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 Articles | Bernd Sturmfels 289. Linear PDE with Constant Coefficients (with Rida Ait El Manssour and Marc Härkönen), 29pp, submitted to Glasgow Mathematical Journal. 288. Primary Decomposition with Differential Operators (with Yairon Cid-Ruiz), 16pp, submitted to Inventiones mathematicae. 287. Likelihood Equations and Scattering Amplitudes (with Simon Telen), 18pp, submitted to Algebraic Statistics. 286. KP Solitons from Tropical Limits (with Daniele Agostini, Claudia Fevola and Yelena Mandelshtam), 21pp, to be presented at MEGA 2021, Tromso. 285. Tangent Quadrics in Real 3-Space (with Taylor Brysiewicz and Claudia Fevola), 13pp, to appear in Le Matematiche. 284. Jordan Algebras of Symmetric Matrices (with Arthur Bik and Henrik Eisenmann), 15pp, to appear in Le Matematiche. 283. Pencils of Quadrics: Old and New (with Claudia Fevola and Yelena Mandelshtam), 15pp, to appear in Le Matematiche. 282. D-Modules and Holonomic Functions (with Anna-Laura Sattelberger), 36pp, presented at the Math+ Fall School in Algebraic Geometry (FU Berlin, October 2019). 281. The Dubrovin Threefold of an Algebraic Curve (with Daniele Agostini and Türkü Özlüm Çelik), 28pp, to appear in Nonlinearity. 280. Bad Projections of the PSD Cone (with Yuhan Jiang), 18pp, to appear in Collectanea Mathematica. 279. Primary Ideals and their Differential Equations (with Yairon Cid-Ruiz and Roser Homs), 33pp, to appear in Foundations of Computational Mathematics. 278. Positivity Certificates via Integral Representations (with Khazhgali Kozhasov and Mateusz Michalek), 22pp, to appear in Fulton 80 - LMS volume. 277. Theta Surfaces (with Daniele Agostini, Türkü Özlüm Çelik and Julia Struwe), 30pp, to appear in Vietnam Journal of Mathematics; Lecture slides. 276. Voronoi Cells of Varieties (with Diego Cifuentes, Kristian Ranestad and Madeleine Weinstein), 18pp, to appear in Journal of Symbolic Computation. 275. Maximum Likelihood Estimation for Totally Positive Log-Concave Densities (with Elina Robeva, Ngoc Tran and Caroline Uhler), 27pp, to appear in Scandinavian Journal of Statistics. 274. K3 Polytopes and their Quartic Surfaces (with Gabriele Balletti and Marta Panizzut), Advances in Geometry 21 (2021) 85--98. 273. Wasserstein Distance to Independence Models (with Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar and Lorenzo Venturello), Journal of Symbolic Computation 104 (2021) 855--873. 272. Discrete Statistical Models with Rational Maximum Likelihood Estimator (with Eliana Duarte and Orlando Marigliano), Bernoulli 27 (2021) 135-154. 271. Moment Varieties of Measures on Polytopes (with Kathlén Kohn and Boris Shapiro), Annali della Scuola Normale Superiore di Pisa 21 (2020) 739--770. 270. Brownian Motion Tree Models are Toric (with Caroline Uhler and Piotr Zwiernik), Kybernetika 56 (2020) 1154-1175. 269. Algebraic Analysis of Rotation Data (with Michael Adamer, András Lörincz and Anna-Laura Sattelberger), Algebraic Statistics 11 (2020) 189-211. 268. Estimating Linear Covariance Models with Numerical Nonlinear Algebra (with Sascha Timme and Piotr Zwiernik), Algebraic Statistics 11 (2020) 31-52. 267. An Octanomial Model for Cubic Surfaces (with Marta Panizzut and Emre Sertöz), Le Matematiche 75 (2020) 517-536. 266. Twenty-Seven Questions about the Cubic Surface (with Kristian Ranestad), Le Matematiche 75 (2020) 411-424. 265. The Schläfli Fan (with Michael Joswig and Marta Panizzut), Discrete and Computational Geometry 64 (2020) 355-381. 264. The Geometry of SDP-Exactness in Quadratic Optimization (with Diego Cifuentes and Corey Harris), Mathematical Programming, Ser. A 182 (2020) 399-428. 263. Optimal Transport to a Variety (with Türkü Özlüm Çelik, Asgar Jamneshan, Guido Montúfar and Lorenzo Venturello), Mathematical Aspects of Computer and Information Sciences, MACIS 2019, Istanbul, Springer Lecture Notes in Computer Science 11989 (2020) 364-381. 262. 3264 Conics in a Second (with Paul Breiding and Sascha Timme), Notices of the American Mathematical Society 67 (2020) 30-37. 261. Computing Convex Hulls of Trajectories (with Daniel Ciripoi, Andreas Löhne and Nidhi Kaihnsa), Revista de la Unión Matemática Argentina. 60 (2019) 637-662. 260. The Geometry of Gaussoids (with Alessio D'Ali, Tobias Boege and Thomas Kahle), Foundations of Computational Mathematics 19 (2019) 775-812. 259. Schottky Algorithms: Classical Meets Tropical (with Lynn Chua and Mario Kummer), Mathematics of Computation 88 (2019) 2541-2558. 258. Sixty-four Curves of Degree Six (with Nidhi Kaihnsa, Mario Kummer, Daniel Plaumann and Mahsa Sayyary), Experimental Mathematics 28 (2019) 132-150. 257. Learning Paths from Signature Tensors (with Max Pfeffer and Anna Seigal), SIAM Journal on Matrix Analysis and Applications 40 (2019) 394-416. 256. Varieties of Signature Tensors (with Carlos Améndola and Peter Friz), Forum of Mathematics, Sigma 7 (2019) e10, 54 pp. 255. Geometry of Log-Concave Density Estimation (with Elina Robeva and Caroline Uhler), Discrete and Computational Geometry 61 (2019) 136-160. 254. Algebraic Identifiability of Gaussian Mixtures (with Carlos Améndola and Kristian Ranestad), International Mathematics Research Notices 21 (2018) 6556-6580. 