Seth M. Sullivant

Works (65)

Updated: April 5th, 2024 06:00

2023 journal article

Identifiability of linear compartmental tree models and a general formula for input-output equations

ADVANCES IN APPLIED MATHEMATICS, 146.

By: C. Bortner n, E. Gross*, N. Meshkat*, A. Shiu* & S. Sullivant n

Source: Web Of Science
Added: February 27, 2023

2023 journal article

On mixing behavior of a family of random walks determined by a linear recurrence

DISCRETE MATHEMATICS, 346(1).

By: C. Stanley* & S. Sullivant n

author keywords: Random walk; Mixing time; Linear recurrence
Source: Web Of Science
Added: October 31, 2022

2023 journal article

The h*-polynomial of the order polytope of the zig-zag poset

ELECTRONIC JOURNAL OF COMBINATORICS, 30(2).

By: J. Coons* & S. Sullivant n

co-author countries: Slovakia 🇸🇰
Source: Web Of Science
Added: July 10, 2023

2022 journal article

Directed Gaussian graphical models with toric vanishing ideals

ADVANCES IN APPLIED MATHEMATICS, 138.

By: P. Misra n & S. Sullivant n

author keywords: Clique sum; d-Separation; t-Separation; Shortest trek map; Safe gluing
Source: Web Of Science
Added: August 15, 2022

2022 article

Exchangeable and sampling-consistent distributions on rooted binary trees

Hollering, B., & Sullivant, S. (2022, January 14). JOURNAL OF APPLIED PROBABILITY.

By: B. Hollering n & S. Sullivant n

author keywords: Beta-splitting model; multinomial model; random trees
Source: Web Of Science
Added: January 24, 2022

2022 journal article

Structural identifiability of series-parallel LCR systems

JOURNAL OF SYMBOLIC COMPUTATION, 112, 79–104.

By: C. Bortner n & S. Sullivant n

author keywords: Identifiability; Structural identifiability; LCR circuit; Resultant; Algebraic geometry; Algebraic statistics
Source: Web Of Science
Added: March 14, 2022

2021 journal article

Identifiability in phylogenetics using algebraic matroids

JOURNAL OF SYMBOLIC COMPUTATION, 104, 142–158.

By: B. Hollering n & S. Sullivant n

author keywords: Identifiability; Algebraic matroids; Phylogenetics; Group-based models; Mixture models
Source: Web Of Science
Added: January 19, 2021

2021 journal article

Quasi-independence models with rational maximum likelihood estimator

JOURNAL OF SYMBOLIC COMPUTATION, 104, 917–941.

By: J. Coons n & S. Sullivant n

author keywords: Algebraic statistics; Maximum likelihood estimation; Quasi-independence models; Log-linear models; Maximum likelihood degree
Source: Web Of Science
Added: January 19, 2021

2019 journal article

BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE FOR A GIVEN TREE SHAPE

SIAM JOURNAL ON DISCRETE MATHEMATICS, 33(4), 2316–2325.

By: P. Misra* & S. Sullivant*

author keywords: maximum agreement subtree; exchangeability; sampling consistency
Source: Web Of Science
Added: June 29, 2020

2019 journal article

Strongly Robust Toric Ideals in Codimension 2

Journal of Algebraic Statistics, 10(1), 128–136.

By: S. Sullivant*

author keywords: toric ideal; Graver basis; robust; Hilbert basis
Source: Crossref
Added: June 20, 2019

2018 monograph

Algebraic Statistics

By: S. Sullivant n

Source: Crossref
Added: June 30, 2019

2018 journal article

Identifiability of Phylogenetic Parameters from k-mer Data Under the Coalescent

Bulletin of Mathematical Biology, 81(2), 431–451.

By: C. Durden n & S. Sullivant n

author keywords: k-mer method; Coalescent; Algebraic geometry
MeSH headings : Algorithms; Computational Biology; Evolution, Molecular; Markov Chains; Mathematical Concepts; Models, Genetic; Models, Statistical; Mutation; Phylogeny; Probability; Sequence Alignment / statistics & numerical data; Stochastic Processes
Sources: Web Of Science, Crossref
Added: February 11, 2019

2018 journal article

The maximum likelihood threshold of a graph

BERNOULLI, 24(1), 386–407.

