Abstract
Pulse-interval distributions are obtained for a counting system in which there is a gradual, rather than abrupt, increase in excitability following the registration of a pulse (relative refractoriness). The results are applicable to systems in which Poisson counting would be observed in the absence of such effects, and in which the memory reaches back at most one pulse. Choosing a particular functional form for the recovery function, the theory fits the experimentally measured distribution for the maintained discharge in the cat's retinal ganglion cell. It is also consistent with the notion that Weber's Law emerges from refractoriness in the visual system, as first proposed by van der Velden.
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Aguilar, M., Stiles, W.S.: Saturation of the rod mechanism of the retina at high levels of stimulation. Opt. Acta 1, 59–65 (1954)
Barlow, H.B., Levick, W.R.: Three factors limiting the reliable detection of light by the retinal ganglion cells of the cat. J. Physiol. (London) 200, 1–24 (1969a)
Barlow, H.B., Levick, W.R.: Changes in the maintained discharge with adaptation level in the cat retina. J. Physiol. (London) 202, 699–718 (1969b)
Barlow, H.B., Levick, W.R., Yoon, M.: Responses to single quanta of light in retinal ganglion cells of the cat. Vision Res. 11 [Suppl. 3], 87–101 (1971)
Bédard, G.: Dead-time corrections to the statistical distribution of photoelectrons. Proc. Phys. Soc., London 90, 131–141 (1967)
Cantor, B.I., Teich, M.C.: Dead-time-corrected photocounting distributions for laser radiation. J. Opt. Soc. Am. 65, 786–791 (1975)
Cox, D.R.: Renewal theory. New York: Wiley 1962
Cox, D.R., Lewis, P.A.W.: The statistical analysis of series of events. New York: Wiley 1966
DeLotto, I., Manfredi, P.F., Principi, P.: Counting statistics and dead-time losses, Part 1. Energ. Nucl. (Milan) 11, 557–564 (1964)
DeLotto, I., Manfredi, P.F.: Time-distribution of events at the output of systems with variable dead-time. Energ. Nucl. (Milan) 12, 95–97 (1965a)
DeLotto, I., Manfredi, P.F.: Statistical behavior of systems with variable dead-time. Nucl. Instrum. Methods 32, 175–176; 34, 180 (1965b)
Holden, A.V.: Models of the stochastic activity of neurones, pp. 76–81. (Lecture Notes in Biomathematics, Vol. 12.) Berlin, Heidelberg, New York. Springer 1976
Kuffler, S.W., FitzHugh, R., Barlow, H.B.: Maintained activity in the cat's retina in light and darkness. J. Gen. Physiol. 40, 683–702 (1957)
Lee, P.A.: Output response of non-linear switching element with stochastic dead time. Kybernetik 15, 187–191 (1974)
Levine, M.W., Shefner, I.M.: A model for the variability of interspike intervals during sustained firing of a retinal neuron. Biophys. J. 19, 241–252 (1977)
Müller, J.W.: Some formulae for a dead-time-distorted Poisson process. Nucl. Instrum. Methods 117, 401–404 (1974)
Parzen, E.: Stochastic processes, pp. 117–186. San Francisco: Holden-Day 1962
Ricciardi, L.M., Esposito, F.: On some distribution functions for non-linear switching elements with finite dead time. Kybernetik 3, 148–152 (1966)
Rodieck, R.W.: Maintained activity of cat retinal ganglion cells. J. Neurophysiol. 30, 1043–1071 (1967)
Rodieck, R.W.: The vertebrate retina, pp. 646–672. San Francisco: Freeman 1973
Smith, C.E.: A comment on a retinal neuron model. Biophys. J. 25, 385–386 (1979)
Souček, B.: Losses in systems with variable dead time. Nucl. Instrum. Methods 27, 306–308 (1964)
Teich, M.C., McGill, W.J.: Neural counting and photon counting in the presence of dead time. Phys. Rev. Lett. 36, 754–758; 1473 (1976)
Teich, M.C., Cantor, B.I.: Information, error, and imaging in dead-time-perturbed doubly stochastic Poisson counting systems. IEEE J. Quant. Electron. QE-14, 993–1003 (1978)
Teich, M.C., Matin, L., Cantor, B.I.: Refractoriness in the maintained discharge of the cat's retinal ganglion cell. J. Opt. Soc. Am. 68, 386–402 (1978)
Teich, M.C., Vannucci, G.: Observation of dead-time-modified photocounting distributions for modulated laser radiation. J. Opt. Soc. Am. 68, 1338–1342 (1978)
Welden, H.A. van der: Quanteuse verschijnselen bij het zien. Ned. Tijdschr. v. Natuurk. 15, 147–151 (1949)
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This work was supported in part by the National Science Foundation
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Teich, M.C., Diament, P. Relative refractoriness in visual information processing. Biol. Cybernetics 38, 187–191 (1980). https://doi.org/10.1007/BF00337011
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DOI: https://doi.org/10.1007/BF00337011