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A Kalman Filter Theory of the Cerebellum

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Dynamic Interactions in Neural Networks: Models and Data

Part of the book series: Research Notes in Neural Computing ((NEURALCOMPUTING,volume 1))

Abstract

A variety of evidence suggests that the cerebellum is directly involved in certain sensory tasks. The specific hypothesis developed in this article is that the cerebellum is a neural analog of a Kalman-Bucy filter, whose function is to estimate state variables of the motor system and of external dynamical systems.

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Bibliography

  1. T. C. Tricas. Bioelectric-mediated Predation by Swell Sharks, Cephaloscyllium ventriosum. Copeia 4, 1982.

    Google Scholar 

  2. R. G. Northcutt. Brain Organization in the Cartilaginous Fishes. In: The Sensory Biology of Sharks, Skates and Rays. E.S. Hodgson and RF Mathewson (eds.). ONR, 1978.

    Google Scholar 

  3. T.H. Bullock and W. Heiligenberg. Electroreception. Wiley, 1986.

    Google Scholar 

  4. R.R. Llinas, J.R. Bloedel and D.E. Hillman. Functional Characterization of Neuronal Circuitry of Frog Cerebellar Cortex. Journal of Neurophysiology 32, 1969.

    Google Scholar 

  5. W. Welker. Spatial Organization of Somatosensory Projection to Rat Cerebellar Cortex: Functional and Connectional Implications of Fractured Somatotopy (Summary of Wisconsin Studies). In: New Concepts in Cerebellar Neurobiology, Alan R. Liss Inc. 1987.

    Google Scholar 

  6. M. Ito. The Cerebellum and Neural Control. Raven, 1984.

    Google Scholar 

  7. C.M. Oman. A Heuristic Mathematical Model for the Dynamics of Sensory Conflict and Motion Sickness. Acta OtoLaryngobgica s392,1982.

    Google Scholar 

  8. R.E. Kalman. A New Approach to Linear Filtering and Predition Problems. Journal of Basic Engineering, March 1960.

    Google Scholar 

  9. R.E. Kalman and R.S. Bucy. New Results in Linear Filtering and Prediction Theory. Journal of Basic Engineering, March 1961.

    Google Scholar 

  10. G.L. Goodwin and K.S. Sin. Adaptive Filtering, Prediction and Control. Prentice-Hall, 1984.

    MATH  Google Scholar 

  11. N. Wiener. Cybernetics. 1948.

    Google Scholar 

  12. D.L. Tomko, R.J. Peterka, R.N. Schor and D.P. O’Leary. Response Dynamics of Horizontal Canal Afferents in Barbiturate Anaesthetized Cats. Journal of Neurophysiology 45,1981.

    Google Scholar 

  13. M.G. Paulin and J.C. Montgomery. Elasmobranch Eye Motor Dynamics Characterized using Pseudorandom Stimulus. Journal of Comparitive Physiology A 158,1986.

    Google Scholar 

  14. M.G. Paulin and J.C. Montgomery. A Vestibulo-Ocular Reflex with no Head Movement. Biological Cybernetics 55,1986.

    Google Scholar 

  15. D.A. Robinson. Adaptive Gain Control of the Vestibulo-Oculer Reflex by the Cerebellum. Journal of Neurophysiology, 36,1976.

    Google Scholar 

  16. A.J. Pellionisz and R.R. Llinas. Brain Modeling by Tensor Network Theory and Computer Simulation. The Cerebellum: Distributed Processor for Predictive Coordination. Neuroscience 4,1979.

    Google Scholar 

  17. M.A. Arbib and S. Amari. Sensori-Motor Transformations in the Brain (With a Critique of the Tensor Theory of Cerebellum). Journal of Theoretical Biology 112,1985.

    Google Scholar 

  18. M.G. Paulin. Cerebellar Control of Vestibular Reflexes. Ph.D. Thesis. University of Auckland, 1985.

    Google Scholar 

  19. H. Collewijn. Integration of Adaptive Changes of the Optokinetic Reflex, Pursuit and the Vestibulo-Ocular Reflex. In: A. Berthoz and G. Melvill-Jones (eds.) Adaptive Mechanisms of Gaze Control. Elsevier, 1985.

