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Journal of Mathematical Biology

, Volume 63, Issue 1, pp 173–200 | Cite as

Parameter estimation with a novel gradient-based optimization method for biological lattice-gas cellular automaton models

  • Carsten Mente
  • Ina Prade
  • Lutz Brusch
  • Georg Breier
  • Andreas Deutsch
Article

Abstract

Lattice-gas cellular automata (LGCAs) can serve as stochastic mathematical models for collective behavior (e.g. pattern formation) emerging in populations of interacting cells. In this paper, a two-phase optimization algorithm for global parameter estimation in LGCA models is presented. In the first phase, local minima are identified through gradient-based optimization. Algorithmic differentiation is adopted to calculate the necessary gradient information. In the second phase, for global optimization of the parameter set, a multi-level single-linkage method is used. As an example, the parameter estimation algorithm is applied to a LGCA model for early in vitro angiogenic pattern formation.

Keywords

Lattice-gas cellular automata Parameter estimation Algorithmic differentiation Angiogenic pattern formation 

Mathematics Subject Classification (2000)

92C15 92C50 65D25 49M37 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Carsten Mente
    • 1
  • Ina Prade
    • 2
  • Lutz Brusch
    • 1
  • Georg Breier
    • 2
  • Andreas Deutsch
    • 1
  1. 1.Department for Innovative Methods of Computing, Center for Information Services and High Performance ComputingTechnische Universität DresdenDresdenGermany
  2. 2.Institute of Pathology, Universitätsklinikum Carl Gustav CarusTechnische Universität DresdenDresdenGermany

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