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- Luis David García-Puente, Michael Stillman, Bernd Sturmfels
- J. Symb. Comput.
- 2005

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 variables. Hidden variables are related to the geometry of higher secant varieties.

- David Bayer, Michael Stillman
- J. Symb. Comput.
- 1992

- E. Becker, M. Bronstein, +6 authors Bernd Sturmfels
- 2001

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 systems from a partial specification of dynamic properties, e.g., from a collection of state transition measurements. Here, we consider static models, which… (More)

- Roberto La Scala, Michael Stillman
- J. Symb. Comput.
- 1998

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 application of special selection strategies to the Schreyer algorithm. The resulting algorithm is efficient and, in the graded case, allows a straightforward… (More)

- Raazesh Sainudiin, Kevin Thornton, +6 authors Peter Donnelly
- Bulletin of mathematical biology
- 2011

Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are… (More)

- David Bayer, Michael Stillman
- J. Symb. Comput.
- 1988

- Bjarke Hammersholt Roune, Michael Stillman
- ISSAC
- 2012

We report on our experiences exploring state of the art Gröbner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature based Gröbner basis algorithms and more traditional variations of the classic Buchberger algorithm. Our… (More)

- David Eisenbud, Mircea Mustala, Michael Stillman
- J. Symb. Comput.
- 2000

In this note we describe aspects of the cohomology of coherent sheaves on a complete toric variety X over a field k and, more generally, the local cohomology, with supports in a monomial ideal, of a finitely generated module over a polynomial ring S. This leads to an efficient way of computing such cohomology, for which we give explicit algorithms. The… (More)

- Elena S. Dimitrova, Luis David García-Puente, +5 authors Paola Vera-Licona
- Theor. Comput. Sci.
- 2011

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 service, that helps users construct Boolean network models based on experimental data and biological input. The key feature is a discrete analog of parameter… (More)