Abstract
The Marr-Albus model of the cerebellum has been reformulated with linear system analysis. This adaptive linear filter model of the cerebellum performs a filtering action of a phase lead-lag compensator with learning capability, and will give an account for the phenomena which have been termed “cerebellar compensation”. It is postulated that a Golgi cell may act as a phase lag element; for example, as a leaky integrator with time constant about several seconds. Under this assumption, a mossy fiber-granule cell-Golgi cell input network functions as a phase lead-lag compensator. Output signals from Golgi-granule cell systems, namely, parallel fiber signals, are gathered together through variable synaptic connections to form a Purkinje cell output. From a general theory of adaptive linear filters, learning principles for these modifiable connections are derived. By these learning principles, a Purkinje cell output converges to the “desired response” to minimize the mean square error of the performance. In a more general sense, a Purkinje cell acquires a filtering function on the basis of multiple pairs of input signals and corresponding desired output signals. The mode of convergence of the output signal is described when the input signal is sinusoidal.
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References
Albus, J.S.: A theory of cerebellar function. Math. Biosci. 10, 25–61 (1971)
Amari, S.: Neural theory of association and concept formation. Biol. Cybern. 26, 175–185 (1977)
Amari, S.: Topographic organization of nerve fields. Bull. Math. Biol. 42, 339–364 (1980)
Amari, S., Takeuchi, A.: Mathematical theory on formation of category detecting nerve cells. Biol. Cybern. 29, 127–136 (1978)
Andersson, G., Oscarsson, O.: Climbing fiber microzones in cerebellar vermis and their projection to different groups of cells in the lateral vestibular nucleus. Exp. Brain Res. 32, 565–579 (1978)
Bell, C.C., Kawasaki, T.: Relations among climbing fiber responses nearby Purkinje cells. J. Neurophysiol. 35, 155–169 (1972)
Calvert, T.W., Meno, F.: Neural systems modeling applied to the cerebellum. IEEE Trans. Syst. Man Cybern. SMC-2, 363–374 (1972)
Davies, P., Melvill Jones, G.: An adaptive neural model compatible with plastic changes induced in the human vestibulo-ocular reflex by prolonged optical reversal of vision. Brain Res. 103, 546–550 (1976)
Denoth, F., Magherini, P.C., Pompeiano, O., Stanojevic, M.: Responses of Purkinje cells of cerebellar vermis to sinusoidal rotation of neck. J. Neurophysiol. 43, 46–59 (1980)
Dufossé, M., Ito, M., Jastreboff, P.J., Miyashita, Y.: A neuronal correlate in rabbit's cerebellum to adaptive modification of the vestibulo-ocular reflex. Brain Res. 150, 611–616 (1978)
Eccles, J.C.: An instruction-selective theory of learning in the cerebellar cortex. Brain Res. 127, 327–352 (1977)
Eccles, J.C., Ito, M., Szentágothai, J.: The cerebellum as a neuronal machine. Berlin, Heidelberg, New York: Springer 1967
Fernandez, C., Goldberg, J.M.: Physiology of peripheral neurons innervating semicircular canals of the squirrel monkey. II. Response to sinusoidal stimulation and dynamics of peripheral vestibular system. J. Neurophysiol. 34, 661–675 (1971)
Ghelarducci, B., Ito, M., Yagi, N.: Impulse discharges from flocculus Purkinje cells of alert rabbits during visual stimulation combined with horizontal head rotation. Brain Res. 87, 66–72 (1975)
Gonshor, A., Melvill Jones, G.: Extreme vestibulo-ocular adaptation induced by prolonged optical reversal of vision. J. Physiol. (London) 256, 381–414 (1976)
