Mathematical Psychology and Psychophysiology

By Stephen Grossberg | Go to book overview

REFERENCES

1. S. I. Amari, Characteristics of random nets of analog neuron-like elements, IEEE Trans. on Systems, Man and Cybernetics, vol. SMC-2, 1972, pp. 643-657.

2. _____, Neural theory of association and concept-formation, Biol. Cybernet. 26 ( 1977), 175-185.

3. _____, Topographic organization of nerve fields, Bull. Math. Biol. 42 ( 1980), 339-364.

4. S. I. Amari and A. Takeuchi, Mathematical theory on formation of category detecting nerve cells, Biol. Cybernet. 29 ( 1978), 127-136.

5. E. L. Bienenstock, L. N. Cooper and P. Munro, On the development of neuronal selectivity: orientation specificity and binocular interaction in visual cortex (in preparation).

6. R. O. Duda and P. E. Hart, Pattern classification and scene analysis, Wiley, New York, 1973.

7. J. L. Feldman and J. D. Cowan, Large-scale activity in neural nets. II. A model for the brainstem respiratory oscillator, Biol. Cybernet. 17 ( 1975), 39-51.

8. S. Geman, Application of stochastic averaging to learning systems, Brain Theory Newsletter 3 ( 1978), 69-71.

9. _____, Some averaging and stability results for random differential equations, SIAM J. Appl. Math. 36 ( 1979), 86-105.

10. _____, A method of averaging for random differential equations with applications to stability and stochastic approximations, Approximate Solution of Random Equations ( A. T. Bharucha-Reid, ed.), North-Holland Series in Probability and Appl. Math., North-Holland, Amsterdam, 1979, pp. 49-85.

11. _____, Notes on a self-organizing machine, Parallel Models of Associative Memory ( G. Hinton and J. Anderson, eds.), Erlbaum Associates, Hillsdale, N. J., 1980.

12. _____, Almost sure stable oscillations in a large system of randomly coupled equations, Reports on Pattern Analysis, no. 97, Div. Appl. Math., Brown University, 1980 (submitted).

13. S. Geman and M. Miller, Computer simulation of brainstem respiratory activity, J. Appl. Physiol. 41 ( 1976), 931-938.

14. S. Geman and C. R. Hwang, A chaos hypothesis for some large systems of random equations, Reports on Pattern Analysis, no. 82, Div. Appl. Math., Brown University, 1980 (submitted).

15. S. Grossberg, A neural theory of punishment and avoidance. I. Qualitative theory. Math. Biosci. 15 ( 1972), 39-67.

16. _____, A neural theory of punishment and avoidance. II. Quantitative theory. Math. Biosci. 15 ( 1972), 253-285.

17. _____, Pattern learning by functional-differential neural networks with arbitrary path weights, Delay and Functional Differential Equations and Their Applications ( K. Schmitt, ed.), Academic Press, New York, 1972, pp. 121-160.

18. _____, Classical and instrumental learning by neural networks, Progress in Theoret. Biol. 3 ( 1974), 51-141.

19. A. E. Hoerl and R. W. Kennard, Ridge regression. Biased estimation for non-orthogonal problems, Technometrics 12 ( 1970), 55-67.

20. K. Kadiyala, Operational ridge regression estimator under the prediction goal, Comm. Statist. A-Theory Methods 8 ( 1979), 1377-1391.

21. Iu. A. Mitropolsky, Averaging method in non-linear mechanics, Internat. J. Non-Linear Mech. 2 ( 1967), 69-96.

22. A. M. Uttley, A two-pathway informon theory of conditioning and adaptive pattern recognition, Brain Res. 102 ( 1976), 23-35.

23. _____, Simulation studies of learning in an informon network, Brain Res. 102 ( 1976), 37-53.

24. _____, Neurophysiological predictions of a two-pathway informon theory of neural conditioning, Brain Res. 102 ( 1976), 55-70.

25. M. T. Wasan, Stochastic approximation, Cambridge Univ. Press, Cambridge, 1969.

26. H. R. Wilson and J. D. Cowan, A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue, Kybernetik 13 ( 1973), 55-80.

DIVISION OF APPLIED MATHEMATICS, BROWN UNIVERSITY, PROVIDENCE, RHODE ISLAND 02912

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