Publications

Positive steady-state varieties of small chemical reaction networks.
with Maize Curiel, Elise Farr, Galileo Fries, Julian Hutchins, and Vuong Nguyen Hoang, Involve (Submitted).
- arXiv
- pdf
Absolute concentration robustness: Algebra and geometry.
with Elizabeth Gross, Heather Harrington, Matthew Johnston, Nicolette Meshkat, and Anne Shiu. Journal of Symbolic Computation, 102398, doi: https://doi.org/10.1016/j.jsc.2024.102398.
Using Exact Tests from Algebraic Statistics in Sparse Multi-way Analyses: An Application to Analyzing Differential Item Functioning.
with Shishir Agrawal, Minho Kim, and Flavia Sancier-Barbosa, The American Statistician, 1-13. https://doi.org/10.1080/00031305.2024.2388526
Computing algebraic degrees of phylogenetic varieties
with Marina Garrote-López, Elima Shehu. Algebraic Statistics Vol. 14 (2023), No. 2, 215-231. DOI: 10.2140/astat.2023.14.215.
- AStat
- arXiv
- pdf
Computing Maximum Likelihood Estimates for Gaussian Graphical Models with Macaulay2
with Carlos Améndola, Roser Homs, Olga Kuznetsova, and Harshit J. Motwani. In Journal of Software for Algebra and Geometry Vol. 12 (2022), 1–10. DOI: 10.2140/jsag.2022.12.1
- JSAG
- arXiv
- pdf
Arithmetical structures on bidents
with Kassie Archer, Abigail Bishop, Alexander Diaz-Lopez, Darren Glass, and Joel Lowsma. In Discrete Mathematics Volume 343, Issue 7, July 2020, 111850
- ScienceDirect
- arXiv
- pdf
Counting arithmetical structures on paths and cycles
with Benjamin Braun, Hugo Corrales, Scott Corry, Darren Glass, Nathan Kaplan, Jeremy L. Martin, Gregg Musiker, and Carlos E. Valencia. In Discrete Mathematics Volume 341, Issue 10, October 2018, Pages 2949-2963.
- ScienceDirect
- arXiv
- pdf
Tapas of Algebraic Statistics
with Carlos Amémdola and Marta Casanellas. In Notices of the American Mathematical Society Volume 65, Number 8, September 2018, Pages 936-938.
- AMS Notices
Neural Ideals in SageMath
with Ethan Petersen, Nora Youngs, Ryan Kruse, Dane Miyata, and Rebecca Garcia. In Davenport J., Kauers M., Labahn G., Urban J. (eds) Mathematical Software - ICMS 2018. ICMS 2018. Lecture Notes in Computer Science, vol 10931. Springer, Cham.
- SpringerLink
- arXiv
- pdf
- Software
Gröbner Bases of Neural Ideals
with Rebecca Garcia, Ryan Kruse, Jessica Liu, Dane Miyata, Ethan Petersen, Kaitlyn Phillipson, and Anne Shiu. In International Journal of Algebra and Computation Vol. 28, No. 04, pp. 553-571 (2018)
- IJAC
- arXiv
- pdf
The multivariate avalanche polynomial
with Demara Austin, Megan Chambers, Rebecca Funke, and Lauren Keough. In The Australasian Journal of Combinatorics Volume 72(3) (2018), Pages 421-445.
- arXiv
- pdf
Hybrid Schemes for Exact Conditional Inference in Discrete Exponential Families
with David Kahle and Ruriko Yoshida. Ann Inst Stat Math (2017). https://doi.org/10.1007/s10463-017-0615-z
- SpringerLink
- Calhoun
- abstract
- pdf
- Software
Multisided toric Bézier patches
In Multivariate Splines and Algebraic Geometry (organized by H. Schenck, L. Schumaker and T. Sorokina). Oberwolfach Reports. Volume 12, Issue 2, 2015, pp. 1139-1200.
- EMS
- abstract
An algebra-based method for inferring gene regulatory networks
with Paola Vera-Licona, Abdul Salam Jarrah, John McGee and Reinhard Laubenbacher. BMC Systems Biology 2014, 8:37.
Graphical models in Macaulay2
with Sonja Petrović and Seth Sullivant in The Journal of Software for Algebra and Geometry Vol. 5 (2013), 1-7.
- JSAG
- arXiv
- pdf
- Macaulay2
- Code
Algebraic and combinatorial aspects of sandpile monoids on directed graphs
with Scott Chapman, Rebecca Garcia, Martin Malandro and Ken Smith in Journal of Combinatorial Theory, Series A. Volume 120, Issue 1, January 2013, Pages 245-265
- ScienceDirect
- arXiv
- pdf
The secant conjecture in the real Schubert calculus
with Nickolas Hein, Christopher Hillar, Abraham Martin del Campo, James Ruffo, Frank Sottile and Zach Teitler in Experimental Mathematics. Vol. 21, Issue 3, (2012) pp. 252-265
- Taylor & Francis
- arXiv
- pdf
- website
