Nonsearch Paradigm for Large-Scale Parameter-Identification Problems in Dynamical Systems Related to Oncogenic Hyperplasia

  • E. Mamontov
  • A. Koptioug
Part of the IFIP International Federation for Information Processing book series (IFIPAICT, volume 202)

Abstract

In many engineering and biomedical problems there is a need to identify parameters of the systems from experimental data. A typical example is the biochemical-kinetics systems describing oncogenic hyperplasia where the dynamical model is nonlinear and the number of the parameters to be identified can reach a few hundreds. Solving these large-scale identification problems by the local- or global-search methods can not be practical because of the complexity and prohibitive computing time. These difficulties can be overcome by application of the non-search techniques which are much less computation- demanding. The present work proposes key components of the corresponding mathematical formulation of the nonsearch paradigm. This new framework for the nonlinear large-scale parameter identification specifies and further develops the ideas of the well-known approach of A. Krasovskii. The issues are illustrated with a concise analytical example. The new results and a few directions for future research are summarized in a dedicated section.

Keywords

nonlinear dynamic system non-search parameter identification Krasovskii method biochemical kinetics 

References

  1. [1]
    A. V. Koptioug, E. Mamontov. Toward prevention of hyperplasia in oncogeny and other proliferative diseases: The role of the cell genotoxicity in the model-based strategies. Abstracts: 7th Ann. Conf.: Functional Genomics-From Birth to Death. Göteborg, Sweden, August 19–20, 2004.Google Scholar
  2. [2]
    A. V. Koptioug, E. Mamontov, Z. Taib, M. Willander. The phase-transition morphogenic model for oncogeny as a genotoxic homeostatic dysfunction: Interdependence of modeling, advanced measurements, and numerical simulation. Abstracts: ICSB2004, 5th Int. Conf. Systems Biology. Heidelberg, Germany, October 9–13, 2004.Google Scholar
  3. [3]
    K. Psiuk-Maksymowicz, E. Mamontov. The time-slice method for rapid solving the Cauchy problem for nonlinear reaction-diffusion equations in the competition of home-orhesis with genotoxically activated oncogenic hyperplasia. Abstracts: The European Conference on Mathematical and Theoretical Biology. Dresden, Germany, July 18–22, 2005.Google Scholar
  4. [4]
    J. H. Miller, F. Zheng. Large-scale simulations of cellular signaling processes. Parallel Computing 30: 1137–1149, 2004.MathSciNetCrossRefGoogle Scholar
  5. [5]
    J. Yen, J. C. Liao, B. Lee, D. Randolph. A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method. IEEE Trans. Systems, Man, and Cybernetics 28(2): 173–191, 1998.Google Scholar
  6. [6]
    C.-Y. F. Huang, J. E. Ferrel, Jr. Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl. Acad. Sci. USA 93 (September): 10078–10083, 1996.Google Scholar
  7. [7]
    P. A. Ioannou, J. Sun. Robust Adaptive Control. Prentice-Hall, Upper Saddle River, NJ, USA, 1996.MATHGoogle Scholar
  8. [8]
    Y. V. Mamontov, M. Willander. Asymptotic method of finite equation for bounded solutions of nonlinear smooth ODEs. Mathematica Japonica 46(3): 451–461, 1997.MATHMathSciNetGoogle Scholar
  9. [9]
    E. Mamontov. Nonstationary invariant distributions and the hydrodynamic-style generalization of the Kolmogorov-forward/Fokker-Planck equation. Appl. Math. Lett. 18(9): 976–982, 2005.MATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    J. M. Ortega, W. C. Rheinboldt. Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York, 1970.MATHGoogle Scholar
  11. [11]
    A. A. Krasovskii. Optimal algorithms in identification problem with an adaptive model. Automation and Remote Control (May 10): 1851–1857, 1977.Google Scholar
  12. [12]
    N. Rouche, P. Habets, and M. Laloy. Stability Theory by Liapunov’s Direct Method. Springer-Verlag, 1977.Google Scholar
  13. [13]
    Y. V. Mamontov, M. Willander. High-Dimensional Nonlinear Diffusion Stochastic Processes. Modeling for Engineering Applications. World Scientific, Singapore, 2001.Google Scholar
  14. [14]
    E. Mamontov, A. Koptioug, M. Mångård, K. Marti. Asymptotic trajectory matching in self-navigation of autonomous manless interceptors: Nonsearch method and a formulation of the functional optimization of the stability of random systems. Abstracts: 5th MATH-MOD Vienna Conf., Special Session “Stochastic Optimization Methods”, Chair: K. Marti. Austria, Vienna, Vienna Univ. of Technol., 7–9 February, 2006. http://www.mathmod.at/.Google Scholar

Copyright information

© International Federation for Information Processing 2006

Authors and Affiliations

  • E. Mamontov
    • 1
  • A. Koptioug
    • 2
  1. 1.Department of PhysicsGothenburg UniversityGothenburgSweden
  2. 2.Department of Electronics, Institute of Information Technology and MediaMid Sweden UniversityÖstersundSweden

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