Computing with the leaky integrate-and-fire neuron: Logarithmic computation and multiplication

Neural Computation

Volumn 9, Issue 2, 1997, Pages 305-318

  Tal, Doron ^a   Schwartz, Eric L ^a  

^a BOSTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; NERVE CELL; NONLINEAR SYSTEM; PHYSIOLOGY; REPRODUCIBILITY; STATISTICAL MODEL;

ACTION POTENTIALS; COMPUTER SIMULATION; LOGISTIC MODELS; MODELS, NEUROLOGICAL; NEURONS; NONLINEAR DYNAMICS; REPRODUCIBILITY OF RESULTS;

EID: 0031568365     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/neco.1997.9.2.305     Document Type: Article

References (25)

1. Agin, D. 1964. Hodgkin-Huxley equations: Logarithmic relation between membrane current and frequency of repetitive activity. Nature 201, 625-626.
2. Amit, D. J., Evans, M. R., and Abeles, M. 1990. Attractor neural networks with biological probe records. Network 1, 381-405.
3. Barlow, H. B. 1969. Trigger features, adaptation and economy of impulses. In Information Processing in the Nervous System, K. N. Leibovic, ed., pp. 209-230. Springer-Verlag, Berlin.
4. Bugmann, G. 1991. Summation and multiplication: Two distinct operation domains of leaky integrate-and-fire neurons. Network 2, 489-509.
5. Cornsweet, T. N. 1970. Visual Perception. Academic Press, New York.
6. Harmon, L. D. 1961. Studies with artificial neurons, I: Properties and functions of an artificial neuron. Kybernetik 3, 89-101.
7. Hillman, D. E. 1979. Neural shape parameters and substructures as a basis of neuronal form. In The Neurosciences (4th Study Program), F. O. Schmitt and F. G. Worden, eds., pp. 432-437. MIT Press, Cambridge, MA.
8. Hodgkin, A. L., and Huxley, A. F. 1952. A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology 117, 500-544.
9. Horowitz, P., and Hill, W. 1989. The Art of Electronics. Cambridge University Press, Cambridge.
10. Jack, J. 1979. An introduction to linear cable theory. In The Neurosciences (4th Study Program), F. O. Schmitt and F. G. Worden, eds., pp. 423-437. MIT Press, Cambridge, MA.
11. Kawato, M., Hamaguchi, T., Murakami, F., and Tsukahara, N. 1984. Quantitative analysis of electrical properties of dendritic spines. Biol. Cybern. 50, 447-454.
12. Knight, B. W. 1972. Dynamics of encoding in a population of neurons. Journal of General Physiology 59, 734-766.
13. Koch, C., and Poggio, T. 1992. Multiplying with synapses and neurons. In Single Neuron Computation, T. McKenna, J. Davis, and S. F. Zornetzer, eds., pp. 315-345. Harcourt Brace Jovanovich, San Diego, CA.
14. Land, E. H. 1977. The retinex theory of color vision. Scientific American 237, 108-128.
15. Ratliff, F. 1965. Mach Bands: Quantitative Studies on Neural Networks in the Retina. Holden-Day, New York.
16. Reichardt, W., Egelhaaf, M., and Ai-ke, G. 1989. Processing of figure and background motion in the visual system of the fly. Biol. Cybern. 61, 327-345.
17. Schwindt, P. C., and Crill, W. E. 1982. Factors influencing motorneuron rhythmic firing: Results from a voltage clamp study. J. Neurophysiol. 64, 206-224.
18. Shadlen, M. N., and Newsome, W. T. 1995. Is there a signal in the noise? Current Opinion in Neurobiology 5, 248-250.
19. Softky, W. R. 1995. Simple codes versus efficient codes. Current Opinion in Neurobiology 5, 239-247.
20. Softky, W. R., and Koch, C. 1993. The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. Journal of Neuroscience 13, 334-350.
21. Srinivasan, M. V., and Bernard, G. D. 1976. A proposed mechanism for multiplication of neural signals. Biol. Cybernetics 21, 227-236.
22. Stein, R. B. 1967. The frequency of nerve action potentials generated by applied currents. Proceedings of the Royal Society B 167, 64-86.
23. Usher, M., Schuster, H. G., and Niebur, E. 1993. Dynamics of populations of integrate-and-fire neurons, partial synchronization and memory. Neural Computation 5, 570-586.
24. Wolfson, B., Gutnick, M. J., and Baldino, F. J. 1989. Electrophysiological characteristics of neurons in neocortical explant cultures. Exp. Brain Res. 76, 122-130.
25. Yeshurun, Y., and Schwartz, E. L. 1989. Cepstral filtering on a columnar image architecture: A fast algorithm for binocular stereo segmentation. IEEE Trans. Pattern Analysis and Machine Intelligence 11(7), 759-767.