1
Computer Physics Communications 121-122 (1999) 731 ComputerPhysics Communications www.elsevier.nl/locateJcpc Abstract Computational operators for dynamical complex pattern recognition R.R. Rosa a, C.R. Neto a, EM. Ramos a, A.S. Sharma b, J.A. Valdivia c a Laboratory for Computing and Applied Mathematics, National Institute for Space Research (INPE), CX Postal 515, 12201-970 S.J. dos Campos, SP, Brazil b Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA c Goddard Space Fligth Center, NASA, Greenbelt, MD 20771, USA Spatially extended systems yield complex pattems arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator (the so-called RSV operator), .T A, for the characterization of asymmeuic amplitude fragmentation in extended systems. For a given matrix of ,amplitudes this operation results in an asymmetric-triangulation field composed by L points and I straigth lines. The parameter (I - L)/L is a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amphtudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator ~.,4 and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns. We also compare the performance of correlation length, entropies and RSV operators applied mainly in non-equilibrium plasma extended systems [1]. The complex regimes we study are stochasticity, symmetry breaking, chaoticity and localized turbulence. The main result is the high performance of the complex entropy and RSV operator to quantify non-finear amplitude fragmentation and localized turbulence in spatio-temporal dynamics. © 1999 Elsevier Science B.V. All rights reserved. References [1] R.R. Rosa et al., Adv. Space Res. 20 (12) (1997) 2303-2308. 0010-4655/99/5 - see front matter © 1999 Elsevier Science B.V. All rights reserved.

Computational operators for dynamical complex pattern recognition

  • Upload
    rr-rosa

  • View
    212

  • Download
    0

Embed Size (px)

Citation preview

Computer Physics Communications 121-122 (1999) 731

Computer Physics Communications

www.elsevier.nl/locateJcpc

Abstract

Computational operators for dynamical complex pattern recognition

R.R. Rosa a, C.R. Neto a, E M . Ramos a, A.S. Sharma b, J.A. Valdivia c

a Laboratory for Computing and Applied Mathematics, National Institute for Space Research (INPE), CX Postal 515, 12201-970 S.J. dos Campos, SP, Brazil

b Department of Astronomy, University of Maryland, College Park, MD 20742-2421, USA c Goddard Space Fligth Center, NASA, Greenbelt, MD 20771, USA

Spatially extended systems yield complex pattems arising from the coupled dynamics of its different regions. In this paper we introduce a matrix computational operator (the so-called RSV operator), .T A, for the characterization of asymmeuic amplitude fragmentation in extended systems. For a given matrix of ,amplitudes this operation results in an asymmetric-triangulation field composed by L points and I straigth lines. The parameter (I - L ) / L is a new quantitative measure of the local complexity defined in terms of the asymmetry in the gradient field of the amphtudes. This asymmetric fragmentation parameter is a measure of the degree of structural complexity and characterizes the localized regions of a spatially extended system and symmetry breaking along the evolution of the system. For the case of a random field, in the real domain, which has total asymmetry, this asymmetric fragmentation parameter is expected to have the highest value and this is used to normalize the values for the other cases. Here, we present a detailed description of the operator ~.,4 and some of the fundamental conjectures that arises from its application in spatio-temporal asymmetric patterns.

We also compare the performance of correlation length, entropies and RSV operators applied mainly in non-equilibrium plasma extended systems [1]. The complex regimes we study are stochasticity, symmetry breaking, chaoticity and localized turbulence. The main result is the high performance of the complex entropy and RSV operator to quantify non-finear amplitude fragmentation and localized turbulence in spatio-temporal dynamics. © 1999 Elsevier Science B.V. All rights reserved.

References

[1] R.R. Rosa et al., Adv. Space Res. 20 (12) (1997) 2303-2308.

0010-4655/99/5 - see front matter © 1999 Elsevier Science B.V. All rights reserved.