By: E. Gross & S. Sullivant*

author keywords: algebraic matroids; Gaussian graphical models; matrix completion; maximum likelihood estimation; maximum likelihood threshold; rigidity theory; score matching estimator; weak maximum likelihood threshold
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Normal Binary Hierarchical Models

EXPERIMENTAL MATHEMATICS, 26(2), 153–164.

By: D. Bernstein n & S. Sullivant n

author keywords: algebraic statistics; contingency tables; Hilbert basis; Groebner basis; combinatorics
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Statistically Consistent k-mer Methods for Phylogenetic Tree Reconstruction

JOURNAL OF COMPUTATIONAL BIOLOGY, 24(2), 153–171.

By: E. Allman*, J. Rhodes* & S. Sullivant n

author keywords: phylogenetic trees; alignment-free methods; k-mer
MeSH headings : Algorithms; Base Sequence; Computer Simulation; Evolution, Molecular; Models, Genetic; Phylogeny; Sequence Alignment; Sequence Analysis, DNA
Source: Web Of Science
Added: August 6, 2018

2017 journal article

Unimodular binary hierarchical models

JOURNAL OF COMBINATORIAL THEORY SERIES B, 123, 97–125.

By: D. Bernstein n & S. Sullivant n

author keywords: Graver basis; Algebraic statistics; Log-linear models; Hierarchical models; Toric ideal
Source: Web Of Science
Added: August 6, 2018

2016 journal article

Lifting Markov bases and higher codimension toric fiber products

Journal of Symbolic Computation, 74, 276–307.

By: J. Rauh* & S. Sullivant n

co-author countries: Germany 🇩🇪
author keywords: Markov bases; Toric fiber product; Lifting; Grobner bases
Source: Crossref
Added: June 30, 2019

2016 journal article

Matrix Schubert varieties and Gaussian conditional independence models

JOURNAL OF ALGEBRAIC COMBINATORICS, 44(4), 1009–1046.

By: A. Fink*, J. Rajchgot* & S. Sullivant n

co-author countries: United Kingdom of Great Britain and Northern Ireland 🇬🇧
author keywords: Gaussian random variables; Conditional independence; Gaussian graphical models; Matrix Schubert varieties; Kazhdan-Lusztig varieties
Source: Web Of Science
Added: August 6, 2018

2015 journal article

BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE

SIAM JOURNAL ON DISCRETE MATHEMATICS, 29(4), 2065–2074.

By: D. Bernstein*, L. Ho, C. Long*, M. Steel, K. St John & S. Sullivant*

author keywords: random trees; agreement subtrees; Yule-Harding distribution
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Identifiability Results for Several Classes of Linear Compartment Models

BULLETIN OF MATHEMATICAL BIOLOGY, 77(8), 1620–1651.

By: N. Meshkat n, S. Sullivant n & M. Eisenberg*

author keywords: Identifiability; Linear compartment models; Identifiable functions; Differential algebra
MeSH headings : Animals; Endosomes / metabolism; Humans; Linear Models; Manganese / pharmacokinetics; Mathematical Concepts; Models, Biological; Rats
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Identifiability of 3-class Jukes-Cantor mixtures

ADVANCES IN APPLIED MATHEMATICS, 64, 89–110.

By: C. Long n & S. Sullivant n

author keywords: Phylogenetic mixture models; Identifiability; Tropical geometry; Disentangling number
Source: Web Of Science
Added: August 6, 2018

2015 journal article

Tying up loose strands: Defining equations of the strand symmetric model

Journal of Algebraic Statistics, 6(1), 17–23.

By: C. Long* & S. Sullivant*

Source: NC State University Libraries
Added: August 6, 2018

2014 journal article

Distance-Based Phylogenetic Methods Around a Polytomy

IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, 11(2), 325–335.

By: R. Davidson n & S. Sullivant n

author keywords: Neighbor-joining; phylogeny; polyhedra; polytomy; UPGMA
MeSH headings : Algorithms; Computational Biology / methods; Evolution, Molecular; Models, Genetic; Phylogeny
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Identifiable reparametrizations of linear compartment models

JOURNAL OF SYMBOLIC COMPUTATION, 63, 46–67.

