269.
Discrete Statistical Models with Rational Maximum Likelihood Estimator
(with Eliana Duarte and Orlando Marigliano), 19pp,
submitted to Bernoulli.
268.
Brownian Motion Tree Models are Toric (with Caroline Uhler and Piotr Zwiernik), 22pp,
submitted to Kybernetika.
267.
3264 Conics in a Second (with Paul Breiding and Sascha Timme), 12pp,
submitted to Notices of the American Mathematical Society.
266.
Computing Convex Hulls of Trajectories (with Daniel Ciripoi,
Andreas Löhne and Nidhi Kaihnsa), 24pp, submitted to
Revista de la Unión Matemática Argentina.
265.
Maximum Likelihood Estimation for Totally
Positive LogConcave Densities (with
Elina Robeva, Ngoc Tran and Caroline Uhler), 27pp,
submitted to Journal of the American Statistical Association.
264.
K3 Polytopes and their Quartic Surfaces (with
Gabriele Balletti and Marta Panizzut), 12pp,
submitted to Advances in Geometry.
263.
The Geometry of SDPExactness in Quadratic Optimization
(with Diego Cifuentes and Corey Harris), 26pp,
to appear in Mathematical Programming.
262.
Moment Varieties of Measures on Polytopes (with
Kathlén Kohn and Boris Shapiro), 28pp,
to appear in Annali della Scuola Normale Superiore di Pisa.
261.
Voronoi Cells of Varieties (with
Diego Cifuentes, Kristian Ranestad and Madeleine Weinstein), 18pp,
to be presented
at MEGA 2019 (Effective Methods in Algebraic Geometry).
260.
Schottky Algorithms: Classical Meets Tropical (with Lynn Chua and Mario Kummer), 17pp,
to appear in Mathematics of Computation.
259.
The Geometry of Gaussoids (with Alessio D'Ali,
Tobias Boege and Thomas Kahle), 32pp, to appear in
Foundations of Computational Mathematics.
258.
Sixtyfour Curves of Degree Six
(with Nidhi Kaihnsa, Mario Kummer, Daniel Plaumann and Mahsa Sayyary),
29pp, to appear in Experimental Mathematics.
257. Learning Paths from Signature Tensors (with Max Pfeffer and Anna Seigal),
SIAM Journal on Matrix Analysis and Applications
40 (2019) 394416.
256.
Varieties of Signature Tensors (with
Carlos Améndola and Peter Friz),
Forum of Mathematics, Sigma
7 (2019) e10, 54 pp.
255.
Geometry of LogConcave Density Estimation
(with Elina Robeva and Caroline Uhler),
Discrete and Computational Geometry
61 (2019) 136160.
254.
Algebraic Identifiability of Gaussian Mixtures
(with Carlos Améndola and Kristian Ranestad),
International Mathematics Research Notices
21 (2018) 65566580.
253.
Learning Algebraic Varieties from Samples
(with Paul Breiding, Sara Kalisnik and Madeleine Weinstein),
Revista Matematica Complutense
31 (2018) 545593;
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, 247254.
251.
Distortion Varieties
(with Joe Kileel, Zuzana Kukelova and Tomas Pajdla),
Foundations of Computational Mathematics
18 (2018) 10431071.
250.
Nearest Points on Toric Varieties
(with Martin Helmer), Mathematica Scandinavica
122 (2018) 213238.
249. Changing Views on Curves
and Surfaces (with Kathlén Kohn and Matthew Trager),
Acta Mathematica Vietnamica
43 (2018) 129.
248.
Fitness, Apprenticeship, and Polynomials,
In: Combinatorial Algebraic Geometry,
(eds. G. Smith and B. Sturmfels), Fields Institute
Communications, Springer, New York, vol 80, (2017) 119.
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 TwoSlit 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) 141162
244.
Convexity in Tree Spaces (with Bo Lin, Xiaoxian Tang and Ruriko Yoshida),
SIAM Journal on Discrete Mathematics
31 (2017) 20152038.
243.
