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Phase and Amplitude Modulation in a Neural Oscillatory Model of the Orientation Map

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Neural Information Processing (ICONIP 2018)

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Abstract

The traditional approach to characterization of orientation maps as they were expounded by Hubel and Wiesel treats them as static representations. Only the magnitude of a neuron’s firing response to orientation is considered and the neuron with the highest response is said to be “tuned” to that response. But the neuronal response to orientation is a time-varying spike train and, if the response of an entire cortical area that potentially responds to orientations in a given part of the visual field is considered, the response must be considered as a spatio-temporal wave. We propose a neural field model consisting of FitzHugh-Nagumo neurons, that generates such a wave. Reflecting the dynamics of a single FitzHugh-Nagumo neuron, the neural field also exhibits excitatory and oscillatory regimes as an offset parameter is increased. We consider the question of the manner in which the input orientation is coded in the response of the neural field and discovered that two different codes − Amplitude Modulation and Phase Modulation − are present. Whereas for smaller offset values, when the model is in excitatory regime the orientation is coded in terms of amplitude, for larger offset values when the model is in the oscillatory regime, the orientation is coded in terms of phase.

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References

  1. Başar, E., Başar-Eroglu, C., Karakaş, S., Schürmann, M.: Gamma, alpha, delta, and theta oscillations govern cognitive processes. Int. J. Psychophysiol. 39(2–3), 241–248 (2001)

    Article  Google Scholar 

  2. Bonhoeffer, T., Grinvald, A.: Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns. Nature 353(6343), 429 (1991)

    Article  Google Scholar 

  3. Bosman, C.A., et al.: Attentional stimulus selection through selective synchronization between monkey visual areas. Neuron 75(5), 875–888 (2012)

    Article  Google Scholar 

  4. Buzsaki, G.: Rhythms of the Brain. Oxford University Press, New York (2006)

    Book  Google Scholar 

  5. Christopher deCharms, R., Merzenich, M.M.: Primary cortical representation of sounds by the coordination of action-potential timing. Nature 381(6583), 610 (1996)

    Article  Google Scholar 

  6. Colgin, L.L., et al.: Frequency of gamma oscillations routes flow of information in the hippocampus. Nature 462(7271), 353 (2009)

    Article  Google Scholar 

  7. Einevoll, G.T., Kayser, C., Logothetis, N.K., Panzeri, S.: Modelling and analysis of local field potentials for studying the function of cortical circuits. Nat. Rev. Neurosci. 14(11), 770 (2013)

    Article  Google Scholar 

  8. Engel, A.K., König, P., Singer, W.: Temporal coding in the visual cortex: new vistas on integration in the nervous system. Trends Neurosci. 15(6), 218–226 (1992)

    Article  Google Scholar 

  9. Freeman, W.J., Schneider, W.: Changes in spatial patterns of rabbit olfactory eeg with conditioning to odors. Psychophysiology 19(1), 44–56 (1982)

    Article  Google Scholar 

  10. Fries, P.: Neuronal gamma-band synchronization as a fundamental process in cortical computation. Annu. Rev. Neurosci. 32, 209–224 (2009)

    Article  Google Scholar 

  11. Georgopoulos, A.P., Schwartz, A.B., Kettner, R.E.: Neuronal population coding of movement direction. Science 233(4771), 1416–1419 (1986)

    Article  Google Scholar 

  12. Gray, C.M., Singer, W.: Stimulus-specific neuronal oscillations in orientation columns of cat visual cortex. Proc. Natl. Acad. Sci. 86(5), 1698–1702 (1989)

    Article  Google Scholar 

  13. Grossberg, S., Olsen, S.J.: Rules for the cortical map of ocular dominance and orientation columns. Technical report. Boston University Center for Adaptive Systems and Department of Cognitive and Neural Systems (1994)

    Google Scholar 

  14. Hubel, D.H., Wiesel, T.N.: Receptive fields of single neurones in the cat’s striate cortex. J. Physiol. 148(3), 574–591 (1959)

    Article  Google Scholar 

  15. Katzner, S., et al.: Local origin of field potentials in visual cortex. Neuron 61(1), 35–41 (2009)

    Article  Google Scholar 

  16. Klimesch, W.: Memory processes, brain oscillations and eeg synchronization. Int. J. Psychophysiol. 24(1–2), 61–100 (1996)

    Article  Google Scholar 

  17. Klimesch, W., Fellinger, R., Freunberger, R.: Alpha oscillations and early stages of visual encoding. Front. Psychol. 2, 118 (2011)

    Article  Google Scholar 

  18. Kohonen, T.: Self-organized formation of topologically correct feature maps. Biol. Cybern. 43(1), 59–69 (1982)

    Article  MathSciNet  Google Scholar 

  19. Lee, C., Rohrer, W.H., Sparks, D.L.: Population coding of saccadic eye movements by neurons in the superior colliculus. Nature 332(6162), 357 (1988)

    Article  Google Scholar 

  20. Liu, J., Newsome, W.T.: Local field potential in cortical area mt: stimulus tuning and behavioral correlations. J. Neurosci. 26(30), 7779–7790 (2006)

    Article  Google Scholar 

  21. Miikkulainen, R., Bednar, J.A., Choe, Y., Sirosh, J.: Self-organization, plasticity, and low-level visual phenomena in a laterally connected map model of the primary visual cortex. In: Psychology of Learning and Motivation. volume 36: Perceptual Learning, pp. 257–308. Academic Press, San Diego CA (1997)

    Google Scholar 

  22. Miikkulainen, R., Bednar, J.A., Choe, Y., Sirosh, J.: Computational maps in the visual cortex. Springer, New York (2006). https://doi.org/10.1007/0-387-28806-6

    Book  Google Scholar 

  23. Miller, K.D., Keller, J.B., Stryker, M.P.: Ocular dominance column development: analysis and simulation. Science 245(4918), 605–615 (1989)

    Article  Google Scholar 

  24. Milner, P.M.: A model for visual shape recognition. Psychol. Rev. 81(6), 521 (1974)

    Article  Google Scholar 

  25. Mitzdorf, U.: Current source-density method and application in cat cerebral cortex: investigation of evoked potentials and eeg phenomena. Physiol. Rev. 65(1), 37–100 (1985)

    Article  Google Scholar 

  26. Niebur, E., Wörgötter, F.: Orientation columns from first principles. In: Eeckman, F.H., Bower, J.M. (eds.) Computation and Neural Systems, pp. 409–413. Springer, Boston (1993). https://doi.org/10.1007/978-1-4615-3254-5_62

    Chapter  MATH  Google Scholar 

  27. Obermayer, K., Ritter, H., Schulten, K.: A principle for the formation of the spatial structure of cortical feature maps. Proc. Natl. Acad. Sci. 87(21), 8345–8349 (1990)

    Article  Google Scholar 

  28. Pasupathy, A., Connor, C.E.: Population coding of shape in area v4. Nat. Neurosci. 5(12), 1332 (2002)

    Article  Google Scholar 

  29. Singer, W.: Synchronization of cortical activity and its putative role in information processing and learning. Annu. Rev. Physiol. 55(1), 349–374 (1993)

    Article  Google Scholar 

  30. Singer, W., Gray, C.M.: Visual feature integration and the temporal correlation hypothesis. Annu. Rev. Neurosci. 18(1), 555–586 (1995)

    Article  Google Scholar 

  31. Sirota, A., Montgomery, S., Fujisawa, S., Isomura, Y., Zugaro, M., Buzsáki, G.: Entrainment of neocortical neurons and gamma oscillations by the hippocampal theta rhythm. Neuron 60(4), 683–697 (2008)

    Article  Google Scholar 

  32. Tanaka, S.: Theory of self-organization of cortical maps: mathematical framework. Neural Netw. 3(6), 625–640 (1990)

    Article  Google Scholar 

  33. Tort, A.B., Komorowski, R.W., Manns, J.R., Kopell, N.J., Eichenbaum, H.: Theta-gamma coupling increases during the learning of item-context associations. Proc. Natl. Acad. Sci. 106(49), 20942–20947 (2009)

    Article  Google Scholar 

  34. Van Der Meer, M.A., Redish, A.D.: Low and high gamma oscillations in rat ventral striatum have distinct relationships to behavior, reward, and spiking activity on a learned spatial decision task. Front. Integr. Neurosci. 3, 9 (2009)

    Google Scholar 

  35. Womelsdorf, T., Fries, P., Mitra, P.P., Desimone, R.: Gamma-band synchronization in visual cortex predicts speed of change detection. Nature 439(7077), 733 (2006)

    Article  Google Scholar 

  36. Yuille, A., Kammen, D., Cohen, D.: Quadrature and the development of orientation selective cortical cells by hebb rules. Biol. Cybern. 61(3), 183–194 (1989)

    Article  Google Scholar 

  37. Zold, C.L., Shuler, M.G.H.: Theta oscillations in visual cortex emerge with experience to convey expected reward time and experienced reward rate. J. Neurosci. 35(26), 9603–9614 (2015)

    Article  Google Scholar 

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Correspondence to V. Srinivasa Chakravarthy .

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Kumar, B.S., Kori, A., Elango, S., Chakravarthy, V.S. (2018). Phase and Amplitude Modulation in a Neural Oscillatory Model of the Orientation Map. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11302. Springer, Cham. https://doi.org/10.1007/978-3-030-04179-3_19

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  • DOI: https://doi.org/10.1007/978-3-030-04179-3_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04178-6

  • Online ISBN: 978-3-030-04179-3

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