    Google Scholar 

  20. S.G. Lisberger, F.A. Miles and L.M. Optican. Frequency-Selective Adaptation: Evidence for Channels in the Vestibulo-Ocular Reflex? Journal of Neuroscience 3,1983.

    Google Scholar 

  21. J.J. DiStefano, A.R. Stubberud, I.J. Williams. Feedback and Control Systems. Schaums Outline Series, McGraw-Hill, 1967.

    Google Scholar 

  22. R.F. Thompson. The Neurobiology of Learning and Memory. Science 233,1986.

    Google Scholar 

  23. M. Kano and M. Kato. Quisqualate Receptors are Specifically Involved in Cerebellar Synaptic Plasticity. Nature. 325,1987.

    Google Scholar 

  24. R.R. Llinas and K. Walton. Vestibular Compensation: A Distributed Property of the Central Nervous System. In: Integration in the Nervous System. H. Asanuma and V.J. Wilson (eds.). Igaku-Shoin, 1979.

    Google Scholar 

  25. R.R. Llinas and A.J. Pellionisz. Cerebellar Function and the Adaptive Feature of the Central Nervous System. In: Adaptive Mechanisms of Gaze Control. A. Berthoz and G. Melvill-Jones (eds.). Elsevier, 1985.

    Google Scholar 

  26. S. Salmons. Functional Adaptation in Skeletal Muscle. In: The Motor System in Neurobiology. Evarts, Wise and Bousfield (eds.). Elsevier, 1985.

    Google Scholar 

  27. A. Newman, A. Kuruvilla, A. Pereda and V. Honrubia. Regeneration of the 8th Cranial Nerve. I. Anatomical Verification in the Bullfrog. Laryngoscope 96, 1986.

    Google Scholar 

  28. J.L McClelland, D.E. Rumelhart and the PDP Research Group. Parallel Distributed Processing, volume 1. MIT Press, 1986.

    Google Scholar 

  29. A.G. Barto (ed.). Simulation Experiments with Goal-Seeking Adaptive Elements. DTIC Technical Report AFWAL-TR-84-1022, 1984.

    Google Scholar 

  30. M. Fujita. Adaptive Filter Model of the Cerebellum. Biological Cybernetics, 45,1982.

    Google Scholar 

  31. M. Fujita. Simulation of Adaptive Modification of Vestibulo-Ocular Reflex with an Adaptive Filter Model of the Cerebellum. Biological Cybernetics 45,1982.

    Google Scholar 

  32. G. Melvill-Jones. Plasticity in the Adult Vestibulo-Ocular Reflex Arc. Philosophical Transactions of the Royal Society, London (B). 278,1977.

    Google Scholar 

  33. R.H.S. Carpenter. Movements of the Eyes. Pion, 1977.

    Google Scholar 

  34. P.J. Daltos and R.W. Jones. Learning Behavior of the Eye Fixation and Control System. IEEE AC-8,1963.

    Google Scholar 

  35. G.J. St. Cyr and D.H. Fender. Nonlinearities in the Human Oculomotor System: Time Delays. Vision Research, 24,1969.

    Google Scholar 

  36. H. Collewijn. Direction-Selective Units in the Rabbits Nucleus of the Optic Tract. Brain Research 100,1975.

    Google Scholar 

  37. H. Collewijn. The Modifiability of the Adult Vestibulo-Ocular Reflex. TINS 1, 1979.

    Google Scholar 

  38. H.H. Barmack and D.T. Hess. Multiple-Unit Activity Evoked in Dorsal Cap of Inferior Olive of the Rabbit by Visual Stimulation. Journal of Neurophysiology 43,1980.

    Google Scholar 

  39. D. Hyden, B. Larsby and LM. Odkvist. Quantification of Eye Movements in Light and Darkness. Acta Otolaryngologica s406,1984.

