dorsal/arxiv
View SchemaReverse-engineering of polynomial dynamical systems
| Authors | Abdul Salam Jarrah, Reinhard Laubenbacher, Brandilyn Stigler, Michael Stillman |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0605032 |
| URL | https://arxiv.org/abs/q-bio/0605032 |
| DOI | 10.1016/j.aam.2006.08.004 |
| Journal | Advances in Applied Mathematics 39 (2007), 477-489 |
Abstract
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 are directed graphs that represent the causal relationships between system variables, so-called wiring diagrams. This paper contains an algorithm which computes all possible minimal wiring diagrams for a given set of state transition measurements. The paper also contains several statistical measures for model selection. The algorithm uses primary decomposition of monomial ideals as the principal tool. An application to the reverse-engineering of a gene regulatory network is included. The algorithm and the statistical measures are implemented in Macaulay2 and are available from the authors.
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"abstract": "Multivariate polynomial dynamical systems over finite fields have been\nstudied in several contexts, including engineering and mathematical biology. An\nimportant problem is to construct models of such systems from a partial\nspecification of dynamic properties, e.g., from a collection of state\ntransition measurements. Here, we consider static models, which are directed\ngraphs that represent the causal relationships between system variables,\nso-called wiring diagrams. This paper contains an algorithm which computes all\npossible minimal wiring diagrams for a given set of state transition\nmeasurements. The paper also contains several statistical measures for model\nselection. The algorithm uses primary decomposition of monomial ideals as the\nprincipal tool. An application to the reverse-engineering of a gene regulatory\nnetwork is included. The algorithm and the statistical measures are implemented\nin Macaulay2 and are available from the authors.",
"arxiv_id": "q-bio/0605032",
"authors": [
"Abdul Salam Jarrah",
"Reinhard Laubenbacher",
"Brandilyn Stigler",
"Michael Stillman"
],
"categories": [
"q-bio.QM",
"math.AC",
"q-bio.MN"
],
"doi": "10.1016/j.aam.2006.08.004",
"journal_ref": "Advances in Applied Mathematics 39 (2007), 477-489",
"title": "Reverse-engineering of polynomial dynamical systems",
"url": "https://arxiv.org/abs/q-bio/0605032"
},
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