Mathematical constraints for building learning rules in the Purkinje cell system

Journal of Integrative Neuroscience

Volumn 5, Issue 2, 2006, Pages 171-185

  Daya, Bassam ^a   Chauvet, Pierre ^b   Rammal, Mohamad ^c  

^a LEBANESE UNIVERSITY   (Lebanon)

^b UNIVERSITÉ CATHOLIQUE DE L'OUEST   (France)

^c Institut Universitaire de Technologie de Saida   (Lebanon)

Author keywords

Cerebellum; Climbing fibers; Convergence; Error signal; Gradient method; Learning rules; Neural network; Optimization

Indexed keywords

ANALYTICAL ERROR; ARTICLE; CEREBELLUM CORTEX; CLIMBING FIBER; CONTROLLED STUDY; GOLGI COMPLEX; GRANULE CELL; LEARNING; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MOSSY FIBER; NERVE CELL NETWORK; NEUROTRANSMISSION; PROCESS OPTIMIZATION; PURKINJE CELL; SIGNAL TRANSDUCTION; SYNAPTIC TRANSMISSION;

AFFERENT PATHWAYS; ANIMALS; HUMANS; LEARNING; MATHEMATICS; NEURAL INHIBITION; NEURAL NETWORKS (COMPUTER); PURKINJE CELLS;

EID: 33745280093     PISSN: 02196352     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219635206001148     Document Type: Article

References (30)

1. Albus JS, A theory of cerebellar function, Math Biosci 10:25-61, 1971.
2. Boonyanit M, Randall D Beer, Center-crossing recurrent neural networks for the evolution of rhythmic behavior, Neural Comput 14:2043-2051, 2002.
3. Chauvet G, Habituation rules for a theory of the cerebellar cortex, Biol Cybern 55:1-9, 1986.
4. Chauvet GA, Berger TW, Hierarchical model of the population dynamics of hippocampal dentate granule cells, Hippocampus 12:698-712, 2002.
5. Chauvet GA, Chauvet P, The Purkinje local circuit as an example of functional unit in the nervous system, in Baudry M, Davis JL, Thompson RF (eds.), Advances in Synaptic Plasticity, The MIT Press, Cambridge 12:277-298, 1999.
6. Chauvet P, Chauvet GA, Purkinje local circuits with delays: Mathematical conditions of stability for learning and retrieval, Neural Networks 12:59-77, 1999.
7. Ciarlet PG, Introduction to Numerical Linear Algebra and Optimization, Cambridge Univ Press, 1986.
8. Darlot C, The cerebellum as a predictor of neural messages - I. The stable estimator hypothesis, Neuroscience 56:617-646, 1993.
9. Darlot C, Zupan L, Etard O, Denise P, Computation of inverse dynamics for the control of movements, Biol Cybern 75:173-186, 1996.
10. Daya B, Abdul-halim J, Chauvet GA, Error signal in cerebellar climbing fibers, IEEE World Congress on Computational Intelligence, Anchorage, Alaska, 1998.
11. Daya B, Chauvet GA, On the role of anatomy in learning by the cerebellar cortex, Math Biosci 155:111-138, 1999.
12. Daya B, Chauvet GA, Simulations of learning in a cerebellar cortex model using an optimization method, 12th European Simulation Multiconference, ESM98, Manchester, pp. 301-304, 1998.
13. Doya K, Kimura H, Miyamura H, Motor control: Neural models and system theory, ATR International, 2000.
14. Ebadzadeh M, Tondu B, Darlot C, Model des voies réflexes et cérébelleuses, CNRS, Center of Direct Scientific Communication, CCSD, Lyon, 2004.
15. Eccles JC, Ito M, Szentagothai J, The Cerebellum as a Neuronal Machine, Springer-Verlag, New York, 1976.
16. Fletcher R, Practical Methods of Optimization, Wiley, New York, 1987.
17. Floreano D, Urzelai J, Evolution of neural controllers with adaptive synapses and compact genetic encoding, 5th European Conference on Artificial Life, 1999.
18. Fox CA, Hillman DE, Siegesmund KA, Dutta CR, The primate cerebellar cortex: A Golgi and electron microscope study, Prog Brain Res 25:174-225, 1976.
19. Garenne A, Chauvet P, Daya B, Chauvet GA, Dynamic learning model of eyeblink conditioned reflex: Computational simulation and implications, Proc of the IASTED International Conference on Artificial Intelligence and Applications, (2004).
20. Gerstner W, Kistler WM, Spiking Neuron Models, Cambridge Univ Press, 2002.
21. Gilman S, Bloedel JR, Lechtenberg R, Disorders of the Cerebellum, F.A. Davis Company, 1981.
22. Ito M, The modifiable neuronal network of the cerebellum, J Physiol-London 34: 781-792 (1984).
23. Ito M, Sakurai M, Tongroach P, Climbing fibre induced depression of both mossy fibre responsiveness and glutamate sensitivity of cerebellar Purkinje cells, J Physiol-London 324:113-134, 1982.
24. Ito M, Movement and thought: Identical control mechanisms by the cerebellum, Trends Neurosci 16:448-450, 1993.
25. Kotaro H, Sung-ho K, Jinglu H, Junichi M, Min H, Chunzhi J, Improvement of generalization ability for identifying dynamical systems by using universal learning networks, Neural Networks 14:1389-1404, 2001.
26. Marr D, A theory of cerebellar cortex, J Physiol-London 202:437-470, 1969.
27. Maas W, Bishop CM, Pulsed Neural Networks, MIT Press, 1998.
28. Pierre DA, Optimization Theory with Applications, Wiley, New York, 1969.
29. Strang G, Introduction to Applied Mathematics, Wellesley-press, Cambridge, 1986.
30. Tyrrell T, Willshaw D, Cerebellar cortex: Its simulation and the relevance of Marr's theory, Philos T Roy Soc B 336:239-257, 1992.