Reverse-engineering of polynomial dynamical systems

DOI10.1016/j.aam.2006.08.004zbMath1129.93026arXivq-bio/0605032OpenAlexW2026726507MaRDI QIDQ2467344

Reinhard C. Laubenbacher, Brandilyn Stigler, Abdul Salam Jarrah, Michael Stillman

Publication date: 21 January 2008

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/q-bio/0605032

zbMATH Keywords

decompositionmonomial idealfinite fieldgene regulatory networkfinite dynamical systemreverse-engineering

Mathematics Subject Classification ID

Neural networks for/in biological studies, artificial life and related topics (92B20) Multivariable systems, multidimensional control systems (93C35) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10)

Related Items

On the dynamics of endomorphisms of finite groups, Noise-tolerant algebraic method for reconstruction of nonlinear dynamical systems, Inferring biologically relevant models: nested canalyzing functions, The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes, Why did the shape of your network change? (On detecting network anomalies via non-local curvatures), Identification and stabilization of faulty Boolean control networks, The Minimal Hitting Set Generation Problem: Algorithms and Computation, Primary decomposition of squarefree pseudomonomial ideals, A Unified Approach to Reverse Engineering and Data Selection for Unique Network Identification, Quantifier Elimination over Finite Fields Using Gröbner Bases, Geometric characterization of data sets with unique reduced Gröbner bases, Parameter estimation for Boolean models of biological networks, Reduction of Boolean network models, Neural codes and the factor complex, Algebraic Models and Their Use in Systems Biology, Computing Linear Extensions for Polynomial Posets Subject to Algebraic Constraints, Probability estimates for reachability of linear systems defined over finite fields

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Logical identification of all steady states: The concept of feedback loop characteristic states
• Assessing cellular automata based models using partial differential equations
• The topology of the regulatory interactions predicts the expression pattern of the segment polarity genes in \textit{Drosophila melanogaster}
• A computational algebra approach to the reverse engineering of gene regulatory networks
• Algebraic dependency models of protein signal transduction networks from time-series data
• Computing irredundant irreducible decompositions of large scale monomial ideals
• Linear analysis of switching nets