Parameter estimation for Boolean models of biological networks (2009)
Dimitrova, Elena, Garcia-Puente, Luis David, Hinkelmann, Franziska, Jarrah, Abdul S., Laubenbacher, Reinhard, Stigler, Brandilyn, ...
Boolean networks have long been used as models of molecular networks and play an increasingly important role in systems biology. This paper describes a software package, Polynome, offered as a web...
Article No. sy980221 Strategies for Computing Minimal Free Resolutions † (2008)
In the present paper we study algorithms based on the theory of Gröbner bases for computing free resolutions of modules over polynomial rings. We propose a technique which consists in the...
Reverse-engineering of polynomial dynamical systems (2006)
Jarrah, Abdul Salam, Laubenbacher, Reinhard, Stigler, Brandilyn, Stillman, Michael
Multivariate polynomial dynamical systems over finite fields have been studied in several contexts, including engineering and mathematical biology. An important problem is to construct models of such...
Algebraic Geometry of Bayesian Networks (2003)
Garcia, Luis David, Stillman, Michael, Sturmfels, Bernd
We study the algebraic varieties defined by the conditional independence statements of Bayesian Networks. A complete algebraic classification is given for Bayesian Networks on at most five random...
Algorithms for the Toric Hilbert Scheme (2000)
Stillman, Michael, Sturmfels, Bernd, Thomas, Rekha R.
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a...
Multigraded Hilbert schemes (1999)
Michael Stillman, Bernd Sturmfels, Rekha Thomas
The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vector space. All components of the scheme are toric varieties, and among them, there is a...