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The Minimum-Variance Theory Revisited

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Computational Methods in Neural Modeling (IWANN 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2686))

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Abstract

The minimum-variance theory [12] was proposed to account for the eye and arm movement. However, we point out here that i) the input signals used in the the simulations are not Poisson processes; ii) when the input signal is a Poisson process, the solution of the minimumvariance is degenerate.

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References

  1. Albright T.D., Jessell T. M., Kandel E.R., and Posner M. I. (2000). Neural science: A century of progress and the mysteries that remain. Cell 100, s1–s55.

    Article  Google Scholar 

  2. de Vries G., and Sherman A. (2000). Channel sharing in pancreatic beta-cells revisited: Enhancement of emergent bursting by noise. J. Theor. Biol., 207:513–530

    Article  Google Scholar 

  3. Doya K., Kimura H., Kawato M. (2001). Neural mechanisms of learning and control. IEEE Control Systems Magazine, 21, 42–54.

    Article  Google Scholar 

  4. Brown D., Feng J., and Feerick, S. (1999) Variability of firing of Hodgkin-Huxley and FitzHugh-Nagumo neurons with stochastic synaptic input. Phys. Rev. Letts. 82, 4731–4734.

    Article  Google Scholar 

  5. Feng J. (2001). Is the integrate-and-fire model good enough?-a review. Neural Networks 14 955–975.

    Article  Google Scholar 

  6. Feng, J. (2002). Frontiers In Computational Neuroscience Feng J. (Ed.) CRC Publisher: Boca Raton.

    Google Scholar 

  7. Feng, J., Tartaglia, G.G., and Tirozzi B. (2001). A note on minimum-variance theory and beyond (submitted).

    Google Scholar 

  8. Gammaitoni L., Hänggi P., Jung P. and Marchesoni F. (1998). Stochastic resonance. Reviews of Modern Physics 70 224–287.

    Article  Google Scholar 

  9. Gerstner W., Kreiter A.K., Markram H., and Herz A.V. M. (1997). Neural codes: firing rates and beyond. Proc. Natl. Acad. Sci. USA 94, 12740–12741.

    Google Scholar 

  10. Hopfield J. J., and Brody C.D. (2000). What is a moment? ‘Cortical’ sensory integration over a brief interval. Proc. Natl. Acad. Sci. USA 97 13919–13924.

    Google Scholar 

  11. Hopfield J. J., and Brody C.D. (2001). What is a moment? Transient synchrony as a collective mechanism for spatiotemporal integration. Proc. Natl. Acad. Sci. USA 98 1282–1287.

    Google Scholar 

  12. Harris C.M., and Wolpert D. M. (1998). Signal-dependent noise determines motor planning Nature 394: 780–784.

    Article  Google Scholar 

  13. Kawato M. (1999). Internal models for motor control and trajectory planning. Current Opinion in Neurobiology 9,718–727.

    Article  Google Scholar 

  14. Koch, C. (1999). Biophysics of Computation, Oxford University Press: Oxford.

    Google Scholar 

  15. Ricciardi, L.M., and Sato, S. (1990). Diffusion process and first-passage-times problems. Lectures in Applied Mathematics and Informatics Ricciardi, L.M. (ed.), Manchester: Manchester University Press.

    Google Scholar 

  16. Salinas E., and Sejnowski T. (2001). Correlated neuronal activity and the flow of neural information. Nature Reviews Neuroscience 2, 539–550.

    Article  Google Scholar 

  17. Sejnowski T. J. (1998). Making smooth moves Nature 394 725–726.

    Article  Google Scholar 

  18. Shadlen M.N., and Newsome W.T.(1994). Noise, neural codes and cortical organization, Curr. Opin. Neurobiol. 4, 569–579.

    Article  Google Scholar 

  19. Tuckwell H. C. (1988). Stochastic processes in the neurosciences. Philadelphia: SIAM.

    Google Scholar 

  20. Wolpert D.M. (2001). The code for [12] is not available (private communication).

    Google Scholar 

  21. Wolpert D.M., and Ghahramani Z. (2000). Computational principles of movement neuroscience Nature Neuroscience 3:1212–1217

    Article  Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Feng, J. (2003). The Minimum-Variance Theory Revisited. In: Mira, J., Álvarez, J.R. (eds) Computational Methods in Neural Modeling. IWANN 2003. Lecture Notes in Computer Science, vol 2686. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44868-3_9

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  • DOI: https://doi.org/10.1007/3-540-44868-3_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40210-7

  • Online ISBN: 978-3-540-44868-6

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