253. Learning Algebraic Varieties from Samples (with Paul Breiding, Sara Kalisnik and Madeleine Weinstein), Revista Matematica Complutense 31 (2018) 545-593; News story, Lecture. 252. Real Space Sextics and their Tritangents (with Avinash Kulkarni, Yue Ren and Mahsa Sayyary), Proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2018), ACM, New York, 2018, 247-254. 251. Distortion Varieties (with Joe Kileel, Zuzana Kukelova and Tomas Pajdla), Foundations of Computational Mathematics 18 (2018) 1043-1071. 250. Nearest Points on Toric Varieties (with Martin Helmer), Mathematica Scandinavica 122 (2018) 213-238. 249. Changing Views on Curves and Surfaces (with Kathlén Kohn and Matthew Trager), Acta Mathematica Vietnamica 43 (2018) 1-29. 248. Fitness, Apprenticeship, and Polynomials, In: Combinatorial Algebraic Geometry, (eds. G. Smith and B. Sturmfels), Fields Institute Communications, Springer, New York, vol 80, (2017) 1-19. 247. A Clever Elimination Strategy for Efficient Minimal Solvers (with Joe Kileel, Zuzana Kukelova and Tomas Pajdla), 13pp, IEEE Conference on Computer Vision and Pattern Recognition 2017 (CVPR 2017). 246. General Models for Rational Cameras and the Case of Two-Slit Projections (with Matthew Trager, John Canny, Martial Hebert and Jean Ponce), 9pp, IEEE Conference on Computer Vision and Pattern Recognition 2017 (CVPR 2017). 245. How to Flatten a Soccer Ball (with Kaie Kubjas and Pablo Parrilo), In: Homological and Computational Methods in Commutative Algebra, (eds. A. Conca, J. Gubeladze and T. Römer), Springer INdAM series, vol 20, (2017) 141-162 244. Convexity in Tree Spaces (with Bo Lin, Xiaoxian Tang and Ruriko Yoshida), SIAM Journal on Discrete Mathematics 31 (2017) 2015-2038. 243. Real Rank Two Geometry (with Anna Seigal), Journal of Algebra 484 (2017) 310-333. 242. Real Rank Geometry of Ternary Forms (with Mateusz Michalek, Hyunsuk Moon and Emanuele Ventura), Annali di Matematica Pura ed Applicata 196 (2017) 1025-1054. 241. Congruences and Concurrent Lines in Multi-View Geometry (with Jean Ponce and Matthew Trager), Advances in Applied Mathematics 88 (2017) 62-91. 240. Eigenconfigurations of Tensors (with Hirotachi Abo and Anna Seigal), in Algebraic and Geometric Methods in Discrete Mathematics, Contemporary Mathematics, vol 685, American Mathematical Society, (2017) 1-25. 239. On the Existence of Epipolar Matrices (with Sameer Agarwal, Hon-Leung Lee and Rekha Thomas), International Journal of Computer Vision 121 (2017) 403-415. 238. Does Antibiotic Resistance Evolve in Hospitals? (with Anna Seigal, Portia Mira and Miriam Barlow), Bulletin of Mathematical Biology 79 (2017) 191-208; News story. 237. The Hurwitz Form of a Projective Variety, Journal of Symbolic Computation 79 (2017) 186-196. 236. Tropicalization of Del Pezzo surfaces (with Qingchun Ren and Kristin Shaw), Advances in Mathematics 300 (2016) 156-189. 235. Tensors and their Eigenvectors, Notices of the American Mathematical Society 63 (2016) 604-606. 234. Symmetric Matrices, Catalan Paths, and Correlations (with Emmanuel Tsukerman and Lauren Williams), Journal of Combinatorial Theory, Series A 144 (2016) 496-510. 233. Rigid Multiview Varieties (with Michael Joswig, Joe Kileel and André Wagner), International Journal of Algebra and Computation 26 (2016) 775-788. 232. Moment Varieties of Gaussian Mixtures (with Carlos Améndola and Jean-Charles Faugère), Journal of Algebraic Statistics 7 (2016) 14-28. 231. Maximum Likelihood Estimates for Gaussian Mixtures Are Transcendental (with Carlos Améndola and Mathias Drton), Mathematical Aspects of Computer and Information Sciences, (eds. I. Kotsireas, S. Rump and C. Yap), MACIS 2015, Berlin, (2016) 579-590. 230. Computing the Chow Variety of Quadratic Space Curves (with Peter Bürgisser, Kathlén Kohn and Pierre Lairez), Mathematical Aspects of Computer and Information Sciences, (eds. I. Kotsireas, S. Rump and C. Yap), MACIS 2015, Berlin, (2016) 130-136. 229. Exponential Varieties (with Mateusz Michalek, Caroline Uhler and Piotr Zwiernik), Proceedings of the London Mathematical Society 112 (2016) 27-56. 228. The Euclidean distance degree of an algebraic variety (with Jan Draisma, Emil Horobet, Giorgio Ottaviani, and Rekha Thomas), Foundations of Computational Mathematics 16 (2016) 99-149. 227. Algebraic Systems Biology: a Case Study for the Wnt Pathway (with Elizabeth Gross, Heather Harrington and Zvi Rosen), Bulletin of Mathematical Biology 78 (2016) 21-51. 226. Decomposing Tensors into Frames (with Luke Oeding and Elina Robeva), Advances in Applied Mathematics 73 (2016) 125-153. 225. Duality of Multiple Root Loci (with Hwangrae Lee), Journal of Algebra 446 (2016) 499-526. 224. Cayley-Bacharach Formulas (with Qingchun Ren and Jurgen Richter-Gebert), American Mathematical Monthly 122 (2015) 845-854. 223. Generic Spectrahedral Shadows (with Rainer Sinn), SIAM Journal on Optimization 25 (2015) 1209-1220. 222. Quartic spectrahedra (with John Christian Ottem, Kristian Ranestad, and Cynthia Vinzant), Mathematical Programming, Ser. B, 151 (2015) 585-612. 221. A Family of Quasisymmetry Models (with Maria Kateri and Fatemeh Mohammadi), Journal of Algebraic Statistics 6 (2015) 1-16. 