Real Rank Two Geometry
(with Anna Seigal), Journal of Algebra
484 (2017) 310333.
242.
Real Rank Geometry of Ternary Forms
(with Mateusz Michalek, Hyunsuk Moon and Emanuele Ventura),
Annali di Matematica Pura ed Applicata
196 (2017) 10251054.
241.
Congruences and Concurrent Lines in MultiView Geometry
(with Jean Ponce and Matthew Trager),
Advances in Applied Mathematics
88 (2017) 6291.
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) 125.
239.
On the Existence of Epipolar Matrices
(with Sameer Agarwal, HonLeung Lee and Rekha Thomas),
International Journal of Computer Vision
121 (2017) 403415.
238.
Does Antibiotic Resistance Evolve in Hospitals?
(with Anna Seigal, Portia Mira and Miriam Barlow),
Bulletin of Mathematical Biology
79 (2017) 191208;
News story.
237.
The Hurwitz Form of a Projective Variety,
Journal of Symbolic Computation
79 (2017) 186196.
236.
Tropicalization of Del Pezzo surfaces
(with Qingchun Ren and Kristin Shaw),
Advances in Mathematics
300 (2016) 156189.
235. Tensors and their Eigenvectors,
Notices of the American Mathematical Society
63 (2016) 604606.
234. Symmetric Matrices, Catalan Paths, and Correlations (with Emmanuel Tsukerman and Lauren Williams),
Journal of Combinatorial Theory, Series A
144 (2016) 496510.
233. Rigid Multiview Varieties
(with Michael Joswig, Joe Kileel and André Wagner),
International Journal of Algebra and Computation
26 (2016) 775788.
232. Moment Varieties of Gaussian Mixtures
(with Carlos Améndola and JeanCharles Faugère),
Journal of Algebraic Statistics 7
(2016) 1428.
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) 579590.
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) 130136.
229. Exponential Varieties
(with Mateusz Michalek, Caroline Uhler and Piotr Zwiernik),
Proceedings of the London Mathematical Society
112 (2016) 2756.
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) 99149.
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) 2151.
226.
Decomposing Tensors into Frames
(with Luke Oeding and Elina Robeva),
Advances in Applied Mathematics
73 (2016) 125153.
225.
Duality of Multiple Root Loci (with Hwangrae Lee), Journal
of Algebra 446 (2016) 499526.
224.
CayleyBacharach Formulas
(with Qingchun Ren and Jurgen RichterGebert),
American Mathematical Monthly
122 (2015) 845854.
223.
Generic Spectrahedral Shadows (with Rainer Sinn),
SIAM Journal on Optimization
25 (2015) 12091220.
222.
Quartic spectrahedra
(with John Christian Ottem, Kristian Ranestad, and Cynthia Vinzant),
Mathematical Programming, series B,
151 (2015) 585612.
221.
A Family of Quasisymmetry Models
(with Maria Kateri and Fatemeh Mohammadi),
Journal of Algebraic Statistics
6 (2015) 116.
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) 3753.
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) 422461.
216.
Exact solutions in structured lowrank approximation
(with PierreJean Spaenlehauer and Giorgio Ottaviani),
SIAM Journal on Matrix Analysis and Applications
35 (2014) 15211542.
215.
Hypersurfaces and their singularities in partial
correlation testing
(with Shaowei Lin, Caroline Uhler and Peter Bühlmann),
Foundations of Computational Mathematics
5 (2014) 10791116.
214.
Tropicalization of classical moduli spaces
(with Steven Sam and Qingchun Ren),
Mathematics in Computer Science
8 (2014) 119145.
213.
Maximum likelihood for matrices with rank constraints
(with Jonathan Hauenstein and Jose Rodriguez),
Journal of Algebraic Statistics
5 (2014) 1838.
212.
Likelihood geometry (with June Huh),
in Combinatorial Algebraic Geometry
(eds. Aldo Conca et al.),
Lecture Notes in Mathematics 2108,
Springer, (2014) 63117.
211.
The universal Kummer threefold
(with Gus Schrader, Steven Sam and Qingchun Ren),
Experimental Mathematics
22 (2013) 327362.
