Abstract
The sequence of action potentials produced by a neuron is best characterized in terms of a stochastic point process. In this contribution we will be primarily concerned with different variants of stochastic leaky-integrator models for the membrane potential. The point process representation is then achieved by the first passage time transformation of the underlying membrane potential model. Different sources of the noise in the diffusion neuronal models resulting from the stochastic leaky-integrator model will be discussed.
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References
L.F. Abbot and T.B. Kepler. Model neurons: From Hodgkin-Huxley to Hopfield. In: L. Danto (ed.) Statistical Mechanics of Neural Networks. Springer, Berlin, 1990.
D.H. Johnson. Point process models of single-neuron discharges. J. Comput. Neurosci. 3:275–300,1996.
P. Lánský and J.-P. Rospars. Omstein-Uhlenbeck neuronal model revisited. Biol. Cybernet 72:397–406, 1995.
H.C. Tuckwell. Introduction to Theoretical Neurobiology. Cambridge Univ. Press, Cambridge, 1988.
G. Bugmann. Summation and multiplication: two distinct operation domainsof leaky integrate-and-fire neurons. Network 2:489–509, 1991.
D. Tal and E.L. Schwartz. Computing with the leaky integrate-and-fire neuron: Logarithmic computation adn multiplication. Neural Computation 9:305–318, 1997.
R.B. Stein. A theoretical analysis of neuronal variability. Biophys. J. 5:173–195, 1965.
P. Lánský and J.-P. Rospars. Coding of odor intensity. BioSystems 31:15–38, 1993.
P. Lánský. Sources of periodical force in noisy integrate-and-fire models of neuronal dynamics. Phys. Rev. E 55:2040–2043, 1997.
G. Kallianpur and R.L. Wolpert. Weak convergence of stochastic neuronal models, In: M. Kimura, G. Kallianpur, T. Hida (eds.) Stochastic Methods in Biology. Springer, Berlin, 1987.
P. Lánský and V. Lánská Diffusion approximations of the neuronal model with synaptic reversal potentials, Biol. Cybernet. 56:19–26, 1987.
V. Lánnská, P. Lánksý and C.E. Smith. Synaptic transmission in a diffusion model for neural activity. J. theor. Biol. 166:393–406, 1994.
P. Lánský, L. Sacerdote and F. Tomassetti. On the comparison of Feller and OrnsteinUhlenbeck models for neural activity. Biol. Cybernet. 75:457–465, 1995.
W.J. McGill and M.C. Teich. Alerting signals and detection in a sensory network. J. Math. Psvchol. 39:146–163, 1995.
J.P. Segundo, J.-F. Vibert, K. Pakdaman, M. Stiber and O. Diez Martinez. Noise and the neurosciences: A long history, a recent revival and some theory. In: K.H. Pribram (ed.) Origins: Brain & Self Organization. Lawrence Erlbaum, Hillsdale, 1994.
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© 1997 Springer-Verlag Berlin Heidelberg
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Lánsky, P., Lánská, V. (1997). Noise in integrate-and-fire models of neuronal dynamics. In: Gerstner, W., Germond, A., Hasler, M., Nicoud, JD. (eds) Artificial Neural Networks — ICANN'97. ICANN 1997. Lecture Notes in Computer Science, vol 1327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0020131
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DOI: https://doi.org/10.1007/BFb0020131
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