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Localized Activity States for Neuronal Field Equations of Feature Selectivity in a Stimulus Space with Toroidal Topology

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Nonlinear and Complex Dynamics
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Abstract

Spatially localized activity profiles have long been proposed as a mechanism for feature selectivity in models of cortex. Cortical neurons show selectivity to many features of the stimulus space. Recent experimental evidence shows strong correlations between population activity and the topology of the stimulus space. Here we focus on a case where neurons respond preferentially to two independent circular variables to examine the influence of a Torus topology on the computational properties of the neuronal network.

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References

  1. Amari, S. (1977). Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybernetics, 27, 77–87.

    Article  MathSciNet  MATH  Google Scholar 

  2. Barlowe, H. B. (1986). Why have multiple cortical areas? Vision Res, 26, 81–90.

    Article  Google Scholar 

  3. Conway, B. R., & Tsao, D. Y. (2009). Color-tuned neurons are spatially clustered according to color preference within alert macaque posterior inferior temporal cortex. PNAS, 106, 18034– 18039.

    Article  Google Scholar 

  4. Haskell, E. C., & Bressloff, P. C. (2003). On the Formation of Persistent States in Neuronal Network Models of Feature Selectivity. J Integ Neurosci, 2, 103–123.

    Article  Google Scholar 

  5. Horton, J. C., & Adams, D. L. (2005). The cortical column: A structure without a function. Philos Trans R Soc Lond B Biol Sci, 360, 837–862.

    Article  Google Scholar 

  6. Hubel, D. H., & Wiesel, T. N. (1968). Receptive fields and functional echitecture of monkey striate cortex. J Physiol, 195, 215–243.

    Google Scholar 

  7. Hubel, D. H., & Wiesel, T. N. (1974). Sequence regularity and geometry of orientation columns in the monkey striate cortex. J Comp Neurol, 158, 267–293.

    Article  Google Scholar 

  8. Laing, C. R., & Chow, C. C. (2001). Stationary bumps in networks of spiking neurons. Neural Comp, 13, 1473–1494.

    Article  MATH  Google Scholar 

  9. Laing, C. R., Troy, W. C., Gutkin, B., & Ermentrout, G. B. (2002). Multiple bumps in a neuronal model of working memory. SIAM J on Appl Math, 63, 62–97.

    Article  MathSciNet  MATH  Google Scholar 

  10. Potthast, R., & Graben, P. B. (2010). Existence and Properties of solutions for neural field equations. Math Meth Appl Sci, 33, 935–949.

    MathSciNet  MATH  Google Scholar 

  11. Simoncelli, E.P., & Olshausen, B.A. (2001). Natural image statistics and neural representation. Ann Rev Neurosci, 24, 1193–1216.

    Article  Google Scholar 

  12. Singh, G., Memoli, F., Ishkhanov, T., Sapiro, G., Carlsson, G., & Ringach, D. L. (2008). Topological analysis of population activity in visual cortex. J Vis, 8, 1–18.

    Article  Google Scholar 

  13. Taylor, J. G. (1999). Neural ‘bubble’ dynamics in two dimensions: foundations. Biol Cybernetics, 80, 393–409.

    Article  MATH  Google Scholar 

  14. Werner, H., & T. Richter. (2001). Circular stationary solutions in two-dimensional neural fields. Biol Cybernetics, 85, 211–217.

    Article  MATH  Google Scholar 

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Correspondence to Evan C. Haskell .

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Haskell, E.C., Paksoy, V.E. (2011). Localized Activity States for Neuronal Field Equations of Feature Selectivity in a Stimulus Space with Toroidal Topology. In: Nonlinear and Complex Dynamics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0231-2_17

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  • DOI: https://doi.org/10.1007/978-1-4614-0231-2_17

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