Skip to main content
SpringerLink
Log in

Computational Methods and Tools for Modeling and Analysis of Complex Processes

  • Conference paper
Unconventional Models of Computation, UMC’2K

Part of the book series: Discrete Mathematics and Theoretical Computer Science ((DISCMATH))

  • 142 Accesses

Abstract

This review is devoted to the computational methods and tools for modeling and analysis of various complex processes in physics, medicine, social dynamics and nature. We consider: 1) the multivariate data analysis based on Ω k n -criteria and artificial neural networks (ANN), 2) the applications of neural networks for the function approximation and for the reconstruction and prediction of chaotic time series, and 3) the use of cellular automata (CA) in pattern recognition and in modeling of complex dynamical systems.

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

Access this chapter

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 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Prigogine I., “From Being to Becoming”, Freeman, San Francisco (1980).

    Google Scholar 

  2. I. Prigogine, “The End of Certainty: Time, Chaos and Laws of Nature”, The Free Press, New York (1997).

    Google Scholar 

  3. I. Antoniou and S. Tasaki, International J. of Quantum Chemistry 46, 425–474, (1993).

    Article  Google Scholar 

  4. I. Antoniou and Z. Suchanecki, Nonlinear Analysis: Theory, Methods and Applications, 30, 1939–1958 (1997).

    MathSciNet  MATH  Google Scholar 

  5. I. Antoniou and Z. Suchanecki, Found. Phys. 27, 333–362 (1997).

    Article  MathSciNet  Google Scholar 

  6. A. Lasota and M. Mackey, Chaos, Fractals and Noise, Springer Verlag, 1994.

    MATH  Google Scholar 

  7. O. Barndorf-Nielsen, J. Jensen, W. Kendalf, “Networks and Chaos — Statistical and Probabilistic Aspects”, Chapman & Hall, London (1993).

    Google Scholar 

  8. R.A. Fisher: Ann. Eugen.7 (1936), p.179.

    Google Scholar 

  9. Th. Nauman and H. Schiller: “Multidimensional Data Analysis”, in “Formulae and Methods in Experimental Data Evaluation”, vol.3 (European Physical Society, Geneve, 1983).

    Google Scholar 

  10. R. Brun et al. LINTRA, CERN Program Library E 5002.

    Google Scholar 

  11. V.V. Ivanov and P.V. Zrelov, Int. J. Comput. & Math. with Appl., vol. 34, No. 7/8, (1997) 703–726; JINR Communication P10-92-461, 1992 (in Russian).

    Article  MathSciNet  MATH  Google Scholar 

  12. P.V. Zrelov and V.V. Ivanov, In: Collection of Scientific Papers in Collaboration with Joint Institute for Nuclear Research, Dubna, USSR and Central Research Institute for Physics, Budapest, Hungary. “Algorithms and Programs for Solution of Some Problems in Physics”. Sixth Volume. Preprint KFKI-1989-62/M, 1989, p. 127-142.

    Google Scholar 

  13. L.S. Azhgirey et al, “Russian Nucl. Phys.”, 46, issue 4 (10), (1986) 1134–1141.

    Google Scholar 

  14. P.V. Zrelov and V.V. Ivanov, Nucl. Instr. and Meth. in Phys. Res., A310 (1991) 623–630.

    Google Scholar 

  15. P.V. Zrelov et al, JINR Preprint, P10-92-369, Dubna, 1992; Mathematical Modeling, vol. 4, N%11, (1993)56–74 (in Russian).

    MathSciNet  Google Scholar 

  16. S. Haykin, “Neural Networks: A Comprehensive Foundation”, Prentice-Hall, Inc., 1999.

    Google Scholar 

  17. C. Peterson and Th. Rögnvaldsson, in Proc. II Int. Workshop on “Software Engineering, Artificial Intelligence and Expert Systems in High Energy Physics”. New Compo Tech. in Phys. Res. II, edited by D. Perret-Gallix, World Scientific, (1992) 113.

    Google Scholar 

  18. B. Denby, in Proc. II Int. Workshop on “Software Engineering, Artificial Intelligence and Expert Systems in High Energy Physics”. New Compo Tech. in Phys. Res. II, edited by D. Perret-Gallix, World Scientific, (1992)287.

    Google Scholar 

  19. D.T. Pham and L. Xing, “Neural Networks for Identification, Prediction and Control”, Springer-Verlag Berlin (1995).

    Book  Google Scholar 

  20. A.Yu. Bonushkina et al, in Proc. IV Int. Workshop on Software Engineering, Artificial Intelligence and Expert Systems for High Energy and Nuclear Physics, April 3-8,1995, Pisa, Italy; “New Computing Techniques in Physics Research IV”, edited by B. Denby & D. Perret-Galix, “World Scientific”, (1995)751.