    Google Scholar 

  40. U. Reker. The High Frequency Limit of the Fundamental Vestibulo-Ocular Reflex. Arch. Oto-Rhino-Laryngofogy 239,1984.

    Google Scholar 

  41. A. Benson. Compensatory Eye Movements Produced by Angular Oscillation. Proc. XXVIUPS, Munich, 1971.

    Google Scholar 

  42. A.A. Skavenski, R.M. Hansen, R.M. Steinman and B.J. Winterson. Quality of Retinal Image Stabilization During Small Natural and Artificial Body Rotations in Man. Vision Research 19,1979.

    Google Scholar 

  43. G.M. Gauthier, J. Piron, J. Roll, E. Marchetti and B. Martin. High Frequency Vestibulo-Ocular Reflex Activation THrough Forced Head Rotation in Man. Aviation, Space and Environmental Medicine 55,1984.

    Google Scholar 

  44. B.J. Winterson, H. Collewijn and R.M. Steinman. Compensatory Eye Movements to Miniature Rotations in the Rabbit: Implications for Retinal Image Stability. Vision Research 19,1979.

    Google Scholar 

  45. E.L. Keller. Gain of the Vestibulo-Oculer Reflex in Monkey at High Rotational Frequency. Vision Research 18,1978.

    Google Scholar 

  46. J.M. Furman, D.P. O’Leary and J.W. Wolfe. Application of Linear Systems Analysis to the Horizontal Vestibulo-Ocular Reflex in the Alert Rhesus Monkey using Pseudorandom Binary Sequence and Single Frequency Sinusoidal Stimulation. Biological Cybernetics 33,1979.

    Google Scholar 

  47. D.H. Brandwood and C.J. Tarran. Adaptive Arrays for Communications. Proc IEE F 129,1982.

    Google Scholar 

  48. H.L Galiana and J.S. Outerbridge. A Bilateral Model for Central Neural Pathways in Vestibulo-Ocular Reflex. Journal of Neurophysiology 51,1984.

    Google Scholar 

  49. S.C. Cannon, D.A. Robinson and S. Shamma. A Proposed Neural Network for the Integrator of the Oculomotor System. Biological Cybernetics 49 1983.

    Google Scholar 

  50. C.C. Boylls. A Theory of Cerebellar Function with Applications to Locomotion. I. The Physiological Role of Climbing Fiber Inputs in Anterior Lobe Operation. COINS Technical Report 75C-6,1975.

    Google Scholar 

  51. C.C. Boylls. A Theory of Cerebellar Function with Applications to Locomotion. I. The Relation of Anterior Lobe Climbing Fiber Function to Locomotor Behavior in the Cat. COINS Technical Report 76-1,1975.

    Google Scholar 

  52. N. Tsukahara. The Properties of the Cerebello-Pontine Reverberating Circuit. Brain Research 19,1972..

    Google Scholar 

  53. W. Waespe, B. Cohen and T. Raphan. Dynamic Modification of the Vestibulo-Ocular Reflex by the Nodulus and Uvula. Science 228,1985.

    Google Scholar 

  54. G. Palm. On the Representation and Approximation of Nonlinear Systems. Part I: Discrete Time. Biological Cybernetics 34,1979.

    Google Scholar 

  55. A. Lapides and R. Farber. Nonlinear Signal Processing Using neural Networks. Prediction and System Modeling. Los Alamos National Laboratory Preprint LA-UR-87-2662,1987.

    Google Scholar 

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Author information

Authors and Affiliations

  1. California Institute of Technology, Pasadena, CA, USA

    Michael Paulin

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  1. Michael Paulin
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Editor information

Editors and Affiliations

  1. Center for Neural Engineering, University of Southern California, Los Angeles, CA, 90089-0782, USA

    Michael A. Arbib

  2. Department of Mathematical Engineering and Instrumentation Physics, University of Tokyo, Tokyo, 113, Japan

    Shun-ichi Amari

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© 1989 Springer-Verlag New York Inc.

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Paulin, M. (1989). A Kalman Filter Theory of the Cerebellum. In: Arbib, M.A., Amari, Si. (eds) Dynamic Interactions in Neural Networks: Models and Data. Research Notes in Neural Computing, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4536-0_15

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  • DOI: https://doi.org/10.1007/978-1-4612-4536-0_15

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96893-3

  • Online ISBN: 978-1-4612-4536-0

  • eBook Packages: Springer Book Archive

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