Publications and Preprints -- Seth Sullivant

    Books

  1. Algebraic Statistics (in preparation)
    Seth Sullivant
    American Mathematical Society, Graduate Studies in Mathematics

  2. Lectures on Algebraic Statistics
    Mathias Drton, Bernd Sturmfels, Seth Sullivant
    Oberwolfach Seminar Series 39, Birkhauser, 2009

  3. Emerging Applications of Algebraic Geometry
    Mihai Putinar, Seth Sullivant (editors),
    IMA Series 149, Springer, 2008
  4. Submitted Papers and Preprints

  5. On mixing behavior of a family of random walks determined by a linear recurrence
    Caprice Stanley, Seth Sullivant
    1710.03845

  6. Strongly robust toric ideals in codimension 2.
    Seth Sullivant
    1610.07476

  7. Sequential importance sampling for the Ising model
    Jing Xi, Seth Sullivant
    1410.4217

  8. Papers in Press

  9. Identifiability of phylogenetic parameters from k-mer data under the coalescent
    Chris Durden, Seth Sullivant
    To appear in Bulletin of Mathematical Biology Special Issue on Algebraic Methods in Phylogenetics. 1705.06993

  10. Algebraic aspects of conditional independence and graphical models.
    Thomas Kahle, Johannes Rauh, Seth Sullivant
    To appear in Handbook of Graphical Models, CRC Press (Editors: Mathis Drton, Steffen Lauritzen, Marloes Matthuis, Martin Wainwright). 1705.07411

  11. Algebraic tools for the analysis of state space models
    Nicolette Meshkat, Zvi Rosen, Seth Sullivant
    To appear in Proceedings of Mathematical Society of Japan, 2015 Summer Institute on Grobner bases 1609.07985

  12. Papers in Print

  13. The maximum likelihood threshold of a graph
    Elizabeth Gross, Seth Sullivant
    Bernoulli 24 (2018), no. 1, 386–407. 1404.6989

  14. Statistically consistent k-mer methods for phylogenetic tree reconstruction
    Elizabeth Allman, John Rhodes, Seth Sullivant
    Journal of Computational Biology February 2017, 24(2): 153-171. 1511.01956 Supplementary Materials

  15. Unimodular binary hierarchical models
    Daniel I. Bernstein, Seth Sullivant
    Journal of Combinatorial Theory: Series B 123 (2017), 97–125. 1502.06131 Supplementary Materials

  16. Normal binary hierarchical models
    Daniel I. Bernstein, Seth Sullivant
    Experimental Mathematics 26 (2017), no. 2, 153–164. 1508.05461

  17. Matrix Schubert varieties and Gaussian conditional independence models
    Alex Fink, Jenna Rajchgot, Seth Sullivant
    Journal of Algebraic Combinatorics, 44 (2016), no. 4, 1009-1046. 1510.04124

  18. Lifting Markov bases and higher codimension toric fiber products
    Johannes Rauh, Seth Sullivant
    J. Symbolic Comput. 74 (2016), 276–307. 1404.6392

  19. Identifiability results for several classes of linear compartment models
    Nicolette Meshkat, Marisa Eisenberg, Seth Sullivant
    Bull. Math. Biol. 77 (2015), no. 8, 1620–1651. 1410.8587

  20. Bounds on the expected size of the maximum agreement subtree
    Daniel I. Bernstein, Lam Ho, Colby Long, Mike Steel, Katherine St. John, Seth Sullivant
    SIAM J. Discrete Math. 29 (2015), no. 4, 2065–2074.1411.7338

  21. Tying up loose strands: the defining equations of the strand symmetric model
    Colby Long, Seth Sullivant
    J. Algebr. Stat. 6 (2015), no. 1, 17–23.1410.3344   Supplementary Materials

  22. Identifiability of Jukes-Cantor 3-tree mixtures
    Colby Long, Seth Sullivant
    Adv. in Appl. Math. 64 (2015), 89–110. 1406.7256 Supplementary Materials

  23. Distance-based phylogenetic algorithms around a polytomy
    Ruth Davidson, Seth Sullivant
    IEEE/ACM Transactions in Computational Biology and Bioinformatics 11 (2014) 325-335 1307.5908   Supplementary Materials

  24. Positive margins and primary decomposition.
    Thomas Kahle, Johannes Rauh, Seth Sullivant
    Journal of Commutative Algebra 6 (2), (2014), pp 173-208.1201.2591