    Google Scholar 

  21. E Balestra et al, Nucl. Instr. and Meth. A426 (1999) 385–404.

    Google Scholar 

  22. M.P. Bussa et al, Nuovo Cimento, vol. 109A, (1996)327–339.

    Google Scholar 

  23. A.Yu. Bonushkina et al, JINR Rapid Communications 5(79)-96, (1996)5–14.

    Google Scholar 

  24. V.V. Ivanov, in Proc. IV Int. Workshop on Software Engineering, Artificial Intelligence and Expert Systems for High Energy and Nuclear Physics, April 3-8, 1995, Pisa, Italy; “New Computing Techniques in Physics Research IV”, edited by B. Denby & D. Perret-Galix, “World Scientific”, (1995)765.

    Google Scholar 

  25. A.Yu. Bonushkina et al, Int.J.Comput. & Math. with Appl., vol. 34, No. 7/8, (1997)677–685.

    Article  MathSciNet  MATH  Google Scholar 

  26. A. Babloyantz and V.V. Ivanov, in ICANN’95, Paris, France, 1995.

    Google Scholar 

  27. I.S. Berezin and N.P. Zhydkov, in Computing Methods, vol. 1, Moscow, 1959 (in Russian).

    Google Scholar 

  28. A.F. Nikiforov and S.K. Suslov: “Classical orthogonal polynomials”, “Znanie”, series “Mathematics, cibernatics”, 1985/12,27 (in Russian).

    MathSciNet  Google Scholar 

  29. R.W Hamming, in Numerical Methods for Scientists and Engineers, McGraw-Hiil, 1962.

    Google Scholar 

  30. V. Basios et al, Int. J. Comput. & Math. with Appl., vol. 34, No. 7/8, (1997)687–693.

    Article  MathSciNet  MATH  Google Scholar 

  31. D.E. Rumeihart, G.E. Hinton and R.I. Williams, in Parallel Distributed Processing: Explorations in the Microstructure of Cognition, Ed. D.E. Rumelhart and J.L. McClelland, 1, MIT Press, 1986.

    Google Scholar 

  32. A. Lapedes and R. Farber, Los Alamos Report LA-UR 87–2662 (1987).

    Google Scholar 

  33. P. Akritas et al, Chaos, Solitons and Fractals 11 (2000) 337–344.

    Article  MathSciNet  MATH  Google Scholar 

  34. E.A. Jackson, Perspectives of Nonlinear Dynamics, Cambridge University Press, 1989.

    Google Scholar 

  35. S. Rabinovich, G. Berkolaiko and S. Havlin, J. Math. Phys., 1996, 37, 5828–5836.

    Google Scholar 

  36. S. Wolfram (ed.), Theory and Applications of Cellular Automata, World Scientific, 1986.

    Google Scholar 

  37. T. Toffoli and N. Margolus, Cellular Automata Machines: A New Environment for Modeling, MIT Press, Cambridge, Mass., 1987.

    Google Scholar 

  38. M.P. Bussa M.P. et al, Int. J. Comput. & Math. with Appl., vol. 34, No. 7/8, (1997)695–701.

    Article  MATH  Google Scholar 

  39. I. Antoniou et al, in “Discrete Dynamics in Nature and Society”, v. 3, No. 1 (1999) 15–24.

    Article  MathSciNet  MATH  Google Scholar 

  40. R. Burridge and L Knopoff, “Bulletin of the Seismological Society of America”, 57, No.3, (1967)341–371.

    Google Scholar 

  41. P. Bak and C. Tang, “Journal of Geophysical Research”, 94, No. B11, (1989)15635–15637.

    Article  Google Scholar 

  42. H. Nakanishi, “Phys. Rev. A”, 43, No. 12, (1991)6613–6621.

    Article  Google Scholar 

  43. B. Gutenberg and C.R Richter, “Bulletin of the Seismological Society of America”, 34, (1944)185–188.

    Google Scholar 

  44. P.G. Akishin P.G. et al, in Proc. IFAC LSS’98, Large Scale Systems: Theory and Applications, Rio Patras, Greece, July 15-17, (1998)907–913.

    Google Scholar 

  45. Z. Olarni, H.S. Feder, and K. Christensen, “Phys.Rev.Lett.”, 68, No.8, (1992)1244–1246.

    Article  Google Scholar 

  46. P.G. Akishin et al, in “Discrete Dynamics in Nature and Society”, 2, (1998)267–279.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. International Solvay Institutes for Physics and Chemistry, Brussels, Belgium

    Ioannis Antoniou & Viktor V. Ivanov

  2. Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium

    Ioannis Antoniou

  3. Joint Institute for Nuclear Research, Dubna, Russia

    Viktor V. Ivanov

Authors
  1. Ioannis Antoniou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Viktor V. Ivanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Solvay Institutes, Free University of Brussels, Belgium

    I. Antoniou

  2. Department of Computer Science, University of Auckland, Auckland, New Zealand

    C. S. Calude  & M. J. Dinneen  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag London

About this paper

Cite this paper

Antoniou, I., Ivanov, V.V. (2001). Computational Methods and Tools for Modeling and Analysis of Complex Processes. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds) Unconventional Models of Computation, UMC’2K. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0313-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-1-4471-0313-4_2

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-415-4

  • Online ISBN: 978-1-4471-0313-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation