Publications

Graphical models in Macaulay2
with Sonja Petrović and Seth Sullivant submitted to The Journal of Software for Algebra and Geometry.
- 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 Bezier 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
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
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
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
An optimization algorithm for the inference of biological networks
with Paola Vera-Licona, Abdul Jarrah, John McGee and Reinhard Laubenbacher. In progress.
- pdf
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
- 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