210.
A Hilbert scheme in computer vision
(with Chris Aholt and Rekha Thomas),
Canadian Journal of Mathematics
65 (2013) 961988.
209.
Mixed discriminants
(with Eduardo Cattani, Maria Angelica Cueto, Alicia Dickenstein
and Sandra Di Rocco),
Mathematische Zeitschrift
274 (2013) 761778.
208.
Capacity prelog 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) 42134229.
207.
The entropic discriminant
(with Raman Sanyal and Cynthia Vinzant),
Advances in Mathematics
244 (2013) 678707.
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) 87107.
205.
Monomials, binomials, and RiemannRoch
(with Madhusudan Manjunath),
Journal of Algebraic Combinatorics
37 (2013) 737756.
204.
Toric cubes (with Alex Engström and Patricia Hersh),
Circolo Matematico di Palermo
62 (2013) 6778.
203.
Binary cumulant varieties (with Piotr Zwiernik),
Annals of Combinatorics
17 (2013) 229250.
202.
Combinatorial types of tropical eigenvectors (with Ngoc Tran),
Bulletin of the London Mathematical Society
45 (2013) 2736.
201.
Matrices with eigenvectors in a given subspace (with Giorgio Ottaviani),
Proceedings of the American Mathematical Society
141 (2013) 12191232.
200.
The number of eigenvalues of a tensor (with Dustin Cartwright),
Linear Algebra and its Applications
438 (2013) 942952.
199.
Geometry of higherorder Markov chains,
Journal of Algebraic Statistics
3 (2012) 110.
198.
Algebraic boundaries of Hilbert's SOS cones
(with Grigoriy Blekherman, Jonathan Hauenstein, John Christian Ottem
and Kristian Ranestad), Compositio Mathematica
148 (2012) 17171735.
197.
Graphical models for correlated defaults
(with I.O. Filiz, X. Guo and J. Morton),
Mathematical Finance
22 (2012) 621644.
196. Commutative algebra of statistical ranking (with Volkmar Welker),
Journal of Algebra
361 (2012) 264286.
195.
Computing linear matrix representations of HeltonVinnikov 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. 259277.
194. The central
curve in linear programming (with Jesus De Loera and Cynthia Vinzant),
Foundations of Computational Mathematics
12 (2012) 509540.
193.
On the convex hull of a space curve (with Kristian Ranestad),
Advances in Geometry 12 (2012) 157178.
192.
Mustafin varieties (with D. Cartwright, M. Haebich and A. Werner),
Selecta Mathematica
17 (2011) 757793.
191.
Noncoherent SIMO prelog 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) 275314.
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. 331344.
188.
Tropical quadrics through three points (with S. Brodsky),
Linear Algebra and its Applications
435 (2011) 17781785.
187.
Quartic curves and their bitangents (with D. Plaumann and
C. Vinzant), Journal of Symbolic Computation
46 (2011) 712733.
186.
Dualities in convex algebraic geometry (with P. Rostalski),
Rendiconti di Mathematica, Serie VII
30 (2010) 285327.
185.
Siphons in chemical reaction networks (with A. Shiu),
Bulletin of Mathematical Biology
72 (2010) 14481463.
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) 135153.
183.
Multivariate Gaussians, semidefinite matrix completion, and
convex algebraic geometry (with C. Uhler),
Annals of the Institute of Statistical Mathematics
62 (2010) 603638.
182.
Blowups of P^(n3) at n points and spinor varieties (with M. Velasco),
Journal of Commutative Algebra 2 (2010)
223244.
181.
The Hilbert scheme of the diagonal in a product of projective spaces (with D. Cartwright),
International Mathematics Research Notices
9 (2010) 17411771.
180.
Sagbi bases of CoxNagata rings (with Z. Xu),
Journal of the European Mathematical Society
12 (2010) 429459.
179.
Commuting birthdeath processes (with S. Evans and C. Uhler),
Annals of Applied Probability
20 (2010) 238266.