220. Rational Design of Antibiotic Treatment Plans: A Treatment Strategy for Managing Evolution and Reversing Resistance (with Portia Mira, Kristina Crona, Devin Greene, Juan Meza and Miriam Barlow), PLoS One 10(5) (2015) e0122283 219. Tensors of nonnegative rank two (with Elizabeth Allman, John Rhodes and Piotr Zwiernik), Linear Algebra and its Applications 473 (2015) 37-53. 218. Moduli of Tropical Plane Curves (with Sarah Brodsky, Ralph Morrison and Michael Joswig), Research in the Mathematical Sciences 2:4 (2015) 217. Fixed points of the EM algorithm and nonnegative rank boundaries (with Kaie Kubjas and Elina Robeva), Annals of Statistics 43 (2015) 422-461. 216. Exact solutions in structured low-rank approximation (with Pierre-Jean Spaenlehauer and Giorgio Ottaviani), SIAM Journal on Matrix Analysis and Applications 35 (2014) 1521-1542. 215. Hypersurfaces and their singularities in partial correlation testing (with Shaowei Lin, Caroline Uhler and Peter Bühlmann), Foundations of Computational Mathematics 5 (2014) 1079-1116. 214. Tropicalization of classical moduli spaces (with Steven Sam and Qingchun Ren), Mathematics in Computer Science 8 (2014) 119-145. 213. Maximum likelihood for matrices with rank constraints (with Jonathan Hauenstein and Jose Rodriguez), Journal of Algebraic Statistics 5 (2014) 18-38. 212. Likelihood geometry (with June Huh), in Combinatorial Algebraic Geometry (eds. Aldo Conca et al.), Lecture Notes in Mathematics 2108, Springer, (2014) 63-117. 211. The universal Kummer threefold (with Gus Schrader, Steven Sam and Qingchun Ren), Experimental Mathematics 22 (2013) 327-362. 210. A Hilbert scheme in computer vision (with Chris Aholt and Rekha Thomas), Canadian Journal of Mathematics 65 (2013) 961-988. 209. Mixed discriminants (with Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein and Sandra Di Rocco), Mathematische Zeitschrift 274 (2013) 761-778. 208. Capacity pre-log of noncoherent SIMO channels via Hironaka's theorem (with V. Morgenshtern, E. Riegler, W. Yang, G. Durisi, S. Lin and H. Bolcskei), IEEE Transactions on Information Theory 59 (2013) 4213-4229. 207. The entropic discriminant (with Raman Sanyal and Cynthia Vinzant), Advances in Mathematics 244 (2013) 678-707. 206. Elliptic curves in honeycomb form (with Melody Chan), in "Tropical Geometry", Proceedings Castro Urdiales 2011, editors E. Brugallé, M.A. Cueto, A. Dickenstein, E.M. Feichtner and I. Itenberg, American Mathematical Society, Contemporary Mathematics 589 (2013) 87-107. 205. Monomials, binomials, and Riemann-Roch (with Madhusudan Manjunath), Journal of Algebraic Combinatorics 37 (2013) 737-756. 204. Toric cubes (with Alex Engström and Patricia Hersh), Circolo Matematico di Palermo 62 (2013) 67-78. 203. Binary cumulant varieties (with Piotr Zwiernik), Annals of Combinatorics 17 (2013) 229-250. 202. Combinatorial types of tropical eigenvectors (with Ngoc Tran), Bulletin of the London Mathematical Society 45 (2013) 27-36. 201. Matrices with eigenvectors in a given subspace (with Giorgio Ottaviani), Proceedings of the American Mathematical Society 141 (2013) 1219-1232. 200. The number of eigenvalues of a tensor (with Dustin Cartwright), Linear Algebra and its Applications 438 (2013) 942-952. 199. Geometry of higher-order Markov chains, Journal of Algebraic Statistics 3 (2012) 1-10. 198. Algebraic boundaries of Hilbert's SOS cones (with Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem and Kristian Ranestad), Compositio Mathematica 148 (2012) 1717-1735. 197. Graphical models for correlated defaults (with I.O. Filiz, X. Guo and J. Morton), Mathematical Finance 22 (2012) 621-644. 196. Commutative algebra of statistical ranking (with Volkmar Welker), Journal of Algebra 361 (2012) 264-286. 195. Computing linear matrix representations of Helton-Vinnikov curves (with Daniel Plaumann and Cynthia Vinzant), in Mathematical Methods in Systems, Optimization and Control, (eds. Harry Dym, Mauricio de Oliveira, Mihai Putinar), Operator Theory: Advances and Applications", Vol 222, Birkhauser, Basel, 2012, pp. 259-277. 194. The central curve in linear programming (with Jesus De Loera and Cynthia Vinzant), Foundations of Computational Mathematics 12 (2012) 509-540. 193. On the convex hull of a space curve (with Kristian Ranestad), Advances in Geometry 12 (2012) 157-178. 192. Mustafin varieties (with D. Cartwright, M. Haebich and A. Werner), Selecta Mathematica 17 (2011) 757-793. 191. Noncoherent SIMO pre-log via resolution of singularities (with E. Riegler, V. Morgenshtern, G. Durisi, S. Lin and H. Bolcskei), 6 pp., 2011 IEEE International Symposium on Information Theory, St. Petersburg, Russia. 190. Orbitopes (with R. Sanyal and F. Sottile), Mathematika 57 (2011) 275-314. 189. The convex hull of a variety (with K. Ranestad), in: "Notions of Positivity and the Geometry of Polynomials", (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Springer Verlag, Basel, 2011, pp. 331-344. 188. Tropical quadrics through three points (with S. Brodsky), Linear Algebra and its Applications 435 (2011) 1778-1785. 187. Quartic curves and their bitangents (with D. Plaumann and C. Vinzant), Journal of Symbolic Computation 46 (2011) 712-733. 186. Dualities in convex algebraic geometry (with P. Rostalski), Rendiconti di Mathematica, Serie VII 30 (2010) 285-327. 185. Siphons in chemical reaction networks (with A. Shiu), Bulletin of Mathematical Biology 72 (2010) 1448-1463. 