By: N. Meshkat n & S. Sullivant n

author keywords: Identifiability; Compartment models; Reparametrization
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Multigraded commutative algebra of graph decompositions

JOURNAL OF ALGEBRAIC COMBINATORICS, 39(2), 335–372.

By: A. Engstrom*, T. Kahle* & S. Sullivant n

co-author countries: Germany 🇩🇪 Finland 🇫🇮
author keywords: Toric fiber product; Toric ideal; Segre product; Markov basis; Primary decomposition; Algebraic statistics; Conditional independence ideal; Normality of ideals
Source: Web Of Science
Added: August 6, 2018

2014 journal article

POSITIVE MARGINS AND PRIMARY DECOMPOSITION

JOURNAL OF COMMUTATIVE ALGEBRA, 6(2), 173–208.

By: T. Kahle, J. Rauh & S. Sullivant*

author keywords: Algebraic statistics; Markov basis; connectivity of fibers; binomial primary decomposition
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Structural Identifiability of Viscoelastic Mechanical Systems

PLOS ONE, 9(2).

By: A. Mahdi n, N. Meshkat n & S. Sullivant n

MeSH headings : Algorithms; Arteries / pathology; Blood Pressure; Computer Simulation; Elasticity; Endothelium, Vascular / pathology; Humans; Models, Cardiovascular; Stress, Mechanical; Viscosity
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Graphical models

Journal of Software for Algebra and Geometry, 5(1), 1–7.

By: L. García-Puente*, S. Petrović* & S. Sullivant n

Source: Crossref
Added: June 30, 2019

2013 journal article

Polyhedral combinatorics of UPGMA cones

ADVANCES IN APPLIED MATHEMATICS, 50(2), 327–338.

By: R. Davidson n & S. Sullivant n

author keywords: Phylogenetic trees; Polyhedral combinatorics; Partition lattice
Source: Web Of Science
Added: August 6, 2018

2013 journal article

Positivity for Gaussian graphical models

ADVANCES IN APPLIED MATHEMATICS, 50(5), 661–674.

By: J. Draisma*, S. Sullivant n & K. Talaska*

co-author countries: Netherlands 🇳🇱
author keywords: Gaussian graphical model; Conditional independence; Determinant; Lindstrom-Gessel-Viennot Lemma
Source: Web Of Science
Added: August 6, 2018

2012 journal article

Finite Gröbner bases in infinite dimensional polynomial rings and applications

Advances in Mathematics, 229(1), 1–25.

By: C. Hillar* & S. Sullivant n

author keywords: Grobner basis; Algebraic statistics; Semigroup ring; Well-partial order; Symmetric group; Markov basis
Sources: Web Of Science, Crossref
Added: August 6, 2018

2012 journal article

Geodesics in CAT(0) cubical complexes

ADVANCES IN APPLIED MATHEMATICS, 48(1), 142–163.

By: F. Ardila*, M. Owen* & S. Sullivant n

author keywords: CAT(0); Cubical complex; Partially ordered set; Geodesic; Reconfigurable system; Touring problem
Source: Web Of Science
Added: August 6, 2018

2012 journal article

Identifiability of Large Phylogenetic Mixture Models

BULLETIN OF MATHEMATICAL BIOLOGY, 74(1), 212–231.

By: J. Rhodes* & S. Sullivant n

author keywords: Phylogenetic mixture model; Parameter identifiability
MeSH headings : Evolution, Molecular; Models, Genetic; Models, Statistical; Phylogeny
Source: Web Of Science
Added: August 6, 2018

2012 journal article

THE DISENTANGLING NUMBER FOR PHYLOGENETIC MIXTURES

SIAM JOURNAL ON DISCRETE MATHEMATICS, 26(2), 856–859.

By: S. Sullivant*

author keywords: phylogenetics; mixture models; contingency tables; trees
Source: Web Of Science
Added: August 6, 2018

2012 journal article

When Do Phylogenetic Mixture Models Mimic Other Phylogenetic Models?

SYSTEMATIC BIOLOGY, 61(6), 1049–1059.