178. The algebraic degree of semidefinite programming (with J. Nie and K. Ranestad), Mathematical Programming
122 (2010) 379405.
177.
Polynomial relations among principal minors of a 4x4 matrix
(with S. Lin), Journal of Algebra
322 (2009) 41214131.
176.
Reconstructing spatiotemporal gene expression data from partial observations (with D. Cartwright, S. Brady, D. Orlando, and P. Benfey),
Bioinformatics
25 (2009) 25812587.
175.
Computer algebra in systems biology,
(with R. Laubenbacher), American Mathematical Monthly
116 (2009) 882891.
German version:
Computeralgebra in der Systembiologie,
InformatikSpektrum 32(1) (2009) 2732.
174.
Toric dynamical systems,
(with G. Craciun, A. Dickenstein and A. Shiu),
Journal of Symbolic Computation
44 (2009) 15511565.
173.
Marginal likelihood integrals for mixtures of independence models (with S. Lin and Z. Xu), Journal of Machine Learning Research
10 (2009) 16111631.
172.
Convex rank tests and semigraphoids (with
J. Morton, L. Pachter, A. Shiu and O. Wienand),
SIAM Journal on Discrete Mathematics
23 (2009) 11171134.
171.
Matrix cubes parametrized by eigenvalues (with J. Nie),
SIAM Journal on Matrix Analysis and Applications
31 (2009) 755766.
170.
Normal toric ideals of low codimension,
(with P. Dueck and S. Hosten),
Journal of Pure and Applied Algebra
213 (2009) 16361641.
169.
Tropical mathematics, (with D. Speyer), Mathematics Magazine
82 (2009) 163173.
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 ML. 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) 543562.
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. 351364.
164.
The hyperdeterminant and triangulations of the 4cube,
(with P. Huggins, J. Yu and D. Yuster),
Mathematics of Computation
77 (2008) 16531679.
163.
Toric geometry of cuts and splits
(with S. Sullivant),
Michigan Mathematical Journal
57 (2008) 689709.
162.
Three counterexamples on semigraphoids
(with R. Hemmecke, J. Morton, A. Shiu and O. Wienand),
Combinatorics, Probability and Computing
17 (2008) 239257.
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. 111132.
160.
Semidefinite representation of the kellipse (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. 117132.
159.
Affine buildings and tropical convexity,
(with M. Joswig and J. Yu),
Albanian Journal of Mathematics
1 (2007) 187211.
158.
Conjunctive Bayesian networks
(with N. Beerenwinkel and N. Eriksson),
Bernoulli 13 (2007) 893909.
157.
Towards the human genotope (with P. Huggins and L. Pachter),
Bulletin of Mathematical Biology
69 (2007) 27232735.
156.
Epistasis and shapes of fitness landscapes,
(with N. Beerenwinkel and L. Pachter),
Statistica Sinica
17 (2007) 13171342.
155.
Hyperdeterminantal relations among symmetric principal minors,
(With O. Holtz), Journal of Algebra
316 (2007) 634648
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) 11111133.
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) 367382
150.
The Newton polytope of the implicit equation
(with J. Tevelev and J. Yu) Moscow Mathematical Journal
7 (2007) 327346.
149.
Algebraic factor analysis: tetrads, pentads and beyond,
(with M. Drton and S. Sullivant),
Probability Theory and Related Fields
138 (2007) 463493.
148.
The mathematics of phylogenomics (with L. Pachter),
SIAM Review 49 (2007) 331.
147.
Computing tropical varieties (with T. Bogart, A. Jensen,
D. Speyer and R. Thomas), Journal of Symbolic Computation
42 (2007) 5473.
146.
Monomial dynamical systems over finite fields
(with O. ColonReyes, A. Jarrah and R. Laubenbacher),
Complex Systems
16 (2006) 333342.
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) 409420.
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. 36183623.
142.
The maximum likelihood degree,
(with F. Catanese, S. Hosten and A. Khetan),
American Journal of Mathematics
128 (2006) 671697.
141.
