On the role of anatomy in learning by the cerebellar cortex

Mathematical Biosciences

Volumn 155, Issue 2, 1999, Pages 111-138

  Daya, B ^a   Chauvet, G A ^a,b  

^a UNIVERSITÉ D'ANGERS   (France)

^b University of Southern California ^*  (United States)

Author keywords

Anatomy; Cerebellar cortex; Field equations; Heterosynaptic effect; Hierarchy; Learning; Stability

Indexed keywords

ARTICLE; BIOLOGICAL MODEL; CEREBELLUM CORTEX; HISTOLOGY; LEARNING; MATHEMATICAL COMPUTING; NERVE CELL NETWORK; PHYSIOLOGY; PURKINJE CELL;

CEREBELLAR CORTEX; LEARNING; MODELS, NEUROLOGICAL; NERVE NET; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PURKINJE CELLS;

EID: 0033073777     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0025-5564(98)10056-1     Document Type: Article

References (40)

1. P.J. Cordo, L. Bevan, Successive approximation in targeted movement: An alternative hypothesis, in: P. Cordo, S. Harnad (Eds.), Movement Control, Cambridge University, Cambridge, 1994, p. 127.
2. J.L. Raymond, S.G. Lisberger, M.D. Mauk, The cerebellum: A neuronal learning machine?, Science 272 (1996) 1126.
3. G. Chen, C.P. Hanson, R.L. Dunbar, T.J. Ebner, Spreading of surface stimulation evoked optical responses in the rat cerebellar cortex stained with neutral red, Soc. Neurosci. Abs. 23 (1997) 750.
4. G.A. Chauvet, Cerebellar Purkinje units: Basic functional elements of movement control, Behav. Brain Sci. 20 (1997) 247.
5. D. Marr, A theory of cerebellar cortex, J. Physiol. (London) 202 (1969) 437.
6. L. Simpson, R.B. Emerson, RNA editing (Abstract), Ann. Rev. Neurosci. 19 (1996) 27.
7. D. A. Robinson, Implications of neural networks for how we think about brain function, in: P. Cordo, S. Harnad (Eds.), Movement Control, Cambridge University, Cambridge, 1994, p. 42.
8. D.B. Arnold, D.A. Robinson, A learning network model of the neural integrator of the oculomotor system, Biol. Cybern. 64 (1991) 447.
9. N. Schweighofer, M.A. Arbib, P.F. Dominey, A model of the cerebellum in adaptive control of saccadic gain 1. The model and its biological substrate, Biol. Cybern. 75 (1996) 19.
10. N. Schweighofer, M.A. Arbib, P.F. Dominey, A model of the cerebellum in adaptive control of saccadic gain 2. Simulation results, Biol. Cybern. 75 (1996) 29.
11. S.G. Lisberger, Neural basis for motor learning in the vestibuloocular reflex of primates. III. Computational and behavioral analysis of the sites of learning, J. Neurophysiol. 72 (1994) 974.
12. R.E. Kettner, S. Mahamud, H.C. Leung, N. Sitkoff, J.C. Houk, B.W. Peterson, A.G. Barto, Prediction of complex two-dimensional trajectories by a cerebellar model of smooth pursuit eye movement, J. Neurophysiol. 77 (1997) 2115.
13. M.G. Paulin, The role of the cerebellum in motor control and perception, Brain Behav. Evol. 41 (1993) 39.
14. B. Daya, G.A. Chauvet, Control of dynamic biped locomotion using a neural network, (1996) 147.
15. H. Bischof, A.J. Pinz, Artificial versus real neural networks, in: P. Cordo, S. Harnad (Eds.), Movement Control, Cambridge University, Cambridge, 1994, p. 110.
16. G.A. Chauvet, Hierarchical functional organization of formal biological systems: a dynamical approach. III. The concept of non-locality leads to a field theory describing the dynamics at each level of organization of the (D-FBS) sub-system, Philos. Trans. Roy. Soc. London B 339 (1993) 463.
17. T.L. Clarke, Mathematics is a useful guide to brain function, in: P. Cordo, S. Harnad (Eds.), Movement Control, Cambridge University, Cambridge, 1994, p. 124.