By: E. Allman n, J. Rhodes n & S. Sullivant n

author keywords: Phylogenetic mixture models; parameter identifiability; heterogeneous sequence evolution
MeSH headings : Algorithms; Computer Simulation; Data Interpretation, Statistical; Models, Biological; Phylogeny
Source: Web Of Science
Added: August 6, 2018

2011 journal article

Eulerian-Catalan numbers

Electronic Journal of Combinatorics, 18(1).

By: H. Bidkhori & S. Sullivant

Source: NC State University Libraries
Added: August 6, 2018

2011 journal article

GLOBAL IDENTIFIABILITY OF LINEAR STRUCTURAL EQUATION MODELS

ANNALS OF STATISTICS, 39(2), 865–886.

By: M. Drton, R. Foygel & S. Sullivant*

author keywords: Covariance matrix; Gaussian distribution; graphical model; multivariate normal distribution; parameter identification; structural equation model
Source: Web Of Science
Added: August 6, 2018

2011 journal article

Identifiability of Two-Tree Mixtures for Group-Based Models

IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, 8(3), 710–722.

author keywords: Phylogenetic mixture; group-based model; identifiability of phylogenetic models
MeSH headings : Algorithms; Computational Biology / methods; DNA / genetics; Databases, Nucleic Acid; Markov Chains; Models, Genetic; Models, Statistical; Phylogeny
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Normal binary graph models

ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 62(4), 717–726.

By: S. Sullivant n

author keywords: Marginal cone; Normal semigroup; Algebraic statistics
Source: Web Of Science
Added: August 6, 2018

2010 journal article

Normal binary graph models.

Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics, 64(4), 717–726.

By: S. Sullivant

Source: NC State University Libraries
Added: July 10, 2019

2010 journal article

TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS

ANNALS OF STATISTICS, 38(3), 1665–1685.

By: S. Sullivant*, K. Talaska & J. Draisma

author keywords: Graphical model; Bayesian network; Gessel-Viennot-Lindstrom lemma; trek rule; linear regression; conditional independence
Source: Web Of Science
Added: August 6, 2018

2009 journal article

A Gröbner basis for the secant ideal of the second hypersimplex

Journal of Commutative Algebra, 1(2), 327–338.

By: S. Sullivant*

Source: Crossref
Added: June 30, 2019

2009 book

Emerging Applications of Algebraic Geometry

In The IMA Volumes in Mathematics and its Applications.

Seth Sullivant

Ed(s): M. Putinar & S. Sullivant*

Source: Crossref
Added: June 30, 2019

2009 article

Gaussian conditional independence relations have no finite complete characterization

Sullivant, S. (2009, August). JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 213, pp. 1502–1506.

By: S. Sullivant n

Source: Web Of Science
Added: August 6, 2018

2009 book

Lectures on Algebraic Statistics

By: M. Drton*, B. Sturmfels* & S. Sullivant n

Source: Crossref
Added: June 30, 2019

2009 journal article

Markov models for accumulating mutations

BIOMETRIKA, 96(3), 645–661.

By: N. Beerenwinkel* & S. Sullivant n

co-author countries: Switzerland 🇨🇭
author keywords: Bayesian network; Cancer; Genetic progression; HIV; Partially ordered set; Poset
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Prolongations and Computational Algebra

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 61(4), 930–949.

By: J. Sidman* & S. Sullivant n

Source: Web Of Science
Added: August 6, 2018

2008 journal article

Algebraic geometry of Gaussian Bayesian networks

Advances in Applied Mathematics, 40(4), 482–513.

By: S. Sullivant*

author keywords: Bayesian network; graphical model; algebraic statistics; multivariate Gaussian; Grobbner basis
Source: Crossref
Added: June 30, 2019

2008 journal article

Combinatorial symbolic powers

Journal of Algebra, 319(1), 115–142.

By: S. Sullivant*

author keywords: symbolic power; Grobner basis; perfect graph; edge ideal; determinantal ideal
Source: Crossref
Added: June 30, 2019

2008 journal article

Toric geometry of cuts and splits

The Michigan Mathematical Journal, 57(0), 689–709.

By: B. Sturmfels & S. Sullivant*

Source: Crossref
Added: June 30, 2019

2007 journal article

A finiteness theorem for Markov bases of hierarchical models

Journal of Combinatorial Theory, Series A, 114(2), 311–321.