Combinatorial secant varieties (with S. Sullivant),
Quarterly Journal of Pure and Applied Mathematics
2 (2006) 867891,
(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) 587606.
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) 14631492
137.
Resultants in genetic linkage analysis (with I. Hallgrimsdottir),
Journal of Symbolic Computation 41
(2006) 125137
136.
Can biology lead to new theorems?
Clay Mathematics Institute Annual Report 2005,
Feature Article, pages 13, 2226.
135.
Matroid polytopes, nested sets and Bergman fans,
(with E.M. Feichtner),
Portugaliae Mathematica
62 (2005) 437468.
134.
What is a Grobner basis?,
Notices of the American Mathematical Society
52
(2005) 11991200
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, RM. Roig and K. Ranestad),
De Gruyter, Berlin, 2005, pp. 237255
132.
Solving the likelihood equations,
(with S. Hosten and A. Khetan),
Foundations of Computational Mathematics.
5 (2005) 389407.
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. 213242.
130.
The graph of monomial ideals (with K. Altmann),
Journal of Pure and Applied Algebra
201 (2005) 250263.
129.
First steps in tropical geometry (with J. RichterGebert 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) 289317.
128.
Toric ideals of phylogenetic invariants, (with S. Sullivant),
Journal of Computational Biology
12 (2005) 204228.
127.
Algebraic geometry of Bayesian networks
(with L. Garcia and M. Stillman),
Journal of Symbolic Computation
39 (2005) 331355.
126.
Parametric inference for biological sequence analysis
(with L. Pachter),
Proceedings of the National Academy of Sciences
101 (2004) 1613816143.
125.
Tropical geometry of statistical models
(with L. Pachter),
Proceedings of the National Academy of Sciences
101 (2004) 1613216137.
124.
Algebraic recipes for integer programming,
"Trends in optimization" (Phoenix, AZ, 2004),
99113, 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) 959973.
122.
The tropical Grassmannian (with D. Speyer),
Advances in Geometry 4
(2004) 389411.
121.
Classification of sixpoint 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) 725769.
119. Supernormal
vector configurations (with S. Hosten and
D. Maclagan), Journal of Algebraic Combinatorics
19 (2004) 297313.
118. Tropical Convexity (with M. Develin), Documenta
Mathematica 9 (2004) 127.
117. Algebraic unimodular counting (with J. De
Loera), Mathematical Programming, Series B,
96 (2003) 183203.
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. GonzalezVega), American
Mathematical Society, 2003, pp. 83100.
115. Higher Lawrence Configurations (with F. Santos),
Journal of Combinatorial Theory, Series A,
103 (2003) 151164.
114. Alexander duality in subdivisions of Lawrence
polytopes (with F. Santos), Advances in Geometry,
3 (2003) 177189.
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. 179214.
112. Ideals, varieties and Macaulay 2, in
Computations in Algebraic Geometry with Macaulay 2,
Algorithms Comput. Math., 8, Springer, Berlin, 2002, pp. 315.
111. Toric hyperkahler varieties (with T. Hausel),
Documenta Mathematica 7
(2002) 495534.
110. Elimination theory in codimension two (with
A. Dickenstein), Journal of Symbolic Computation
34 (2002) 119135.
109. Binomial residues (with E. Cattani and
A. Dickenstein), Annales de l'Institute Fourier
(Grenoble), 52 (2002), no. 3,
687708.
108.Syzygies of oriented matroids (with I. Novik
and A. Postnikov), Duke Mathematical Journal
111 (2002) 287317.
