On a stochastic leaky integrate-and-fire neuronal model

Neural Computation

Volumn 22, Issue 10, 2010, Pages 2558-2585

  Buonocore, A ^a   Caputo, L ^b   Pirozzi, E ^a   Ricciardi, L M ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ALGORITHM; ANIMAL; CELL MEMBRANE POTENTIAL; COMPUTER SIMULATION; HUMAN; LETTER; NERVE CELL; PHYSIOLOGY; STANDARD; STATISTICAL MODEL; STATISTICS; SYNAPTIC TRANSMISSION; TIME;

ACTION POTENTIALS; ALGORITHMS; ANIMALS; COMPUTER SIMULATION; HUMANS; MEMBRANE POTENTIALS; MODELS, STATISTICAL; NEURONS; STOCHASTIC PROCESSES; SYNAPTIC TRANSMISSION; TIME FACTORS;

EID: 78149286920     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00023     Document Type: Letter

References (28)

1. Arnold, L. (1974). Stochastic differential equations: Theory and applications. Hoboken, NJ:Wiley.
2. Buonocore, A., Caputo, L., Pirozzi, E., & Ricciardi, L.M. (2009). The first passage time problem for gauss-diffusion processes: Algorithmic approaches and applications to LIF neuronal model. Methodol. Comput. Appl. Probab., doi:10.1007/s11009-009-9132-8.
3. Buonocore, A., Nobile, A. G., & Ricciardi, L. M. (1987). A new integral equation for the evaluation of first-passage-time probability densities. Adv. Appl. Prob., 19, 784-800.
4. Burkitt, A. N. (2006). A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol. Cybern., 95, 1-19.
5. Capocelli, R., & Ricciardi, L. M. (1971). Diffusion approximation and first passage time problem for a model neuron. Kybernetik, 8, 214-233.
6. Feng, J. (2001). Is the integrate-and-fire model good enough?-A review. Neural Networks, 14, 955-975.
7. Fourcaud-Trocmé, N., Hansel, D., van Vreeswijk, C., & Brunel, N. (2003). How spike generation mechanisms determine the neuronal response to fluctuating inputs. Journal of Neuroscience, 23, 11628-11640.
8. Gerstein, G. L., & Mandelbrot, B. (1964). Random walk models for the spike activity of a single neuron. Biophys J., 4, 41-68.
9. Gerstner, W. (2000). Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking. Neural Computation, 12, 43-89.
10. Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Cambridge: Cambridge University Press.
11. Giorno, V., Nobile, A. G., & Ricciardi, L. M. (1990). On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries. Adv. Appl. Prob., 22(4), 883-914.
12. Inoue, J., Sato, S., & Ricciardi, L.M. (1995). On the parameter estimation for diffusion models of a single neuron's activities. Biol. Cybern., 73, 209-221.
13. Johannesma, P. I. M. (1968). Diffusion models for the stochastic activity of neurons. In E. R. Caianiello (Ed.), Neural networks (pp. 116-144). Berlin: Springer-Verlag.
14. Jolivet, R., Lewis, T. J., & Gerstner, W. (2004). Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailedmodel to a high degree of accuracy. J. Neurophysiol., 92, 959-976.
15. Lánský, P. (1997). Sources of periodical force in noisy integrate-and-fire models of neuronal dynamics. Phys. Rev. E, 55(2), 2040-2043.
16. Lánský, P., Sanda, P., & He, J. (2006). The parameters of the stochastic leaky integrateandfire neuronal model. J. Comput. Neurosci., 55, 211-223.
17. Mehr, C. B., & McFadden, J. A. (1965). Certain properties of gaussian processes and their first passage time. J. R. Statist. Soc. B, 27, 505-522.
18. Nobile, A. G., Pirozzi, E., & Ricciardi, L. M. (2008). Asymptotics and evaluations of FPT densities through varying boundaries for Gauss-Markov processes. SCMJ, 67(2), 241-266.
19. Paninski, L. (2007). Statistical analysis of neuronal data: State-space models and application to optimal voltage smoothing, tracking on stationarities, and recursive decoding [Notes of Ph.D. course in statistical analysis of neural data]. Available online at http://www.stat.columbia.edu/~liam/teaching/neurostat-spr07/state-space-notes.pdf.
20. Ricciardi, L.M. (1977). Diffusion processes and related topics in biology. Berlin: Springer-Verlag.
21. Rudolph, M., & Destexhe, A. (2006). Analytical integrate-and-fire neuron models with conductance-based dynamics for event-driven simulation strategies. Neural Computation, 18, 2146-2210.
22. Scheler, G., & Fellous, J. (2000). A neural model of lexical selection and its modulation by dopamine. In Proceedings of the International Joint Conference on Neural Networks. Piscataway, NJ: IEEE Press.
23. Scheler, G., & Fellous, J. (2001). Dopamine modulation of prefrontal delay activity: Signal stability and sharpness of tuning curves. Neurocomputing, 38-40, 1549-1556.
24. Shinomoto, S., Sakai, Y., & Funahashi, S. (1999). The Ornstein-Uhlenbeck process does not reproduce spiking statistics of neurons in prefrontal cortex. Neural Computation, 11, 935-951.
25. Standage, D. I., & Trappenberg, T. P. (2005). Differences in the sub-threshold dynamics of leaky integrate-and-fire and Hodgkin-Huxley neuron models. In Proceedings of the International Joint Conference on Neural Networks (pp. 396-399). Piscataway, NJ: IEEE Press.
26. Stein, R. (1965). A theoretical analysis of neuronal variability. Biophys. J., 5, 173-194.
27. Stevens, C., & Zador, A. (1998). Novel integrate-and-fire-like model of repetitive firing in cortical neurons. In Proc. of the 5th Joint Symposium on Neural Computation. Piscataway, NJ: IEEE Press.
28. Tuckwell, H.C. (1988). Introduction to theoretical neurobiology. Cambridge: Cambridge University Press.