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Graph Transformation for Topology Modelling

  • Mathieu Poudret
  • Agnès Arnould
  • Jean-Paul Comet
  • Pascale Le Gall
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5214)

Abstract

In this paper we present meta-rules to express an infinite class of semantically related graph transformation rules in the context of pure topological modelling with G-maps. Our proposal is motivated by the need of describing specific operations to be done on topological representations of objects in computer graphics, especially for simulation of complex structured systems where rearrangements of compartments are subject to change. We also define application of such meta-rules and prove that it preserves some necessary conditions for G-maps.

Keywords

topology-based geometric modelling graph transformation generalized map 

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References

  1. [Car05]
    Cardelli, L., Calculi, B.: Interactions of biological membranes. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 257–280. Springer, Heidelberg (2005)Google Scholar
  2. [CFS06]
    Calzone, L., Fages, F., Soliman, S.: Biocham: an environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics 22(14), 1805–1807 (2006)CrossRefGoogle Scholar
  3. [EEPT06]
    Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. In: Monographs in Theoretical Computer Science. Springer, Heidelberg (2006)Google Scholar
  4. [HJE06]
    Hoffmann, B., Janssens, D., Van Eetvelde, N.: Cloning and expanding graph transformation rules for refactoring. Electr. Notes Theor. Comput. Sci. 152, 53–67 (2006)CrossRefGoogle Scholar
  5. [Hof05]
    Hoffmann, B.: Graph transformation with variables. In: Kreowski, H.-J., Montanari, U., Orejas, F., Rozenberg, G., Taentzer, G. (eds.) Formal Methods in Software and Systems Modeling. LNCS, vol. 3393, pp. 101–115. Springer, Heidelberg (2005)Google Scholar
  6. [Lie89]
    Lienhardt, P.: Subdivision of n-dimensional spaces and n-dimensional generalized maps. In: SCG 1989, pp. 228–236. ACM Press, New York (1989)CrossRefGoogle Scholar
  7. [Lie94]
    Lienhardt, P.: n-dimensional generalised combinatorial maps and cellular quasimanifolds. In: IJCGA (1994)Google Scholar
  8. [PCG+07]
    Poudret, M., Comet, J.-P., Le Gall, P., Arnould, A., Meseure, P.: Topology-based geometric modelling for biological cellular processes. In: LATA 2007, Tarragona, Spain, March 29 - April 4 (2007), http://grammars.grlmc.com/LATA2007/proc.html
  9. [PCLG+08]
    Poudret, M., Comet, J.-P., Le Gall, P., Képès, F., Arnould, A., Meseure, P.: Topology-based abstraction of complex biological systems: Application to the Golgi apparatus. Theory in Biosciences (2008)Google Scholar
  10. [Roz97]
    Rozenberg, G. (ed.): Handbook of Graph Grammars and Computing by Graph Transformations, Foundations, vol. 1. World Scientific, Singapore (1997)Google Scholar
  11. [RPS+04]
    Regev, A., Panina, E.M., Silverman, W., Cardelli, L., Shapiro, E.: Bioambients: an abstraction for biological compartments. Theor. Comput. Sci. 325(1), 141–167 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  12. [Tut84]
    Tutte, W.: Graph Theory. Encyclopedia of Mathematics and its Applications, vol. 21. Addison-Wesley, Reading (1984)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Mathieu Poudret
    • 1
    • 2
  • Agnès Arnould
    • 2
  • Jean-Paul Comet
    • 3
  • Pascale Le Gall
    • 1
    • 4
  1. 1.Programme d’Épigénomique, GénopoleÉvry
  2. 2.XLIM-SIC UMR 6172 CNRSUniv. de PoitiersFuturoscope 
  3. 3.I3S, UMR 6070 CNRSUniv. de Nice-Sophia-AntipolisSophia-Antipolis 
  4. 4.MAS, Ecole Centrale Paris, Grande Voie des VignesChâtenay-Malabry

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