General methodology for nonlinear modeling of neural systems with Poisson point-process inputs

Mathematical Biosciences

Volumn 196, Issue 1, 2005, Pages 1-13

  Marmarelis, V Z ^a   Berger, T W ^a  

^a Olin Hall 500 ^*  (United States)

Author keywords

Neural systems; Neuronal modeling; Nonlinear modeling; Point process inputs; Poisson inputs; Volterra kernels; Wiener kernels

Indexed keywords

COMPUTER SIMULATION; CORRELATION METHODS; IDENTIFICATION (CONTROL SYSTEMS); POISSON DISTRIBUTION;

NEURAL SYSTEMS; NONLINEAR MODELING; POINT PROCESS INPUTS; VOLTERRA KERNELS; WIENER KERNELS;

NEURAL NETWORKS;

MODELING;

ACCURACY; ACTION POTENTIAL; ARTICLE; ARTIFICIAL NEURAL NETWORK; CORRELATION ANALYSIS; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; METHODOLOGY; NERVE CELL; NERVE FIBER; THEORETICAL STUDY;

ACTION POTENTIALS; MATHEMATICS; MODELS, NEUROLOGICAL; NONLINEAR DYNAMICS; POISSON DISTRIBUTION;

EID: 22144491834     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2005.04.002     Document Type: Article

References (21)

1. T.W. Berger, T.P. Harty, G. Barrionuevo, and R.J. Sclabassi Modeling of neuronal networks through experimental decomposition V.Z. Marmarelis Advanced Methods of Physiological Systems Modeling vol. 2 1989 Plenum New York 113
2. T.W. Berger, G. Barrionuevo, S.P. Levitan, D.N. Krieger, and R.J. Sclabassi Nonlinear systems analysis of network properties of the hippocampal formation M. Gabriel J. Moore Foundations of Adaptive Networks 1990 MIT Massachusetts 283
3. T.W. Berger, T.P. Harty, C. Choi, X. Xie, G. Barrionuevo, and R.J. Sclabassi Experimental basis for an input/output model of the hippocampal formation V.Z. Marmarelis Advanced Methods of Physiological System Modeling vol. 3 1994 Plenum New York 29
4. H.I. Krausz Identification of nonlinear systems using random impulse train inputs Biol. Cybern. 19 1975 217
5. J.P. Kroeker Wiener analysis of nonlinear systems using Poisson-Charlier crosscorrelation Biol. Cybern. 27 1977 221
6. Y.W. Lee, and M. Schetzen Measurement of the Wiener kernels of a nonlinear system by crosscorrelation Int. J. Control 2 1965 237
7. P.Z. Marmarelis, and V.Z. Marmarelis Analysis of Physiological Systems: The White-Noise Approach 1978 Plenum New York Russian translation: Mir, Moscow, 1981. Chinese translation: Academy of Sciences, Beijing, 1990
8. V.Z. Marmarelis Biomedical Simulations Resources Advanced Methods of Physiological System Modeling vol. 1 1987 University of Southern California Los Angeles, California
9. V.Z. Marmarelis Advanced Methods of Physiological System Modeling vol. II 1989 Plenum New York
10. V.Z. Marmarelis Advanced Methods of Physiological System Modeling vol. III 1994 Plenum New York
11. V.Z. Marmarelis Nonlinear Dynamic Modeling of Physiological Systems 2004 Wiley Interscience & IEEE New York
12. V.Z. Marmarelis Identification of nonlinear biological systems using Laguerre expansions of kernels Ann. Biomed. Eng. 21 1993 573
13. V.Z. Marmarelis Modeling methodology for nonlinear physiological systems Ann. Biomed. Eng. 25 1997 239
14. V.Z. Marmarelis, and M.E. Orme Modeling of neural systems by use of neuronal modes IEEE Trans. Biomed. Eng. 40 1993 1149
15. H. Ogura Orthogonal functionals of the Poisson process IEEE Trans. Inform. Theory IT 18 1972 473
16. W.A. Scaringe, Cross-correlation methods for quantification of nonlinear input-output transformations of neural systems using a Poisson random test input. Thesis for Master of Science, University of Southern California, Los Angeles, California, 1995.
17. R.J. Sclabassi, D.N. Krieger, and T.W. Berger Nonlinear systems analysis of the somatosensory system V.Z. Marmarelis Biomedical Simulations Resource Advanced Methods of Physiological System Modeling vol. I 1987 University of Southern California Los Angeles, California 104
18. R.J. Sclabassi, D.N. Krieger, and T.W. Berger A systems theoretic approach to the study of CNS function Ann. Biomed. Eng. 16 1988 17
19. R.J. Sclabassi, B.R. Kosanovic, G. Barrionuevo, and T.W. Berger Computational methods of neuronal network decomposition V.Z. Marmarelis Advanced Methods of Physiological System Modeling vol. III 1994 Plenum New York 55
20. V. Volterra Theory of Functions and of Integral and Integro-differential Equations 1930 Dover Publications New York
21. N. Wiener Nonlinear Problems in Random Theory 1958 The Technology Press of MIT and Wiley New York