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====Cross-correlation in sound localization: Jeffress model====
According to [[Lloyd A. Jeffress|Jeffress]],<ref>{{cite journal | last1 = Jeffress | first1 = L.A. | year = 1948 | title = A place theory of sound localization | url = | journal = Journal of Comparative and Physiological Psychology | volume = 41 | issue = | pages = 35–39 | doi=10.1037/h0061495}}</ref> in order to compute the ___location of a sound source in space from [[interaural time difference]]s, an auditory system relies on [[Analog delay line|delay lines]]: the induced signal from an [[ipsilateral]] auditory receptor to a particular neuron is delayed for the same time as it takes for the original sound to go in space from that ear to the other. Each postsynaptic cell is differently delayed and thus specific for a particular inter-aural time difference. This theory is equivalent to the mathematical procedure of [[cross-correlation]].
Following Fischer and Anderson,<ref>Brian J. Fischer and Charles H. Anderson, 2004. A computational model of sound localization in the barn owl ''Neurocomputing" 58–60 (2004) 1007–1012</ref> the response of the postsynaptic neuron to the signals from the left and right ears is given by
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====Cross-correlation for motion detection: Hassenstein–Reichardt model====
A motion detector needs to satisfy three general requirements: pair-inputs, asymmetry and nonlinearity.<ref>Borst A, Egelhaaf M., 1989. Principles of visual motion detection. "Trends in Neuroscience" 12(8):297–306</ref> The cross-correlation operation implemented asymmetrically on the responses from a pair of photoreceptors satisfies these minimal criteria, and furthermore, predicts features which have been observed in the response of neurons of the lobula plate in bi-wing insects.<ref>{{cite journal | last1 = Joesch | first1 = M. | display-authors = 1 | last2 = et al | year = 2008 | title = Response properties of motion-sensitive visual interneurons in the lobula plate of Drosophila melanogaster | url = | journal = Curr. Biol | volume = 18 | issue = | pages = 368–374 | doi=10.1016/j.cub.2008.02.022}}</ref>
The master equation for response is
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===Anti-Hebbian adaptation: spike-timing dependent plasticity===
<ref>{{cite journal | last1 = Tzounopoulos | first1 = T | last2 = Kim | first2 = Y | last3 = Oertel | first3 = D | last4 = Trussell | first4 = LO | year = 2004 | title = Cell-specific, spike timing-dependent plasticities in the dorsal cochlear nucleus | url = | journal = Nat Neurosci | volume = 7 | issue = | pages = 719–725 | doi=10.1038/nn1272}}</ref>
<ref>{{cite journal | last1 = Roberts | first1 = Patrick D. | last2 = Portfors | first2 = Christine V. | year = 2008 | title = Cell-specific, spike timing-dependent plasticities in the dorsal cochlear nucleus | url = | journal = Biological Cybernetics | volume = 98 | issue = | pages = 491–507 }}</ref>
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