184. Geometry of the restricted Boltzmann machine (with M.A. Cueto and J. Morton), in Algebraic Methods in Statistics and Probability, (eds. M. Viana and H. Wynn), American Mathematical Society, Contemporary Mathematics 516 (2010) 135-153. 183. Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry (with C. Uhler), Annals of the Institute of Statistical Mathematics 62 (2010) 603-638. 182. Blow-ups of P^(n-3) at n points and spinor varieties (with M. Velasco), Journal of Commutative Algebra 2 (2010) 223-244. 181. The Hilbert scheme of the diagonal in a product of projective spaces (with D. Cartwright), International Mathematics Research Notices 9 (2010) 1741-1771. 180. Sagbi bases of Cox-Nagata rings (with Z. Xu), Journal of the European Mathematical Society 12 (2010) 429-459. 179. Commuting birth-death processes (with S. Evans and C. Uhler), Annals of Applied Probability 20 (2010) 238-266. 178. The algebraic degree of semidefinite programming (with J. Nie and K. Ranestad), Mathematical Programming 122 (2010) 379-405. 177. Polynomial relations among principal minors of a 4x4 matrix (with S. Lin), Journal of Algebra 322 (2009) 4121-4131. 176. Reconstructing spatiotemporal gene expression data from partial observations (with D. Cartwright, S. Brady, D. Orlando, and P. Benfey), Bioinformatics 25 (2009) 2581-2587. 175. Computer algebra in systems biology, (with R. Laubenbacher), American Mathematical Monthly 116 (2009) 882-891. German version: Computeralgebra in der Systembiologie, Informatik-Spektrum 32(1) (2009) 27-32. 174. Toric dynamical systems, (with G. Craciun, A. Dickenstein and A. Shiu), Journal of Symbolic Computation 44 (2009) 1551-1565. 173. Marginal likelihood integrals for mixtures of independence models (with S. Lin and Z. Xu), Journal of Machine Learning Research 10 (2009) 1611-1631. 172. Convex rank tests and semigraphoids (with J. Morton, L. Pachter, A. Shiu and O. Wienand), SIAM Journal on Discrete Mathematics 23 (2009) 1117-1134. 171. Matrix cubes parametrized by eigenvalues (with J. Nie), SIAM Journal on Matrix Analysis and Applications 31 (2009) 755-766. 170. Normal toric ideals of low codimension, (with P. Dueck and S. Hosten), Journal of Pure and Applied Algebra 213 (2009) 1636-1641. 169. Tropical mathematics, (with D. Speyer), Mathematics Magazine 82 (2009) 163--173. 168. How to draw tropical planes (with S. Hermann, A. Jensen and M. Joswig), Electronic Journal of Combinatorics 16(2) (2009) R6. 167. Comparison of pattern detection methods in microarray time series of the segmentation clock, (with M-L. Dequeant, 12 others, and O. Pourquie), PLoS ONE 3(8) (2008) e2856. 166. Elimination theory for tropical varieties (with J. Tevelev), Mathematical Research Letters 15 (2008) 543-562. 165. Open problems in algebraic statistics, in Emerging Applications of Algebraic Geometry, (editors M. Putinar and S. Sullivant), I.M.A. Volumes in Mathematics and its Applications, 149, Springer, New York, 2008, pp. 351-364. 164. The hyperdeterminant and triangulations of the 4-cube, (with P. Huggins, J. Yu and D. Yuster), Mathematics of Computation 77 (2008) 1653-1679. 163. Toric geometry of cuts and splits (with S. Sullivant), Michigan Mathematical Journal 57 (2008) 689-709. 162. Three counterexamples on semigraphoids (with R. Hemmecke, J. Morton, A. Shiu and O. Wienand), Combinatorics, Probability and Computing 17 (2008) 239-257. 161. Tropical implicitization and mixed fiber polytopes (with J. Yu) in Software for Algebraic Geometry, (editors M. Stillman, N. Takayama and J. Verschelde), I.M.A. Volumes in Mathematics and its Applications 148, Springer, New York, 2008, pp. 111-132. 160. Semidefinite representation of the k-ellipse (with J. Nie and P. Parrilo), in Algorithms in Algebraic Geometry, (editors A. Dickenstein, F. Schreyer and A. Sommese) I.M.A. Volumes in Mathematics and its Applications, 146, Springer, New York, 2008, pp. 117-132. 159. Affine buildings and tropical convexity, (with M. Joswig and J. Yu), Albanian Journal of Mathematics 1 (2007) 187-211. 158. Conjunctive Bayesian networks (with N. Beerenwinkel and N. Eriksson), Bernoulli 13 (2007) 893-909. 157. Towards the human genotope (with P. Huggins and L. Pachter), Bulletin of Mathematical Biology 69 (2007) 2723-2735. 156. Epistasis and shapes of fitness landscapes, (with N. Beerenwinkel and L. Pachter), Statistica Sinica 17 (2007) 1317-1342. 155. Hyperdeterminantal relations among symmetric principal minors, (With O. Holtz), Journal of Algebra 316 (2007) 634-648 154. The cyclohedron test for finding periodic genes in time course expression studies (with J. Morton, L. Pachter and A. Shiu), Statistical Applications in Genetics and Molecular Biology 6 (2007) 1:21. 153. Tropical discriminants, (with A. Dickenstein and E.M. Feichtner), Journal of the American Mathematical Society 20 (2007) 1111-1133. 152. Analysis of epistatic interactions and fitness landscapes using a new geometric approach (with N. Beerenwinkel, L. Pachter, S. Elena and R. Lenski), BMC Evolutionary Biology 7:60 (2007) 151. Computing the integer programming gap (with S. Hosten), Combinatorica 27 (2007) 367-382 150. The Newton polytope of the implicit equation (with J. Tevelev and J. Yu) Moscow Mathematical Journal 7 (2007) 327-346. 