Modeling stochastic spike train responses of neurons: An extended Wiener series analysis of pigeon auditory nerve fibers

Biological Cybernetics

Volumn 76, Issue 2, 1997, Pages 153-162

  Joeken, Stephan ^a   Schwegler, Helmut ^a   Richter, Claus Peter ^b  

^a UNIVERSITY OF BREMEN   (Germany)

^b GOETHE UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COLUMBA;

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; NERVE CELL; NERVE FIBER; PHYSIOLOGY; PIGEONS AND DOVES; VESTIBULOCOCHLEAR NERVE;

ACTION POTENTIALS; ANIMALS; COLUMBIDAE; MODELS, BIOLOGICAL; NERVE FIBERS; NEURONS; VESTIBULOCOCHLEAR NERVE;

EID: 0031064259     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004220050328     Document Type: Article

References (36)

1. Barrett JF (1963) The use of functionals in the analysis of non-linear physical systems. J Elect Control 15: 567-615
2. Bialek W, Rieke F, de Ruyter van Steveninck RR, Warland D (1991) Reading a neural code. Science 252: 1854-1857
3. Bryant HL, Segundo JP (1976). Spike initiation by transmembrane current: a white-noise analysis. J. Physiol (Lond) 260: 279-314
4. de Boer E (1967). Correlation studies applied to the frequency resolution of the cochlea. J Aud Res 7: 209-217
5. Eggermont JJ (1993) Wiener and Volterra analyses applied to the auditory system. Hear Res 66: 177-201
6. Fréchet M (1910) Sur les fonctionnelles continues. Ann Sci Ecole Normal Superieure 27: 193-219
7. French AS, Korenberg MJ (1989) A nonlinear model for action potential encoding in an insect sensory neuron. Biophys J 55: 655-661
8. Gerstner W (1995) Time structure of the activity in neural network models. Phys Rev E 51: 738-758
9. Gerstner W, van Hemmen JL (1992) Associative memory in a network of 'spiking' neurons. Network 3: 139-164
10. Gummer AW, Smolders JWT, Klinke R (1987) Basilar membrane motion in the pigeon measured with the Mössbauer technique. Hear Res 29: 63-92
11. Hodgkin AL, Huxley AF (1952) A quantitative description of ion currents and its application to conduction and excitation in nerve membranes. J Physiol (Lond) 117: 500-544
12. Hunter IW, Korenberg MJ (1986) The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biol Cybern 55: 135-144
13. Joeken S, Schwegler H (1995) Predicting spike train responses of neuron models. In: Verleysen M (ed) Proc 3rd ESANN'95, Brussels, D facto, pp 93-98
14. Kistler W, Gerstner W, van Hemmen JL (1996) Reduction of Hodgkin-Huxley equations to single-variable threshold model. Neural Comput (in press)
15. Klinke R, Müller M, Richter C-P, Smolders J (1994) Preferred intervals in birds and mammals: a filter response to noise? Hear Res 74: 238-246
16. Korenberg MJ (1985) Orthogonal identification of nonlinear difference equation models. In: Proc 28th Midwest Symp Circuit Syst, vol 1, pp 90-95
17. Korenberg MJ (1988) Identifying nonlinear difference equation and functional expansion representations: the fast orthogonal algorithm. Ann Biomed Eng 16: 123-142
18. Korenberg MJ (1989) A robust orthogonal algorithm for system identification and time-series analysis. Biol Cybern 60: 267-276
19. Korenberg MJ (1991) Parallel cascade identification and kernel estimation for nonlinear systems. Ann Biomed Eng 19: 429-455
20. Korenberg MJ, Hunter IW (1986) The identification of nonlinear biological systems: LNL cascade models. Biol Cybern 55: 125-134
21. Korenberg MJ, French AS, Voo SKL (1988) White-noise analysis of nonlinear behavior in an insect sensory neuron: kernel and cascade approaches. Biol Cybern 58: 313-320
22. Krausz HI (1975) Identification of nonlinear systems using random impulse train inputs. Biol Cybern 19: 217-230
23. Lee YW, Schetzen M (1965) Measurements of the Wiener kernels of nonlinear systems by crosscorrelation. Int J Control 2: 237-254
24. Mainen ZF, Sejnowski T (1995) Reliability of spike timing in neocortical neurons. Science 268: 1503-1507
25. Marmarelis PZ, Marmarelis VZ (1978) Analysis of physiological systems: the white noise approach. Plenum Press, New York
26. Marmarelis PZ, Naka K-I (1972) White noise analysis of a neuron chain: an application of the Wiener theory. Science 175: 1276-1278
27. Marmarelis VZ, Citron MC, Vivo CP (1986) Minimum-order Wiener modelling of spike-output systems. Biol Cybern 54: 115-123
28. Palm G, Poggio T (1977) The Volterra representation and the Wiener expansion: validity and pitfalls. SIAM J Appl Math 33: 195-216
29. Palm G, Poggio T (1978) Stochastic identification methods for nonlinear systems: an extension of the Wiener theory. SIAM J Appl Math 34: 524-534
30. Paulin MG (1993) A method for constructing data-based models of spiking neurons using a dynamic linear-static nonlinear cascade. Biol Cybern 69: 67-76
31. Richter C-P, Heynert S, Klinke R (1995) Rate intensity-functions of pigeon auditory primary afferents. Hear Res 83: 19-25
32. Schermuly L, Klinke R (1990) Infrasound sensitive neurons in the pigeon cochlear ganglion. J Comp Physiol A 166: 355-363
33. van Dijk P, Wit P, Segenhout JM (1994) Wiener kernel analysis of inner ear function in the American bullfrog. J Accoust Soc 95: 904-919
34. Victor JD, Johannesma P (1986) Maximum-entropy approximations of stochastic nonlinear transductions: an extension of the Wiener theory. Biol Cybern 54: 289-300
35. Volterra V (1930) Theory of functionals and of integral and integro-differential equations. Dover, New York
36. Wiener N (1958) Nonlinear problems in random theory. Wiley, New York