18. T. Tyrrell, D. Willshaw, Cerebellar cortex: Its simulation and the relevance of Marr's theory, Phil. Trans. Roy. Soc. London B 336 (1992) 239.
19. A. Pellionisz, R.R. Llinás, Brain modeling by tensor network theory and computer simulation. The cerebellum: Distributed processor for predictive coordination, Neurosci. 4 (1979) 323.
20. A.J. Pellionisz, Brain theory connecting neurobiology to robotics tensor analysis: Utilizing intrinsic coordinates to describe, understand and engineer functional geometries of intelligent organisms, in: Lecture Notes in Biomathematics, vol. 2, Springer, Berlin, 1983, p. 185.
21. C. Koch, T. Poggio, Multiplying with synapses and Neurons, in: T. McKenna, J. Davis, S.F. Zornetzer (Eds.), Single Neuron Computation, Academic Press, Boston, 1992, p. 315.
22. P. Chauvet, G.A. Chauvet, Mathematical conditions for adaptive control in Marr's model of the sensorimotor system, Neural Networks 8 (1995) 693.
23. V. Braitenberg, The cerebellar network: Attempt at a formalization of its structure, Network-Comput. Neural Syst. 4 (1993) 11.
24. V. Braitenberg, D. Heck, F. Sultan, The detection and generation of sequences as a key to cerebellar function: Experiments and theory, Behav. Brain Sci. 20 (1997) 229.
25. M. Garwicz, G. Andersson, Spread of synaptic activity along parallel fibers in cat cerebellar anterior lobe, Exp. Brain Res. 88 (1992) 615.
26. P. Chauvet, G.A. Chauvet, Dynamics of delayed coupled Purkinje units in the cerebellar cortex, WCNN'96, Congress on Neural Networks, San Diego, USA, 1996.
27. G.A. Chauvet, An n-level field theory of biological neural networks, J. Math. Biol. 31 (1993) 771.
28. G. Chauvet, Habituation rules for a theory of the cerebellar cortex, Biol. Cybern. 55 (1986) 201.
29. C. Iadecola, Regulation of the cerebral microcirculation during neural activity: is nitric oxide the missing link, Trends Neurosci. 16 (1993) 206.
30. R. Llinàs, K. Walton, D.E. Hillman, Inferior olive: Its role in motor learning, Science 190 (1975) 1230.
31. M. Ito, The Cerebellum and Neural Control, Raven, New York, 1984.
32. G.A. Chauvet, On associative motor learning by the cerebellar cortex: From Purkinje unit to network with variational learning rules, Math. Biosci. 126 (1995) 41.
33. D.O. Hebb, The Organization of Behavior: A Neuropsychological Theory, Wiley, New York, 1949.
34. G.A. Chauvet, Correlation principle and physiological interpretation of synaptic efficacy, in: J. Delacour, J.C.S. Levy (Eds.), Systems with Learning and Memory abilities, Elsevier, Amsterdam, Paris, 1988.
35. R. Llinàs, M. Sugimori, Electrophysiological properties of in vitro Purkinje cell dendrites in mammalian cerebellar slices, J. Physiol. (London) 305 (1980) 197.
36. J. Hounsgaard, J. Midtgaard, Intrinsic determinants of firing pattern in Purkinje cells of the turtle cerebellum in vitro, J. Physiol. (London) 402 (1988) 731.
37. P. Chauvet and G.A. Chauvet, Purkinje local circuits with delays: Mathematical conditions of stability for learning and retrieval, Neural Networks (in press).
38. G.A. Chauvet, Non-locality in biological systems results from hierarchy: Application to the nervous system, J. Math. Biol. 31 (1993) 475.
39. J.-M. Chrétien, G.A. Chauvet, An algorithmic method for determining the kinetic system of receptor-channel complexes, Math. Biosci. 147 (1998) 227.
40. G.A. Chauvet, Theoretical Systems in Biology: Hierarchical and Functional Integration: Organisation and Regulation, vol. III, Pergamon, Oxford, 1996, p. 1.