149. Algebraic factor analysis: tetrads, pentads and beyond, (with M. Drton and S. Sullivant), Probability Theory and Related Fields 138 (2007) 463-493. 148. The mathematics of phylogenomics (with L. Pachter), SIAM Review 49 (2007) 3-31. 147. Computing tropical varieties (with T. Bogart, A. Jensen, D. Speyer and R. Thomas), Journal of Symbolic Computation 42 (2007) 54-73. 146. Monomial dynamical systems over finite fields (with O. Colon-Reyes, A. Jarrah and R. Laubenbacher), Complex Systems 16 (2006) 333-342. 145. Geometry of rank tests, (with J. Morton, L. Pachter, A. Shiu and O. Wienand), 8 pp., Proceedings of the conference Probabilistic Graphical Models (PGM 3), Prague, Czech Republic, September 2006. 144. Evolution on distributive lattices, (with N. Beerenwinkel and N. Eriksson), Journal of Theoretical Biology 242 (2006) 409-420. 143. An algebraic geometry approach to nonlinear parametric optimization in control (with I. Fotiou, P. Rostalski and M. Morari), American Control Conference, Minneapolis, MN, June 2006, pp. 3618-3623. 142. The maximum likelihood degree, (with F. Catanese, S. Hosten and A. Khetan), American Journal of Mathematics 128 (2006) 671-697. 141. Combinatorial secant varieties (with S. Sullivant), Quarterly Journal of Pure and Applied Mathematics 2 (2006) 867-891, (Special issue: In Honor of Robert MacPherson). 140. Minimizing polynomials via sum of squares over the gradient ideal (with J. Demmel and J. Nie), Mathematical Programming 106 (2006) 587-606. 139. Parametric alignment of Drosophila genomes, (with C. Dewey, P. Huggins, K. Woods and L. Pachter), PLOS Computational Biology, 2(6) (2006) e73. 138. On the toric algebra of graphical models (with D. Geiger and C. Meek), Annals of Statistics 34 (2006) 1463-1492 137. Resultants in genetic linkage analysis (with I. Hallgrimsdottir), Journal of Symbolic Computation 41 (2006) 125-137 136. Can biology lead to new theorems? Clay Mathematics Institute Annual Report 2005, Feature Article, pages 13, 22-26. 135. Matroid polytopes, nested sets and Bergman fans, (with E.M. Feichtner), Portugaliae Mathematica 62 (2005) 437-468. 134. What is a Grobner basis?, Notices of the American Mathematical Society 52 (2005) 1199-1200 133. Phylogenetic algebraic geometry, (with N. Eriksson, K. Ranestad and S. Sullivant), in Projective Varieties with Unexpected Properties, (editors C. Ciliberto, A. Geramita, B. Harbourne, R-M. Roig and K. Ranestad), De Gruyter, Berlin, 2005, pp. 237-255 132. Solving the likelihood equations, (with S. Hosten and A. Khetan), Foundations of Computational Mathematics. 5 (2005) 389-407. 131. On the tropical rank of a matrix (with F. Santos and M. Develin), in Discrete and Computational Geometry, (eds. J.E. Goodman, J. Pach and E. Welzl), Mathematical Sciences Research Institute Publications, Volume 52, Cambridge University Press, 2005, pp. 213-242. 130. The graph of monomial ideals (with K. Altmann), Journal of Pure and Applied Algebra 201 (2005) 250-263. 129. First steps in tropical geometry (with J. Richter-Gebert and T. Theobald), in "Idempotent Mathematics and Mathematical Physics", Proceedings Vienna 2003, (editors G.L. Litvinov and V.P. Maslov), American Mathematical Society, Contemporary Mathematics 377 (2005) 289-317. 128. Toric ideals of phylogenetic invariants, (with S. Sullivant), Journal of Computational Biology 12 (2005) 204-228. 127. Algebraic geometry of Bayesian networks (with L. Garcia and M. Stillman), Journal of Symbolic Computation 39 (2005) 331-355. 126. Parametric inference for biological sequence analysis (with L. Pachter), Proceedings of the National Academy of Sciences 101 (2004) 16138-16143. 125. Tropical geometry of statistical models (with L. Pachter), Proceedings of the National Academy of Sciences 101 (2004) 16132-16137. 124. Algebraic recipes for integer programming, "Trends in optimization" (Phoenix, AZ, 2004), 99-113, Proc. Sympos. Appl. Math, 61, Amer. Math. Soc., Providence, RI, 2004. 123. Short rational functions for toric algebra (with J. A. De Loera, D. Haws, R. Hemmecke, P. Huggins, and R. Yoshida), Journal of Symbolic Computation 38 (2004) 959--973. 122. The tropical Grassmannian (with D. Speyer), Advances in Geometry 4 (2004) 389-411. 121. Classification of six-point metrics (with J. Yu), Electronic Journal of Combinatorics 11 (2004/05) R44. 120. Multigraded Hilbert schemes (with M. Haiman), Journal of Algebraic Geometry 13 (2004) 725-769. 119. Supernormal vector configurations (with S. Hosten and D. Maclagan), Journal of Algebraic Combinatorics 19 (2004) 297-313. 118. Tropical Convexity (with M. Develin), Documenta Mathematica 9 (2004) 1-27. 117. Algebraic unimodular counting (with J. De Loera), Mathematical Programming, Series B, 96 (2003) 183-203. 116. Minimizing polynomial functions (with P. Parrilo), Proceedings of the DIMACS Workshop on Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science (March 2001), (eds. S. Basu and L. Gonzalez-Vega), American Mathematical Society, 2003, pp. 83-100. 115. Higher Lawrence Configurations (with F. Santos), Journal of Combinatorial Theory, Series A, 103 (2003) 151-164. 114. Alexander duality in subdivisions of Lawrence polytopes (with F. Santos), Advances in Geometry, 3 (2003) 177-189. 