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. The Cavender-Farris-Neyman model with a molecular clock
    Jane Coons, Seth Sullivant
    1805.04175

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

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

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

  9. Papers in Press

  10. 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

  11. 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

  12. 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

  13. Papers in Print

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

  15. 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

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

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

  18. 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

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

  20. 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

  21. 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

  22. 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

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

  24. 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

  39. 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

  40. 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

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

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

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

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

  45. 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

  46. 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

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

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

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

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

  51. 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

  52. 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

  53. 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

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

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


  56. 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

  57. 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


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

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


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


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


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


  63. 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


  64. Conference Proceedings and Book Chapters

  65. 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

  66. 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.

  67. 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

  68. 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.

  69. 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.

  70. Theses

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

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

  73. Unpublished Notes

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

  75. 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.