By: S. Hoşten* & S. Sullivant*

author keywords: contingency tables; Markov bases; hierarchical models; graver complexity
Source: Crossref
Added: June 30, 2019

2007 journal article

Algebraic statistical models.

Statistica Sinica, 17(4), 1273–1297.

By: M. Drton & S. Sullivant

Source: NC State University Libraries
Added: July 28, 2019

2007 journal article

Toric fiber products

Journal of Algebra, 316(2), 560–577.

By: S. Sullivant*

author keywords: Grobner basis; algebraic statistics; hierarchical model; phylogenetic invariants
Source: Crossref
Added: June 30, 2019

2006 journal article

Algebraic factor analysis: tetrads, pentads and beyond

Probability Theory and Related Fields, 138(3-4), 463–493.

By: M. Drton*, B. Sturmfels* & S. Sullivant*

Source: Crossref
Added: June 30, 2019

2006 journal article

Combinatorial secant varieties.

Quarterly Journal of Pure and Applied Mathematics, 2, 285–309.

By: B. Sturmfels & S. Sullivant

Source: NC State University Libraries
Added: July 10, 2019

2006 journal article

Compressed polytopes and statistical disclosure limitation

Tohoku Mathematical Journal, 58(3), 433–445.

By: S. Sullivant*

author keywords: compressed polytope; disclosure limitation; algebraic statistics; integer programming; cut polytope
Source: Crossref
Added: June 30, 2019

2006 journal article

Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models

Journal of Symbolic Computation, 41(2), 222–233.

By: N. Eriksson*, S. Fienberg*, A. Rinaldo* & S. Sullivant*

author keywords: maximum likelihood estimate (MLE); marginal cone; tree width; collapsing
Source: Crossref
Added: June 30, 2019

2006 journal article

Sequential importance sampling for multiway tables

The Annals of Statistics, 34(1), 523–545.

By: Y. Chen, I. Dinwoodie* & S. Sullivant*

author keywords: conditional inference; contingency table; exact test; Monte Carlo sequential importance sampling; toric ideal
Source: Crossref
Added: June 30, 2019

2006 journal article

The space of compatible full conditionals is a unimodular toric variety

Journal of Symbolic Computation, 41(2), 196–209.

By: A. Slavkovic* & S. Sullivant*

author keywords: odds ratios; toric ideal; unimodular
Source: Crossref
Added: June 30, 2019

2005 journal article

Small Contingency Tables with Large Gaps

SIAM Journal on Discrete Mathematics, 18(4), 787–793.

By: S. Sullivant*

author keywords: disclosure limitation; integer programming; Grobner basis; contingency table
Source: Crossref
Added: June 30, 2019

2005 journal article

Toric Ideals of Phylogenetic Invariants

Journal of Computational Biology, 12(2), 204–228.

By: B. Sturmfels* & S. Sullivant*

MeSH headings : Animals; Computational Biology / statistics & numerical data; Data Interpretation, Statistical; Humans; Models, Genetic; Phylogeny
Source: Crossref
Added: June 30, 2019

2004 journal article

A Divide-and-Conquer Algorithm for Generating Markov Bases of Multi-way Tables

Computational Statistics, 19(3), 347–366.

By: A. Dobra* & S. Sullivant*

author keywords: contingency tables; decomposable graphical models; disclosure limitation; exact distributions; Grobner bases; Markov bases
Source: Crossref
Added: June 30, 2019

2004 journal article

Ideals of adjacent minors

Journal of Algebra, 277(2), 615–642.

By: S. Hoşten* & S. Sullivant*

Source: Crossref
Added: June 30, 2019

2003 journal article

Markov Bases of Binary Graph Models

Annals of Combinatorics, 7(4), 441–466.

By: S. Sullivant* & M. Develin*

Source: Crossref
Added: June 30, 2019

2002 journal article

Gröbner Bases and Polyhedral Geometry of Reducible and Cyclic Models

Journal of Combinatorial Theory, Series A, 100(2), 277–301.

By: S. Hoşten & S. Sullivant*

Source: Crossref
Added: June 30, 2019

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