113. Algorithms for the toric Hilbert scheme (with M. Stillman and R. Thomas), in Computations in Algebraic Geometry with Macaulay 2, Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 179--214. 112. Ideals, varieties and Macaulay 2, in Computations in Algebraic Geometry with Macaulay 2, Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 3--15. 111. Toric hyperkahler varieties (with T. Hausel), Documenta Mathematica 7 (2002) 495-534. 110. Elimination theory in codimension two (with A. Dickenstein), Journal of Symbolic Computation 34 (2002) 119-135. 109. Binomial residues (with E. Cattani and A. Dickenstein), Annales de l'Institute Fourier (Grenoble), 52 (2002), no. 3, 687-708. 108.Syzygies of oriented matroids (with I. Novik and A. Postnikov), Duke Mathematical Journal 111 (2002) 287-317. 107.Grobner bases of abelian matrix groups, in Symbolic Computation: Solving Equations in Algebra, Geometry, and Engineering, (eds. E. Green, S. Hosten, R. Laubenbacher, V. Powers), Contemporary Mathematics, Volume 286, American Math. Soc, Providence, RI, 2001, pp. 141-143. 106.Rational hypergeometric functions (with E. Cattani and A. Dickenstein), Compositio Mathematica 128 (2001) 217-240. 105. Syzygies of unimodular Lawrence ideals, (with D. Bayer and S. Popescu), Journal fur die Reine und Angewandte Mathematik 534 (2001) 169-186. 104. A sagbi basis for the quantum Grassmannian, (with F. Sottile), Journal for Pure and Applied Algebra 158 (2001) 347-366. 103. Four counterexamples in combinatorial algebraic geometry, Journal of Algebra 230 (2000) 282-294. 102. Generic and cogeneric monomial ideals (with E. Miller and K. Yanagawa), Journal of Symbolic Computation 28 (2000) 691-708. 101. Solving algebraic equations in terms of ${\cal A$-hypergeometric series, Discrete Mathematics 210 (2000) 171-181. 100. Monomial ideals and planar graphs (with E. Miller), in "Applied Algebra, Algebraic Algorithms and Error-Correcting Codes", [M. Fossorier, H. Imai, S. Lin and A. Poli, eds.], Proceedings of AAECC-13 (Honolulu, November 1999), Springer Lecture Notes in Computer Science 1719 (1999) 19-28. 99. Cutting corners (with S. Onn), Advances in Applied Mathematics 23 (1999) 29-48. 98. The Co-Scarf resolution, in "Commutative Algebra, Algebraic Geometry and Computational Methods", Proceedings Hanoi 1996, [editor D. Eisenbud] Springer Verlag, Singapore, 1999, pp. 315-320. 97. Hypergeometric polynomials and integer programming (with M. Saito and N. Takayama), Compositio Mathematica 115 (1999) 185-204. 96. Numerical Schubert calculus (with B. Huber and F. Sottile), Journal of Symbolic Computation 20 (1998) 767-788. 95. Syzygies of codimension $2$ lattice ideals, (with I. Peeva), Mathematische Zeitschrift 229 (1998) 163-194. 94. Cellular resolution of monomial modules (with D. Bayer), Journal fur die Reine und Angewandte Mathematik 502 (1998) 123-140. 93. Grobner deformations of regular holonomic systems (with M. Saito and N.Takayama), Proceedings of the Japan Academy, Ser. A Math. Sci. 74 (1998) 111-113. 92. Polynomial equations and convex polytopes, American Mathematical Monthly 105 (1998) 907-922. 91. Monomial resolutions (with D. Bayer and I. Peeva), Mathematical Research Letters 5 (1998) 31-46. 90. Residues and resultants (with E. Cattani and A. Dickenstein), Journal of Mathematical Sciences of the University of Tokyo 5 (1998) 119-148. 89. Lattice walks and primary decomposition (with P. Diaconis and D. Eisenbud), Mathematical Essays in Honor of Gian-Carlo Rota, eds. B. Sagan and R. Stanley, Progress in Mathematics, Vol. 161, Birkhauser, Boston, 1998, pp. 173-193. 88. Algebraic algorithms for sampling from conditional distributions (with P. Diaconis), Annals of Statistics 26 (1998) 363-397. 87. Generic lattice ideals (with I. Peeva), Journal of the American Mathematical Society 11 (1998) 363-373. 86. Non-commutative Grobner bases for commutative algebras (with D. Eisenbud and I. Peeva), Proceedings of the American Mathematical Society 126 (1998) 687-691. 85. How to shell a monoid (with I. Peeva and V. Reiner), Mathematische Annalen 310 (1998) 379-393. 84. Grobner bases and hypergeometric functions, (with N. Takayama), in Grobner Bases and Applications (Proc. of the Conference 33 Years of Grobner Bases), B. Buchberger and F. Winkler (eds.), Cambridge University Press, London Mathematical Society Lecture Notes Series, 251, (1998), pp. 246-258. 83. A toric ring with irrational Poincare-Betti series (with J.-E. Roos), Comptes Rendus Acad. Sci. Paris, Ser. I Math. 326 (1998) 141-146. 82. Equations defining toric varieties, Algebraic Geometry - Santa Cruz 1995, Proc. Sympos. Pure Math., 62, Part 2, Amer. Math. Soc., Providence, RI, 1997, pp. 437-449. 81. Introduction to resultants, in: D. Cox, B. Sturmfels (eds.), Applications of Computational Algebraic Geometry, Proceedings of Symp. in Applied Math., 53, American Mathematical Society, 1997, pp. 25-39. 80. Variation of cost functions in integer programming, (with R.R. Thomas), Mathematical Programming 77 (1997) 357-387. 79. Computing Hopf bifurcations (with J. Guckenheimer, M. Myers), SIAM J. Numerical Analysis 34 (1997) 1-21. 78. Structural Grobner basis detection (with M. Wiegelmann), Applicable Algebra in Engineering, Communication and Computing (AAECC Journal) 8 (1997) 257-263. 