Toric degenerations of Bézier patches
with Frank Sottile and Chungang Zhu in ACM Transactions on Graphics, Vol. 30, Issue 5, October 2011, Article No. 110.
- ACM
- arXiv
- pdf
- slides
- talk
- website
Parameter estimation for Boolean models of biological networks
with Elena Dimitrova, Franziska Hinkelmann, Abdul S. Jarrah, Reinhard Laubenbacher, Brandilyn Stigler, Michael Stillman and Paola Vera-Licona. in Special Issue on Foundations of Formal Reconstruction of Biochemical Networks. Theoretical Computer Science, Volume 412, Issue 26, pp. 2816-2826. (2011).
- ScienceDirect
- mathscinet
- Zentralblatt
- arXiv
- pdf
- website
Identifying causal effects with computer algebra
with Sarah Spielvogel and Seth Sullivant in Proceedings of the 26^th Conference of Uncertainty in Artificial Intelligence.
- UAI 2010
- arXiv
- pdf
- slides
- website
- Macaulay2
- Singular
Experimentation at the Frontiers of Reality in Schubert Calculus
with Christopher Hillar, Abraham Martin del Campo, James Ruffo, Zach Teitler, Stephen Johnson and Frank Sottile in Gems in Experimental Mathematics, AMS Contemporary Mathematics, Vol. 517 (2010), 365-380.
- AMS
- mathscinet
- Zentralblatt
- arXiv
- pdf
- slides
- website
Some geometrical aspects of control points for toric patches
with Gheorghe Craciun and Frank Sottile in Mathematical Methods for Curves and Surfaces 2008 (M. Dhlen et al. Eds). Lecture Notes in Computer Science 5862, pp. 111-135. Springer, Heidelberg (2010).
- SpringerLink
- Zentralblatt
- arXiv
- pdf
- slides
- español
Linear precision for parametric patches
with Frank Sottile in Advances in Computational Mathematics, Vol. 33, No. 2 (2010) 191-214.
- SpringerLink
- mathscinet
- Zentralblatt
- arXiv
- pdf
- slides
Computing the additive structure of indecomposable modules over Dedekind-like rings using Gröbner bases
with Maria Alicia Avino-Diaz, in Journal of Algebra and Its Applications, Vol. 6, No. 2 (2007) 291-304.
- JAA
- mathscinet
- Zentralblatt
- arXiv
- pdf
Sequential dynamical systems over words
with Abdul Jarrah and Reinhard Laubenbacher, in Applied Mathematics and Computation 174/1 (2006), pp. 500-510.
- AMC
- mathscinet
- Zentralblatt
- pdf
- slides
Catalog of small phylogenetic trees
with Marta Casanellas and Seth Sullivant. In "Algebraic Statistics for Computational Biology" (editors L. Pachter and B. Sturmfels), Cambridge University Press, 2005, pp. 291-304.
- mathscinet
- book
- book @ mathscinet
- website
- slides
Algebraic geometry for Bayesian networks
with Mike Stillman and Bernd Sturmfels, in Journal of Symbolic Computation 39/3-4 (2005), pp. 331-355.
- JSC
- mathscinet
- Zentralblatt
- arXiv
- pdf
- code
- slides
Algebraic statistics in model selection
In Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence (editors M. Chickering and J. Halpern), 2004, pp. 177-184.
- ACM
- UAI 2004
- arXiv
- pdf
- slides
Algebraic geometry of Bayesian networks
Ph.D. dissertation, Department of Mathematics, Virginia Polytechnic Institute and State University, 2004.
- VT
- pdf
Bases de Gröbner asociadas a modulos finitos (Spanish)
In Miscelanea Matematica (MMS) 30 (2000), 65-70.

Presentations

What is Computational Algebraic Geometry?
- slides
Minimal Cohen-Macaulay deformations of matroid ideals
with Mike Falk
- slides
The State Polytope
This talk gives an overview of the first two chapters of the book "Gröbner Bases and Convex Polytopes" by Bernd Sturmfels.
- slides

Manuscripts

A comparison of a Gaussian and a binary ancestral graph model
with Mathias Drton.
- pdf
Polynomial constraints of Bayesian networks with hidden variables
- pdf
- slides
Latino Genius in Mathematics Receives Award (English translation)
News article about Rodrigo Banuelos receiving the Blackwell-Tapia prize written by Jorge Morales Almada (La Opinion).
- article

Expository

An introduction to Singular
Notes introducing the computer algebra system Singular based on a lecture given at the Applications of Algebraic Geometry workshop at Texas A&M University.
- website
- pdf