Groenewegen, H.J., Voogd, J.: The parasagittal zonation within the olivocerebellar projection. I. Climbing fiber destruction in the vermis of cat cerebellum. J. Comp. Neurol. 174, 417–485 (1977)
Hassul, M., Daniels, P.D.: Cerebellar dynamics: The mossy fiber input. IEEE Trans. Biomed. Eng. BME-24, 449–456 (1977)
Higgins, D.C., Partridge, L.D., Glaser, G.H.: A transient cerebellar influence on stretch responses. J. Neurophysiol. 25, 684–692 (1962)
Ito, M.: Neural design of the cerebellar motor control system. Brain Res. 40, 81–84 (1972)
Ito, M.: Learning control mechanisms by the cerebellum investigated in the flocculo-vestibulo-ocular system. In: The Nervous System, Vol. 1, pp. 245–252, Tower, D.B. (ed). New York: Raven Press, 1975
Ito, M.: Recent advances in cerebellar physiology and pathology. In: Advances in Neurology, Vol. 21, pp. 59–84. Kark, R.A., Rosenberg, R.N., Shut, L.J.(eds). New York: Raven Press 1978
Ito, M.: Is the cerebellum really a computer? Trends in Neurosciences 2, 122–126 (1979)
Ito, M., Sakurai, M., Tongroach, P.: Climbing fibre induced depression of both mossy fibre responsiveness and glutamate sensitivity of cerebellar Purkinje cells. J. Physiol. 324, 113–134 (1982)
Lange, W.: Regional differences in the distribution of Golgi cells in the cerebellar cortex of man and some other mammals. Cell Tiss. Res. 153, 219–226 (1974)
Lisberger, S.G., Fuchs, A.F.: Role of primate flocculus during rapid behavioral modification of vestibuloocular reflex. II. Mossy fiber firing patterns during horizontal head rotation and eye movement. J. Neurophysiol. 41, 764–777 (1978)
Marr, D.: A theory of cerebellar cortex. J. Physiol. (London) 202, 437–470 (1969)
Miles, F.A., Fuller, J.H., Braitman, D.J., Dow, B.M.: Long-term adaptive changes in primate vestibuloocular reflex. III. Electrophysiological observations in flocculus of normal monkeys. J. Neurophysiol. 43, 1437–1476 (1980)
Palkovits, M., Magyar, P., Szentagothai, J.: Quantitative histological analysis of the cerebellar cortex in the cat. I. Number and arrangement in space of the Purkinje cells. Brain Res. 32, 1–13 (1971A)
Palkovits, M., Magyar, P., Szentagothai, J.: Quantitative histological analysis of the cerebellar cortex in the cat. II. Cell numbers and densities in the granular layer. Brain Res. 32, 15–30 (1971B)
Sakrison, D.J.: Iterative design of optimum filters for non mean-square-error performance criteria. IEEE Trans. Inform. Theor. IT-3, 161–167 (1963)
Takahashi, Y., Rabins, M.J., Auslander, D.M.: Control and dynamic systems. Massachusetts: Addison-Wesley 1970
Tsukahara, N., Kiyohara, T., Ijichi, Y.: The mode of cerebellar control of pupillary light reflex. Brain Res. 60, 244–248 (1973)
Tsypkin, Ya.Z.: Adaptation and learning in automatic systems. In: Mathematics in Science and Engineering, Vol. 73. Bellman, R.(ed). New York: Academic Press 1971
Wasan, M.T.: Stochastic approximation. Cambridge: Cambridge University Press 1969
Widrow, B., Glover, J.R., McCool, J.M., Kaunitz, J., Williams, C.S., Hearn, R.H., Zeidler, J.R., Dong E., Goodlin, R.C.: Adaptive noise cancelling: Principles and applications. Proc. IEEE 63, 1692–1716 (1975)
Widrow, B., Mantey, P.E., Griffiths, L.J., Goode, B.B.: Adaptive antenna systems. Proc. IEEE. 55, 2143–2159 (1967)
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Fujita, M. Adaptive filter model of the cerebellum. Biol. Cybern. 45, 195–206 (1982). https://doi.org/10.1007/BF00336192
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DOI: https://doi.org/10.1007/BF00336192