77. Bernstein's Theorem in affine space (with B. Huber), Discrete and Computational Geometry 17 (1997) 137-141. 76. Intersection theory on toric varieties (with W. Fulton), Topology 36 (1997) 335-353. 75. A normal form algorithm for modules over $k[x,y]/\langle x y \rangle$ (with R. Laubenbacher), Journal of Algebra 184 (1996) 1001-1024. 74. Binomial ideals (with D. Eisenbud), Duke Mathematical Journal 84 (1996) 1-45. 73. Mixed monomial bases (with P. Pedersen), in Algorithms in Algebraic Geometry and Applications, (eds. L. Gonzalez-Vega and T. Recio), Progress in Mathematics, Vol. 143, Birkhauser, Basel, 1996, pp. 307-316. 72. Computing multidimensional residues (with E. Cattani, A. Dickenstein), in Algorithms in Algebraic Geometry and Applications, (eds. L. Gonzalez-Vega and T. Recio), Progress in Mathematics, Vol. 143, Birkhauser, Basel, 1996, pp. 135-164. 71. Primitive partition identities (with P. Diaconis, R. Graham), in Combinatorics, Paul Erdos is Eighty, (eds. D.Mikl\'os, V.T. S\'os, T. Szonyi), Janos Bolyai Mathematical Society, Budapest, Hungary, 1996, pp. 173-192. 70. The polytope of all triangulations of a point configuration (with J. De Loera, F. Santos, S. Hosten), Documenta Mathematica 1 (1996) 103-119. 69. Initial complexes of prime ideals (with M. Kalkbrener) Advances in Mathematics 116 (1995) 365-376. 68. On vector partition functions, J. of Combinatorial Theory, Ser. A 72 (1995) 302-309. 67. Grobner bases and triangulations of the second hypersimplex (with J. De Loera, R. Thomas), Combinatorica 15 (1995) 409-424. 66. A polyhedral method for solving sparse polynomial systems (with B. Huber), Mathematics of Computation 64 (1995) 1541-1555. 65. Grobner bases of lattices, corner polyhedra, and integer programming (with R. Weismantel, G. Ziegler), Beitrage zur Algebra und Geometrie 36 (1995), 281-298. 64. GRIN: An implementation of Grobner bases for integer programming (with S.Hosten), in Integer Programming and Combinatorial Optimization'', [E. Balas and J. Clausen, eds.], Proceedings of the IV. IPCO Conference (Copenhagen, May 1995), Springer Lecture Notes in Computer Science 920 (1995) 267-276. 63. Bounds for degrees of projective schemes, (with N.V. Trung, W. Vogel), Mathematische Annalen 302 (1995) 417-432. 62. Introduction to Chow forms (with J. Dalbec), in "Invariant Methods in Discrete and Computational Geometry" [N. White, ed.], Proceedings Curacao (June 1994), Kluwer Academic Publishers, 1995, pp. 37-58. 61. Intersection theory on spherical varieties (with W. Fulton, R. MacPherson, F. Sottile), Journal of Algebraic Geometry 4 (1995) 181-193. 60. Viro's theorem for complete intersections, Annali della Scuola Normale Superiore di Pisa. (4) 21 (1994), no. 3, 377-386. 59. On the number of real roots of a sparse polynomial, in Hamiltonian and Gradient Flows: Algorithms and Control, (ed. A. Bloch), Fields Institute Communications Vol. 3, American Math. Soc, Providence, RI, 1994, pp. 137-143. 58. Iterated fibre polytopes (with L.J. Billera), Mathematika 41 (1994) 549-555. 57. Cellular strings on polytopes (with L. Billera, M. Kapranov), Proceedings of the Amer. Math. Soc. 122 (1994) 549-555. 56. A note on lattice simplices and toric varieties, (with S. Onn), American Journal of Mathematics 116 (1994) 1337-1339. 55. Minimal polynomials and sparse resultants, (with J. Yu), in "Zero-Dimensional Schemes", (eds. F. Orecchia and L. Chiantini), Proceedings Ravello (June 1992), De Gruyter, Berlin, 1994, pp. 317-324. 54. A quantitative Steinitz Theorem (with S. Onn), Beitrage zur Algebra und Geometrie 35 (1994) 125-129. 53. Finding sparse systems of parameters (with D. Eisenbud), Journal of Pure and Applied Algebra 94 (1994) 143-157. 52. On the Newton polytope of the resultant, Journal of Algebraic Combinatorics 3 (1994) 207-236. 51. Multigraded resultants of Sylvester type, (with A. Zelevinsky), Journal of Algebra 163 (1994) 115-127. 50. A note on polynomial reduction (with A. Reeves), Journal of Symbolic Computation 11 (1993) 273-277. 49. Product formulas for resultants and Chow forms, (with P. Pedersen), Mathematische Zeitschrift 214 (1993) 377-396. 48. Sparse elimination theory, in "Computational Algebraic Geometry and Commutative Algebra" [D. Eisenbud and L. Robbiano, eds.], Proceedings Cortona (June 1991), Cambridge University Press, 1993, pp. 264-298. 47. Non-extremal Camion bases (with R.G. Bland, C.W. Ko), Linear Algebra and its Applications 187 (1993) 195-199. 46. Extension spaces of oriented matroids (with G. Ziegler), Discrete and Computational Geometry 10 (1993) 23-45. 45. Minkowski addition of polytopes: Computational complexity and applications to Grobner bases, (with P. Gritzmann), SIAM J. Discrete Math. 6 (1993) 246-269. 44. Duality and minors of secondary polyhedra, (with L.J. Billera, I.M. Gel'fand), Journal of Combinatorial Theory B 57 (1993) 258-268. 43. Maximal minors and their leading terms (with A. Zelevinsky), Advances in Mathematics 98 (1993) 65-112. 42. Asymptotic analysis of toric ideals, Memoirs of the Faculty of Sciences, Kyushu University, Series A: Mathematics 46, No. 2, (1992) 217-228. 41. Chow polytopes and general resultants (with M. Kapranov, A. Zelevinsky), Duke Mathematical Journal 67 (1992) 189-218. 