An Algebraic Algorithm for the Identification of Glass Networks with Periodic Orbits along Cyclic Attractors
| Autor: | Yury Chebiryak, Daniel Kroening, Igor Zinovik |
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| Přispěvatelé: | Eidgenössische Technische Hochschule Zürich Departement Informatik |
| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: |
Computer science
Ode MathematicsofComputing_NUMERICALANALYSIS Piecewise linear function Propositional formula NEURONALE NETZWERKE + KONNEKTIONISMUS (KÜNSTLICHE INTELLIGENZ) Data processing computer science Flow (mathematics) Attractor NEURAL NETWORKS + CONNECTIONISM (ARTIFICIAL INTELLIGENCE) PROGRAMS AND ALGORITHMS FOR THE SOLUTION OF SPECIAL PROBLEMS PROGRAMME UND ALGORITHMEN ZUR LÖSUNG SPEZIELLER PROBLEME Applied mathematics ddc:004 Algebraic number Conjunctive normal form Algorithm Eigenvalues and eigenvectors |
| Zdroj: | Algebraic Biology ISBN: 9783540734321 AB Technical Report / ETH Zurich, Department of Computer Science, 557 Scopus-Elsevier |
| DOI: | 10.3929/ethz-a-005684186 |
| Popis: | Glass piecewise linear ODE models are frequently used for simulation of neural and gene regulatory networks. Efficient computational tools for automatic synthesis of such models are highly desirable. However, the existing algorithms for the identification of desired models are limited to four-dimensional networks, and rely on numerical solutions of eigenvalue problems. We suggest a novel algebraic criterion to detect the type of the phase flow along network cyclic attractors that is based on a corollary of the Perron-Frobenius theorem. We show an application of the criterion to the analysis of bifurcations in the networks. We propose to encode the identification of models with periodic orbits along cyclic attractors as a propositional formula, and solving it using state-of-the-art SAT-based tools for real linear arithmetic. New lower bounds for the number of equivalence classes are calculated for cyclic attractors in six-dimensional networks. Experimental results indicate that the runtime of our algorithm increases slower than the size of the search space of the problem. Technical Report / ETH Zurich, Department of Computer Science, 557 |
| Databáze: | OpenAIRE |
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