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An Algebraic Algorithm for the Identification of Glass Networks with Periodic Orbits Along Cyclic Attractors

  • Igor Zinovik
  • Daniel Kroening
  • Yury Chebiryak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4545)

Abstract

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 run-time of our algorithm increases slower than the size of the search space of the problem.

Keywords

Periodic Orbit Gene Regulatory Network Conjunctive Normal Form Glass Network Propositional Formula 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Igor Zinovik
    • 1
  • Daniel Kroening
    • 1
  • Yury Chebiryak
    • 1
  1. 1.Computer Systems Institute, ETH Zurich, 8092 ZurichSwitzerland

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