40. Algorithms for the Quillen-Suslin theorem, (with A. Logar), Journal of Algebra 145 (1992) 231-239. 39. Fiber polytopes (with L.J. Billera), Annals of Mathematics 135 (1992) 527-549. 38. Unimodular fans, toric manifolds and linear codes (with P. Kleinschmidt and N. Schwartz), in "Discrete and Computational Geometry: Papers from the DIMACS Special Year", (eds. J.E. Goodman, R. Pollack, W.L. Steiger), American Math. Soc.. Providence, 1991, pp. 179-186. 37. Computing combinatorial decompositions of rings (with N. White), Combinatorica 11 (1991), 275-293. 36. Quotients of toric varieties (with M. Kapranov, A. Zelevinsky), Mathematische Annalen 290 (1991), 643-655. 35. Computational algebraic geometry of projective configurations, J. Symbolic Computation 11 (1991) 595-618. 34. On the synthetic factorization of projectively invariant polynomials (with W. Whiteley), J. Symbolic Computation 11 (1991) 439-454. 33. Grobner bases of toric varieties, Tohoku Mathematical Journal 43 (1991) 249-261. 32. On the topology and geometric construction of oriented matroids and convex polytopes (with J.Richter), Transactions American Math. Soc. 325 (1991) 389-412. 31. Smooth toric varieties with small Picard number are projective (with P. Kleinschmidt), Topology 30 (1991) 289-299. 30. Stanley decompositions of the bracket ring, (with N. White), Math. Scandinavica 67 (1990) 183-189. 29. Constructions and complexity of secondary polytopes (with L.J. Billera, P. Filliman), Advances in Mathematics 83 (1990) 155-179. 28. Grobner bases and Stanley decompositions of determinantal rings, Mathematische Zeitschrift 205 (1990) 137-144. 27. The intrinsic spread of a configuration in $R^d$ (with J.E. Goodman, R. Pollack), Journal American Math. Society 3 (1990) 639-651. 26. All $11_3$- and $12_3$-configurations are rational (with N. White), Aequationes Mathematicae 39 (1990) 254-260. 25. Nonrealizability proofs in computational geometry, (with J. Bokowski, J. Richter), Discrete Comput. Geometry 5 (1990) 333-350. 24. Lawrence polytopes (with M. Bayer), Canadian J. Mathematics 17 (1990) 62-79. 23. On the existence of certain smooth toric varieties, (with J. Gretenkort, P. Kleinschmidt), Discrete Comput. Geometry 5 (1990) 255-262. 22. Coordinate representation of order types requires exponential storage (with J.E. Goodman, R. Pollack), Proceedings of the 21-st Annual ACM Symposium on Theory of Computing, Seattle, 1989, pp. 405-410. 21. Introduction to invariant theory in superalgebras, (with G-C. Rota), in D. Stanton (ed.): Invariant Theory and Tableaux, I.M.A. Volumes in Mathematics and its Applications, 19, Springer, New York, 1989, pp. 1-35. 20. Proposal for a geometric algebra software package (with T. Havel, N. White), SIGSAM Bulletin 23 (1989) 13-15. 19. Grobner bases and invariant theory (with N. White), Advances in Mathematics 76 (1989) 245-259. 18. On the matroid stratification of Grassmann varieties, specialization of coordinates, and a problem of N. White, Advances in Mathematics 75 (1989) 202-211. 17. Computing final polynomials and final syzygies using Buchberger's Grobner bases method, Resultate der Mathematik 15 (1989) 351-360. 16. An infinite family of minor-minimal nonrealizable $3$-chirotopes (with J. Bokowski), Mathematische Zeitschrift 200 (1989) 583-589. 15. Arrangements of lines and pseudolines without adjacent triangles (with D. Ljubic, J.P. Roudneff), J. Combinatorial Theory A 50 (1989) 24-32. 14. Uniform oriented matroids without the isotopy property (with B. Jaggi, P. Mani-Levitska, N. White), Discrete Comput. Geometry 4 (1989) 97-100. 13. Neighborly polytopes and oriented matroids, European J. Combinatorics 9 (1988) 537-546. 12. Tridiagonalization of complex matrices and a problem of Longstaff, Linear Algebra Appl. 109 (1988) 165-166. 11. Totally positive matrices and cyclic polytopes, Linear Alg. Appl. 107 (1988) 275-281. 10. Simplicial cells in arrangements and mutations of oriented matroids (with J.-P. Roudneff), Geometriae Dedicata 27 (1988) 153-170. 9. Some applications of affine Gale diagrams to polytopes with few vertices, SIAM J. Discrete Mathematics 1 (1988) 121-133. 8. Aspects of computational synthetic geometry - I. Algorithmic coordinatization of matroids, in H. Crapo (ed.) : Computer-aided geometric reasoning, INRIA Rocquencourt, France, June 1987, pp. 57-86. 7. Cyclic polytopes and $d$-order curves, Geometriae Dedicata 24 (1987) 103-107. 6. Boundary complexes of convex polytopes cannot be characterized locally, Journal London Math. Soc. 35 (1987) 314-326. 5. Polytopal and non-polytopal spheres - An algorithmic approach (with J. Bokowski), Israel Journal of Mathematics 57 (1987) 257-271. 4. On the decidability of diophantine problems in combinatorial geometry, Bulletin American Math. Soc. 17 (1987) 121-124. 3. Reell realisierbare orientierte Matroide (with J. Bokowski), in A. Kerber (ed.): "Diskrete Strukturen, algebraische Methoden und Anwendungen", Bayreuther Mathematische Schriften 21 (1986) 1-13. 2. Central and parallel projections of polytopes, Discrete Mathem. 2 (1986) 315-318. 1. On the coordinatization of oriented matroids, (with J. Bokowski), Discrete and Computional Geometry 1 (1986) 293-306.

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