Publications and Preprints -- Seth Sullivant

Books

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

Papers in Preparation

  1. Toric fiber products, II (with Alexander Engström and Thomas Kahle)
  2. Why does the shuttle algorithm work?

Submitted Papers

  1. Identifiability of two-tree mixtures for group-based models. (with Elizabeth Allman, Sonja Petrovic, and John Rhodes) 0909.1854 Supplementary Materials
  2. Finite Gröbner bases in infinite dimensional polynomial rings and applications. (with Christopher Hillar) 0908.1777
  3. Normal binary graph models. 2009, 0906.1784

Papers in Press

  1. Trek separation for Gaussian graphical models. (with Kelli Talaska and Jan Draisma), 2008, to appear in the Annals of Statistics0812.1938
  2. Algebraic complexity of maximum likelihood estimation for bivariate missing data.  (with Serkan Hosten), 2007, to appear in the Pistone Birthday Volume arXiv:0709.0935.

Papers in Print

  1. Markov models for accumulating mutations.  (with Niko Beerenwinkel), Biometrika 96 no. 3 (2009) 645-661
  2. Prolongations and computational algebra.  (with Jessica Sidman), Canadian Journal of Mathematics 61 no. 4 (2009) 930-949 math.AC/0611696
  3. A Gröbner basis for the secant ideal of the second hypersimplex.  Journal of Commutative Algebra 1 no.2 (2009) 0804.2897
  4. 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
  5. 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
  6. Algebraic geometry of Gaussian Bayesian networks. Adv. in Appl. Math. 40 (2008), no. 4, 482--513. 0704.0918
  7. Combinatorial symbolic powers. J. Algebra 319 (2008), no. 1, 115--142. math.AC/0608542
  8. Algebraic statistical models. (with Mathias Drton) Statist. Sinica 17 (2007), no. 4, 1273--1297.  math.ST/0703609
  9. Toric fiber products. J. Algebra 316 (2007), no. 2, 560--577. math.AC/0602052
  10. 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
  11. 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
  12. 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
  13. Compressed polytopes and statistical disclosure limitation.  Tohoku Math. J. (2)  58  (2006),  no. 3, 433--445. math.CO/0412535
  14. Sequential importance sampling for multiway tables.  (with Yuguo Chen and Ian Dinwoodie), Annals of Statistics (2006) 34 No. 1, 523-545  math.ST/0605615
  15. 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
  16. The space of compatible full conditionals is a unimodular toric variety.   (with Aleksandra Slavkovic), Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006) 196-209  math.AG/0405046
  17. Small contingency tables with large gaps.  SIAM Journal of Discrete Mathematics  18 (2005) no.4, 787-793  math.OC/0405038
  18. Toric ideals of phylogenetic invariants.  (with Bernd Sturmfels), Journal of Computational Biology 12 (2005) 204-228.   q-bio.PE/0402015
  19. Ideals of adjacent minors.  (with Serkan Hosten),  Journal of Algebra  277 (2004), 615-642   math.AC/0306318
  20. A divide-and-conquer algorithm for generating Markov bases of multi-way tables.  (with A. Dobra),  Computational Statistics  19 (2004), 347-366
  21. Markov bases of binary graph models.  (with Mike Develin), Annals of Combinatorics  7 (2003), 441-466 math.CO/0308280
  22. Gröbner bases and polyhedral geometry of reducible and cyclic models.  (with Serkan Hosten)  Journal of Combinatorial Theory: Series A 100 (2002) no. 2, 277-301

Conference Proceedings and Book Chapters

  1. 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
  2. Catalog of small trees.  (with Marta Casanellas and Luis David Garcia), in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.
  3. 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

  1. Toric ideals in algebraic statistics, 2005 pdf. (Ph. D. Thesis, UC Berkeley)
  2. Algebraic geometry and combinatorics of hierarchical models, 2002  PS (M.A. Thesis, San Francisco State University)

Unpublished Notes

  1. Tight closure of monomial ideals in Fermat rings.  For Math 274, Fall 2002  PS