107.Grobner bases of abelian matrix groups, in
Symbolic Computation: Solving Equations in Algebra,
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106.Rational hypergeometric functions (with
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105. Syzygies of unimodular Lawrence ideals,
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104. A
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103. Four counterexamples in combinatorial algebraic
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102. Generic and cogeneric monomial ideals (with
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99. Cutting corners (with S. Onn), Advances
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98. The CoScarf resolution, in "Commutative
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97. Hypergeometric polynomials and integer programming
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96. Numerical Schubert calculus (with B. Huber
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95. Syzygies of codimension $2$ lattice ideals,
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94. Cellular resolution of monomial modules (with
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93. Grobner deformations of regular holonomic
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92. Polynomial equations and convex polytopes,
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91. Monomial resolutions (with D. Bayer and
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90. Residues and resultants (with E. Cattani
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89. Lattice walks and primary decomposition (with
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88. Algebraic algorithms for sampling from conditional
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87. Generic lattice ideals (with I. Peeva),
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86. Noncommutative Grobner bases for commutative
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85. How to shell a monoid (with I. Peeva and
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84. Grobner bases and hypergeometric functions,
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83. A toric ring with irrational PoincareBetti
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82. Equations defining toric varieties, Algebraic
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80. Variation of cost functions in integer programming,
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79. Computing Hopf bifurcations (with J. Guckenheimer,
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78. Structural Grobner basis detection (with
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77. Bernstein's Theorem in affine space (with
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76. Intersection theory on toric varieties (with
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75. A normal form algorithm for modules over $k[x,y]/\langle
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74. Binomial ideals (with D. Eisenbud), Duke
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73. Mixed monomial bases (with P. Pedersen),
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72. Computing multidimensional residues (with
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69. Initial complexes of prime ideals (with M.
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68. On vector partition functions, J. of Combinatorial
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67. Grobner bases and triangulations of the second
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66. A polyhedral method for solving sparse polynomial
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65. Grobner bases of lattices, corner polyhedra,
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64. GRIN: An implementation of Grobner bases for
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63. Bounds for degrees of projective schemes,
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62. Introduction
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61. Intersection
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60. Viro's theorem for complete intersections,
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59. On the number of real roots of a sparse polynomial, in Hamiltonian and Gradient Flows: Algorithms
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58. Iterated fibre polytopes (with L.J. Billera),
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57. Cellular strings on polytopes (with L. Billera,
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56. A note on lattice simplices and toric varieties,
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55. Minimal polynomials and sparse resultants,
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54. A quantitative Steinitz Theorem (with S.
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53. Finding sparse systems of parameters (with
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52. On the Newton polytope of the resultant, Journal
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51. Multigraded resultants of Sylvester type,
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50. A note on polynomial reduction (with A. Reeves),
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49. Product formulas for resultants and Chow forms,
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48. Sparse elimination theory,
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47. Nonextremal Camion bases (with R.G. Bland,
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46. Extension spaces of oriented matroids (with
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45. Minkowski addition of polytopes: Computational
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44. Duality and minors of secondary polyhedra,
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43. Maximal minors and their leading terms (with
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42. Asymptotic analysis of toric ideals, Memoirs
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41. Chow polytopes and general resultants (with
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40. Algorithms for the QuillenSuslin theorem,
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39. Fiber polytopes (with L.J. Billera), Annals
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38. Unimodular fans, toric manifolds and linear
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35. Computational algebraic geometry of projective
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33. Grobner bases of toric varieties, Tohoku
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32. On the topology and geometric construction
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31. Smooth toric varieties with small Picard number
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30. Stanley decompositions of the bracket ring,
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29. Constructions and complexity of secondary
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28. Grobner bases and Stanley decompositions of
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27. The intrinsic spread of a configuration in
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26. All $11_3$ and $12_3$configurations are
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25. Nonrealizability proofs in computational geometry,
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24. Lawrence polytopes (with M. Bayer), Canadian
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23. On the existence of certain smooth toric varieties,
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22. Coordinate representation of order types requires
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21. Introduction to invariant theory in superalgebras,
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20. Proposal for a geometric algebra software
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19. Grobner bases and invariant theory (with
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18. On the matroid stratification of Grassmann
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75 (1989) 202211.
17. Computing final polynomials and final syzygies
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der Mathematik 15 (1989)
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16. An infinite family of minorminimal nonrealizable
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15. Arrangements of lines and pseudolines without
adjacent triangles (with D. Ljubic, J.P. Roudneff),
J. Combinatorial Theory A 50
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14. Uniform oriented matroids without the isotopy
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10. Simplicial cells in arrangements and mutations
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