Journal of Computational Neuroscience

, Volume 25, Issue 3, pp 401–438 | Cite as

Theoretical analysis of reverse-time correlation for idealized orientation tuning dynamics

  • Gregor Kovačič
  • Louis Tao
  • David Cai
  • Michael J. Shelley
Article

Abstract

A theoretical analysis is presented of a reverse-time correlation method used in experimentally investigating orientation tuning dynamics of neurons in the primary visual cortex. An exact mathematical characterization of the method is developed, and its connection with the Volterra–Wiener nonlinear systems theory is described. Various mathematical consequences and possible physiological implications of this analysis are illustrated using exactly solvable idealized models of orientation tuning.

Keywords

Random walks Mexican hat Primary visual cortex Orientation tuning dynamics 

Notes

Acknowledgements

The authors would like to thank J. Biello, P. Kramer, D. McLaughlin, D. Nykamp, A. Rangan, R. Shapley, and E. Vanden Eijnden for helpful discussions. G.K. was supported by NSF grants IGMS-0308943 and DMS-0506287, and gratefully acknowledges the hospitality of the Courant Institute of Mathematical Sciences and Center for Neural Science during his visits at New York University in 2000/01 and 2003/04. L.T. was supported by the NSF grant DMS-0506257. D.C. and M.J.S. were partly supported by the NSF grant DMS-0506396.

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Gregor Kovačič
    • 1
  • Louis Tao
    • 2
    • 3
  • David Cai
    • 4
  • Michael J. Shelley
    • 4
  1. 1.Rensselaer Polytechnic InstituteTroyUSA
  2. 2.New Jersey Institute of TechnologyNewarkUSA
  3. 3.Center for Bioinformatics, School of Life SciencesPeking UniversityBeijingChina
  4. 4.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA

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