  25. Structural identifiability of viscoelastic mechanical systems
    Adam Mahdi, Nicolette Meshkat, Seth Sullivant
    PLOS One 9 (2014): e864111 1308.4950

  26. Identifiable reparametrizations of linear compartment models
    Nicolette Meshkat, Seth Sullivant
    Journal of Symbolic Computation 63 (2014), 46–67.1305.5768

  27. Multigraded commutative algebra of graph decompositions.
    Alexander Engström, Thomas Kahle, Seth Sullivant
    J. Algebraic Combinatorics 39 (2014) no. 2, 335-372 1102.2601

  28. Graphical models in Macaulay2
    Luis Garcia-Puente, Sonja Petrovic, Seth Sullivant
    Journal of Software for Algebra and Geometry 5 (2013)1208.6550 Code

  29. Positivity for Gaussian graphical models
    Jan Draisma, Seth Sullivant, Kelli Talaska
    Adv. in Appl. Math. 50 (2013), no. 5, 661–674. 1210.0390

  30. Polyhedral combinatorics of UPGMA cones
    Ruth Davidson, Seth Sullivant
    Adv. in Appl. Math. 50 (2013), no. 2, 327–338.1206.1621   Supplementary Materials

  31. When do phylogenetic mixture models mimic other phylogenetic models?
    Elizabeth Allman, John Rhodes, Seth Sullivant
    Systematic Biology (2012) 61 (6): 1049-1059 1202.2396

  32. The disentangling number for phylogenetic mixtures.
    Seth Sullivant
    SIAM Journal on Discrete Mathematics 26-2 (2012), pp. 856-859 1107.2880

  33. Identifiability of large phylogenetic mixture models.
    John Rhodes, Seth Sullivant
    Bull. Math. Biol. 74 (2012), no. 1, 212–231. 1011.4134

  34. Finite Gröbner bases in infinite dimensional polynomial rings and applications.
    Christopher Hillar, Seth Sullivant
    Advances in Mathematics 221 (2012) 1-25 0908.1777

  35. Geodesics in CAT(0) cubical complexes.
    Federico Ardila, Megan Owen, Seth Sullivant
    Advances in Applied Mathematics 48 (2012) 142-163 1101.2428

  36. Eulerian-Catalan numbers.
    Hoda Bidkhori, Seth Sullivant
    Electronic Journal of Combinatorics 18 no.1 (2011) #P187 1101.1108

  37. Global identifiability of linear structural equation models
    Mathias Drton, Rina Foygel, Seth Sullivant
    Annals of Statistics 39 (2011):865-886. 1003.1146

  38. Identifiability of two-tree mixtures for group-based models.
    Elizabeth Allman, Sonja Petrovic, John Rhodes, Seth Sullivant
    IEEE/ACM Transactions in Computational Biology and Bioinformatics, 8 no. 3 (2011) 710-722. 0909.1854   Supplementary Materials

  39. Normal binary graph models.
    Seth Sullivant
    Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics, 64 no.4 (2010) 717-726 0906.1784

  40. Trek separation for Gaussian graphical models.
    Kelli Talaska, Seth Sullivant, Jan Draisma
    Annals of Statistics 38 no.3 (2010) 1665-1685 0812.1938

  41. Markov models for accumulating mutations.  
    Niko Beerenwinkel, Seth Sullivant
    Biometrika 96 no. 3 (2009) 645-661 0709.2646

  42. Prolongations and computational algebra.  
    Jessica Sidman, Seth Sullivant
    Canadian Journal of Mathematics 61 no. 4 (2009) 930-949 math.AC/0611696

  43. A Gröbner basis for the secant ideal of the second hypersimplex.
    Seth Sullivant
     Journal of Commutative Algebra 1 no.2 (2009) 0804.2897

  44. Gaussian conditional independence relations have no finite complete characterization.
    Seth Sullivant
     Journal of Pure and Applied Algebra, 213 (2009) 1502-1506 (special issue on Theoretical and Practical Effectivity of Gröbner Bases)  0704.2847

  45. Toric geometry of cuts and splits.
    Bernd Sturmfels, Seth Sullivant
    Michigan Mathematical Journal 57 (2008) 689-709 (special issue in honor of Mel Hochster) math.AC/0606683

  46. Algebraic geometry of Gaussian Bayesian networks.
    Seth Sullivant
    Adv. in Appl. Math. 40 (2008), no. 4, 482--513. 0704.0918

