Skip to main content
SpringerLink
Log in
Book cover

International Conference on Membrane Computing

CMC 2012: Membrane Computing pp 311–322Cite as

Multigraphical Membrane Systems Revisited

  • Conference paper

  • 707 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7762))

Abstract

A concept of a (directed) multigraphical membrane system [21], akin to membrane systems in [23] and [20], for modeling complex systems in biology, evolving neural networks, perception, and brain function is recalled and its new inspiring examples are presented for linking it with object recognition in cortex, an idea of neocognitron for multidimensional geometry, fractals, and hierarchical networks.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alexander, C.: A city is not a tree. Reprint from the Magazine Design No. 206, Council of Industrial Design (1966)

    Google Scholar 

  2. Baas, N.B., Emmeche, C.: On Emergence and Explanation. Intellectica 2(25), 67–83 (1997)

    Google Scholar 

  3. Bailly, F., Longo, G.: Objective and Epistemic Complexity in Biology, invited lecture. In: International Conference on Theoretical Neurobiology, New Delhi (February 2003), http://www.di.ens.fr/users/longo

  4. Barr, F., Welles, C.: Category Theory for Computing Science, 2nd edn. Prentice–Hall, New York (1990, 1993)

    Google Scholar 

  5. Barrière, L., et al.: Deterministic hierarchical networks. Networks (2006) (submitted)

    Google Scholar 

  6. Domshlak, C.: On recursively directed hypercubes. Electron. J. Combin. 9, #R23 (2002)

    MathSciNet  Google Scholar 

  7. Edalat, A.: Domains for computation in mathematics, physics and exact real arithmetic. The Bulletin of Symbolic Logic 3, 401–452 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ehresmann, A.C., Vanbremeersch, J.-P.: Multiplicity Principle and Emergence in Memory Evolutive Systems. SAMS 26, 81–117 (1996)

    MATH  Google Scholar 

  9. Ehresmann, A.C., Vanbremeersch, J.-P.: Consciousness as Structural and Temporal Integration of the Context, http://perso.orange.fr/vbm-ehr/Ang/W24A7.htm

  10. Ehresmann, A.C., Vanbremeersch, J.-P.: Memory Evolutive Systems. Studies in Multidisciplinarity, vol. 4. Elsevier, Amsterdam (2007)

    Google Scholar 

  11. Eroni, S., Harel, D., Cohen, I.R.: Toward Rigorous Comprehension of Biological Complexity: Modeling, Execution, and Visualization of Thymic T-Cell Maturation. Genome Research 13, 2485–2497 (2003)

    Article  Google Scholar 

  12. Falconer, K.: Fractal Geometry. Mathematical Foundations and Applications. Wiley, Hoboken (2003)

    Book  MATH  Google Scholar 

  13. Felleman, D.J., Van Essen, D.C.: Distributed hierarchical processing in the primate cerebral cortex. Cerebral Cortex 1(1), 1–47 (1991)

    Article  Google Scholar 

  14. Fukushima, K.: Neocognitron: A hierarchical neural network capable of visual pattern recognition. Neural Networks 1(2), 119–130 (1988)

    Article  Google Scholar 

  15. Fukushima, K.: Neocognitron trained with winner-kill-loser rule. Neural Networks 23, 926–938 (2010)

    Article  Google Scholar 

  16. Gutierrez-Naranjo, M.A., Perez-Jimenez, M.J.: Fractals and P systems. In: Proc. of 4th BWMC, vol. II, pp. 65–86. Sevilla Univ. (2006)

    Google Scholar 

  17. Harel, D.: On Visual Formalisms. Comm. ACM 31, 514–530 (1988)

    Article  MathSciNet  Google Scholar 

  18. Inseberg, A.: Parallel Coordinates: Visual Multidimensional Geometry and its Applications. Springer, Berlin (2008)

    Google Scholar 

  19. Lair, C.: Elements de la theorie des Patchworks. Diagrammes 29 (1993)

    Google Scholar 

  20. Membrane computing web page, http://ppage.psystems.eu

  21. Obtułowicz, A.: Multigraphical membrane systems: a visual formalism for modeling complex systems in biology and evolving neural networks. In: Preproceedings of Workshop of Membrane Computing, Thessaloniki, pp. 509–512 (2007)

    Google Scholar 

  22. Ovchinnikov, S.: Partial cubes: characterizations and constructions. Discrete Mathematics 308, 5597–5621 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  23. Păun, G.: Membrane Computing. An Introduction. Springer, Berlin (2002)

    Book  MATH  Google Scholar 

  24. Ravasz, E., Barabási, A.-L.: Hierarchical organization in complex networks. Physical Review 67, 026112 (2003)

    Google Scholar 

  25. Reisenhuber, M., Poggio, T.: Hierarchical models of object recognition in cortex. Nature Neuroscience 11, 1019–1025 (1999)

    Google Scholar 

  26. Seitz, C.L.: The cosmic cube. Comm. ACM 28, 22–33 (1985)

    Article  Google Scholar 

  27. Shin, S.-J.: The Logical Status of Diagrams, Cambridge (1994)

    Google Scholar 

  28. Thiel, T.: The design of the connection machine, DesignIssues, vol. 10(1), pp. 5–18. MIT Press, Cambridge (1994), see also http://www.mission-base.com/tamiko/theory/cm_txts/di-frames.html

    Google Scholar 

  29. Van Essen, D.C., Maunsell, J.H.R.: Hierarchical organization and functional streams in the visual cortex. Trends in NeuroScience, 370–375 (September 1983)

    Google Scholar 

  30. von der Malsburg, C.: Binding in Models of Perception and Brain Function. Current Opinions in Neurobiology 5, 520–526 (1995)

    Article  Google Scholar 

  31. von der Malsburg, C.: The What and Why of Binding: The Modeler’s Perspective. Neuron, 95–104, 94–125 (1999)

    Google Scholar 

  32. http://commons.wikimedia.org/wiki/File:3D_Cantor_set.jpg

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O.B. 21, 00-956, Warsaw, Poland

    Adam Obtułowicz

Authors
  1. Adam Obtułowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Algorithms and Their Applications, Eötvös Loránd University, , ,, Pázmány Péter sétány 1/c, 1117, Budapest, Hungary

    Erzsébet Csuhaj-Varjú

  2. Department of Computer Science, University of Sheffield, 211 Portobello Street, S1 4DP, Sheffield, UK

    Marian Gheorghe

  3. Leiden Center of Advanced Computer Science (LIACS), Leiden University, Niels Bohrweg 1, 2333, Leiden, CA, The Netherlands

    Grzegorz Rozenberg

  4. Turku Centre for Computer Science (TUCS), Leminkaisenkatu 14, 20520, Turku, Finland

    Arto Salomaa

  5. Department of Computer Science, University of Debrecen, Kassai út 26, 4028, Debrecen, Hungary

    György Vaszil

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Obtułowicz, A. (2013). Multigraphical Membrane Systems Revisited. In: Csuhaj-Varjú, E., Gheorghe, M., Rozenberg, G., Salomaa, A., Vaszil, G. (eds) Membrane Computing. CMC 2012. Lecture Notes in Computer Science, vol 7762. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36751-9_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-36751-9_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36750-2

  • Online ISBN: 978-3-642-36751-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation