinatorics***39**(2014) no. 2, 335-372 1102.2601 - Graphical models in Macaulay2 (with Luis Garcia-Puente and Sonja Petrovic)
*Journal of Software for Algebra and Geometry***5**(2013)1208.6550 Code - Positivity for Gaussian graphical models (with Jan Draisma and Kelli Talaska)
*Adv. in Appl. Math.***50**(2013), no. 5, 661–674. 1210.0390 - Polyhedral combinatorics of UPGMA cones (with Ruth Davidson)
*Adv. in Appl. Math.***50**(2013), no. 2, 327–338.1206.1621 Supplementary Materials - When do phylogenetic mixture models mimic other phylogenetic models? (with Elizabeth Allman and John Rhodes)
*Systematic Biology*(2012)**61**(6): 1049-1059 1202.2396 - The disentangling number for phylogenetic mixtures.
*SIAM Journal on Discrete Mathematics***26**-2 (2012), pp. 856-859 1107.2880 - Identifiability of large phylogenetic mixture models. (with John Rhodes).
*Bull. Math. Biol.***74**(2012), no. 1, 212–231. 1011.4134 - Finite Gröbner bases in infinite dimensional polynomial rings and applications. (with Christopher Hillar).
*Advances in Mathematics***221**(2012) 1-25 0908.1777 - Geodesics in CAT(0) cubical complexes. (with Federico Ardila and Megan Owen).
*Advances in Applied Mathematics***48**(2012) 142-163 1101.2428 - Eulerian-Catalan numbers. (with Hoda Bidkhori).
*Electronic Journal of Combinatorics***18**no.1 (2011) #P187 1101.1108 - Global identifiability of linear structural equation models (with Mathias Drton and Rina Foygel),
*Annals of Statistics***39**(2011):865-886. 1003.1146 - Identifiability of two-tree mixtures for group-based models. (with Elizabeth Allman, Sonja Petrovic, and John Rhodes),
*IEEE/ACM Transactions in Computational Biology and Bioinformatics*,**8**no. 3 (2011) 710-722. 0909.1854 Supplementary Materials - Normal binary graph models.
*Annals of the Institute of Statistical Mathematics,*Special Issue: Algebraic Methods in Computational Statistics,**64**no.4 (2010) 717-726 0906.1784 - Trek separation for Gaussian graphical models. (with Kelli Talaska and Jan Draisma),
*Annals of Statistics***38**no.3 (2010) 1665-1685 0812.1938 - Markov models for accumulating mutations. (with Niko Beerenwinkel),
*Biometrika***96**no. 3 (2009) 645-661 0709.2646 - Prolongations and computational algebra. (with Jessica Sidman),
*Canadian Journal of Mathematics***61**no. 4 (2009) 930-949 math.AC/0611696 - A Gröbner basis for the secant ideal of the second hypersimplex.
*Journal of Commutative Algebra***1**no.2 (2009) 0804.2897 - Gaussian conditional independence relations have no finite complete characterization. Journal of Pure and Applied Algebra,
**213**(2009) 1502-1506 (special issue on Theoretical and Practical Effectivity of Gröbner Bases) 0704.2847 - Toric geometry of cuts and splits. (with Bernd Sturmfels)
*Michigan Mathematical Journal***57**(2008) 689-709 (special issue in honor of Mel Hochster) math.AC/0606683 - Algebraic geometry of Gaussian Bayesian networks.
*Adv. in Appl. Math.***40**(2008), no. 4, 482--513. 0704.0918 - Combinatorial symbolic powers.
*J. Algebra***319**(2008), no. 1, 115--142. math.AC/0608542 - Algebraic statistical models. (with Mathias Drton)
*Statist. Sinica***17**(2007), no. 4, 1273--1297. math.ST/0703609 - Toric fiber products.
*J. Algebra***316**(2007), no. 2, 560--577. math.AC/0602052 - Algebraic factor analysis: tetrads, pentads, and beyond. (with Mathias Drton and Bernd Sturmfels), Probability Theory and Related Fields 138 (2007), no. 3-4, 463--493. math.ST/0509390
- A finiteness theorem for
Markov bases of hierarchical models
*.*(with Serkan Hosten) J. Combin. Theory Ser. A 114 (2007), no. 2, 311--321. math.CO/0401379 - Combinatorial secant varieties. (with Bernd Sturmfels) Quarterly Journal of Pure and Applied Mathematics 2 (2006) 285-309 (Special issue in honor of Robert Macpherson) math.AC/0506223
- Compressed polytopes and statistical disclosure limitation. Tohoku Math. J. (2) 58 (2006), no. 3, 433--445. math.CO/0412535
- Sequential importance sampling
for multiway tables.
- Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models. (with Nicholas Eriksson, Stephen E. Fienberg, and Alessandro Rinaldo), Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006) 222-233 math.CO/0405044
- The space of compatible full
conditionals is a unimodular toric
variety
*.* - Small contingency tables with
large gaps.
- Toric ideals of phylogenetic
invariants
*.**Journal of Computational Biology***12**(2005) 204-228. q-bio.PE/0402015 - Ideals of adjacent minors
*.* - A divide-and-conquer
algorithm for generating Markov bases of
multi-way tables
*.*(with A. Dobra), Computational Statistics 19 (2004), 347-366 - Markov bases of binary graph
models
*.***7**(2003), 441-466 math.CO/0308280 - Gröbner bases and polyhedral
geometry of reducible and cyclic
models
*.***100**(2002) no. 2, 277-301

**Conference Proceedings and Book Chapters**

- Identifying causal effects with computer algebra (with Luis Garcia-Puente and Sarah Spielvogel)
*Uncertainty in Artificial Intelligence,*Proceedings of the 26th Conferences, AUAI Press, 2010. 1007.3784 - Algebraic complexity of maximum likelihood estimation for
bivariate missing data. (with Serkan Hosten), Book chapter in the book
*Algebraic and Geometric Methods in Statistics*, Cambridge University Press, 2009. ISBN-13: 9780521896191 arXiv:0709.0935. - Phylogenetic algebraic geometry
*.*(with Nicholas Eriksson, Kristian Ranestad, and Bernd Sturmfels), in Projective Varieties with Unexpected Properties, edited by C. Ciliberto, et al., Walter de Gruyter, Berlin, 2005 math.AG/0407033 - Catalog of small trees. (with Marta Casanellas and Luis Garcia-Puente), in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.
- The strand symmetric model. (with Marta Casanellas), in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.

**Theses**

- Toric ideals in algebraic statistics, 2005 pdf. (Ph. D. Thesis, UC Berkeley)
- Algebraic geometry and
combinatorics of hierarchical models, 2002

**Unpublished Notes**

- Tight closure
of monomial ideals in Fermat rings
*.*

Research has been supported in part by the U.S. National Science Foundation and the David and Lucille Packard Foundation.