  47. Combinatorial symbolic powers.
    Seth Sullivant
    J. Algebra 319 (2008), no. 1, 115--142. math.AC/0608542

  48. Algebraic statistical models.
    Mathias Drton, Seth Sullivant
    Statist. Sinica 17 (2007), no. 4, 1273--1297.  math.ST/0703609

  49. Toric fiber products.
    Seth Sullivant
    J. Algebra 316 (2007), no. 2, 560--577. math.AC/0602052

  50. Algebraic factor analysis:  tetrads, pentads, and beyond.  
    Mathias Drton, Bernd Sturmfels, Seth Sullivant
     Probability Theory and Related Fields  138 (2007), no. 3-4, 463--493.  math.ST/0509390

  51. A finiteness theorem for Markov bases of hierarchical models.   
    Serkan Hosten, Seth Sullivant  
    J. Combin. Theory Ser. A  114  (2007),  no. 2, 311--321.  math.CO/0401379

  52. Combinatorial secant varieties.  
    Bernd Sturmfels, Seth Sullivant
    Quarterly Journal of Pure and Applied Mathematics 2 (2006) 285-309  (Special issue in honor of Robert Macpherson) math.AC/0506223

  53. Compressed polytopes and statistical disclosure limitation. 
    Seth Sullivant
    Tohoku Math. J. (2)  58  (2006),  no. 3, 433--445. math.CO/0412535

  54. Sequential importance sampling for multiway tables.
    Yuguo Chen Ian Dinwoodie, Seth Sullivant
    Annals of Statistics (2006) 34 No. 1, 523-545  math.ST/0605615


  55. Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models.
    Nicholas Eriksson, Stephen E. Fienberg, Alessandro Rinaldo, Seth Sullivant 
    Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006)  222-233
    math.CO/0405044

  56. The space of compatible full conditionals is a unimodular toric variety
    Aleksandra Slavkovic, Seth Sullivant
    Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006) 196-209  math.AG/0405046


  57. Small contingency tables with large gaps.
    Seth Sullivant
    SIAM Journal of Discrete Mathematics  18 (2005) no.4, 787-793  math.OC/0405038

  58. Toric ideals of phylogenetic invariants
    Bernd Sturmfels, Seth Sullivant
    Journal of Computational Biology 12 (2005) 204-228.   q-bio.PE/0402015


  59. Ideals of adjacent minors
    Serkan Hosten, Seth Sullivant
    Journal of Algebra  277 (2004), 615-642   math.AC/0306318


  60. A divide-and-conquer algorithm for generating Markov bases of multi-way tables
    Adrian Dobra, Seth Sullivant
    Computational Statistics  19 (2004), 347-366


  61. Markov bases of binary graph models
    Mike Develin, Seth Sullivant
    Annals of Combinatorics  7 (2003), 441-466 math.CO/0308280


  62. Gröbner bases and polyhedral geometry of reducible and cyclic models
    Serkan Hosten, Seth Sullivant
    Journal of Combinatorial Theory: Series A 100 (2002) no. 2, 277-301


  63. Conference Proceedings and Book Chapters

  64. Identifying causal effects with computer algebra
    Luis Garcia-Puente, Sarah Spielvogel, Seth Sullivant
    Uncertainty in Artificial Intelligence, Proceedings of the 26th Conferences, AUAI Press, 2010. 1007.3784

  65. Algebraic complexity of maximum likelihood estimation for bivariate missing data.
    Serkan Hosten, Seth Sullivant
    Book chapter in the book Algebraic and Geometric Methods in Statistics, Cambridge University Press, 2009. ISBN-13: 9780521896191 arXiv:0709.0935.

  66. Phylogenetic algebraic geometry
    Nicholas Eriksson, Kristian Ranestad, Bernd Sturmfels, Seth Sullivant),
    in Projective Varieties with Unexpected Properties, edited by C. Ciliberto, et al.,  Walter de Gruyter, Berlin, 2005  math.AG/0407033

  67. Catalog of small trees. 
    Marta Casanellas, Luis Garcia-Puente, Seth Sullivant
    in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.

  68. The strand symmetric model. 
    Marta Casanellas, Seth Sullivant
    in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.

  69. Theses

  70. Toric ideals in algebraic statistics, 2005 pdf.
    (Ph. D. Thesis, UC Berkeley)

  71. Algebraic geometry and combinatorics of hierarchical models, 2002  PS
    (M.A. Thesis, San Francisco State University)

  72. Unpublished Notes

  73. The Markov basis of K_3,N
    Johannes Rauh, Seth Sullivant
    1406.5936

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


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