Gaussian process approach to spiking neurons for inhomogeneous Poisson inputs

Neural Computation

Volumn 13, Issue 12, 2001, Pages 2763-2797

  Amemori, Ken Ichi ^a   Ishii, Shin ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPARATIVE STUDY; NERVE CELL; NORMAL DISTRIBUTION; PHYSIOLOGY; POISSON DISTRIBUTION; PROBABILITY; STATISTICS; TIME;

ACTION POTENTIALS; ANIMALS; MARKOV CHAINS; MODELS, NEUROLOGICAL; NEURONS; NORMAL DISTRIBUTION; POISSON DISTRIBUTION; STOCHASTIC PROCESSES; TIME FACTORS;

EID: 0035650536     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976601317098529     Document Type: Article

References (45)

1. Abbott, L. F., & van Vreeswijk, C. (1993). Asynchronous states in networks of pulse-coupled oscillators. Physical Review E, 48, 1483-1490.
2. Amemori, K., & Ishii S. (2000). Ensemble average and variance of a stochastic spiking neuron model. IEICE Transaction Fundamentals, E83-A, 575-578.
3. Amit, D., & Brunel, N. (1997a). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex, 7, 237-252.
4. Amit, D. J., & Brunel, N. (1997b). Dynamics of a recurrent network of spiking neurons before and following learning. Network: Computation in Neural Systems, 8, 373-404.
5. Arieli, A., Sterkin, A., Grinvald, A., & Aertsen, A. (1996). Dynamics of ongoing activity: Explanation of the large variability in evoked cortical responses. Science, 273, 1868-1871.
6. Bair, W., & Koch, C. (1996). Temporal precision of spike trains in extrastriate cortex of the behaving macaque monkey. Neural Computation, 8, 1185-1202.
7. Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience, 8, 183-208.
8. Brunel, N., & Hakim, V. (1999). Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Computation, 11, 1621-1671.
9. Burkitt, A. N., & Clark, G. M. (1999). Analysis of the integrate-and-fire neurons: Synchronization of synaptic input and spike output. Neural Computation, 11, 871-901.
10. Burkitt, A. N., & Clark, G. M. (2000). Calculation of interspike intervals for integrate-and-fire neurons with Poisson distribution of synaptic inputs. Neural Computation, 12, 1789-1820.
11. Cepeda, C., Radisavljevic, Z., Peacock, W., Levine, M. S., & Buchwald, N. A. (1992). Differential modulation by dopamine of responses evoked by excitatory amino acids in human cortex inputs. Synapses, 11, 330-341.
12. Diesmann, M., Gewaltig, M.-O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402, 529-532.
13. Durstewiz, D., Seamans, J. K., & Sejnowski, T. J. (2000). Dopamine-mediated stabilization of delay-period activity in a network of prefrontal cortex. Journal of Neurophysiology, 83, 1733-1750.
14. Gardiner, C. W. (1985). Handbook of stochastic methods for physics, chemistry and the natural sciences. Berlin: Springer-Verlag.
15. Gerstein, G. L., & Mandelbrot, B. (1964). Random walk models for the spike activity of a single neuron. Biophysics Journal, 4, 41-68.
16. Gerstner, W. (1998). Spiking neurons. In W. Maass & C. M. Bishop (Eds.), Pulsed neural networks (pp. 3-49). Cambridge, MA: MIT Press.
17. Gerstner, W. (2000). Population dynamics of spiking neurons: Fast transients, asynchronous states, and locking. Neural Computation, 12, 43-89.
18. Gomi, H., Shidara, M. Takemura, A., Inoue, Y., Kawano, K., & Kawato, M. (1998). Temporal firing patterns of Purkinje cells in the cerebellar ventral paraflocculus during ocular following responses in monkeys I: Simple spikes. Journal of Neurophysiology, 80, 818-831.
19. Hida, T. (1980). Brownian motion. Berlin: Springer-Verlag.
20. Kempter, R., Gerstner, W., & van Hemmen, J. L. (1999). Hebbian learning and spiking neurons. Physical Review E, 59, 4498-4514.
21. Kistler, W., Gerstner, W., & van Hemmen, J. L. (1997). Reduction of Hodgkin-Huxley equations to a single-variable threshold model. Neural Computation, 9, 1015-1045.
22. Kita, H., Oda, K., & Murase, K. (1999). Effects of dopamine agonists and antagonists on optical responses evoked in rat frontal cortex slices after stimulation of the subcortical white matter. Experimental Brain Research, 125, 383-388.
23. Kubo, M., Saito, K., & Amemori, K. (2000). High variance of ISIs in balanced dynamics of cortical network models (unpublished report). Kyoto: Kyoto University.
24. Papoulis, A. (1984). Probability, random variables, and stochastic processes. New York: McGraw-Hill.
25. Plesser, H. E., & Geisel, T. (1999). Markov analysis of stochastic resonance in a periodically driven integrate-and-fire neuron. Physical Review E, 59, 7008-7017.
26. Plesser, H. E., & Tanaka, S. (1997). Stochastic resonance in a model neuron with reset. Physics Letters A, 225, 228-234.
27. Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. (1988). Numerical Recipes in C (2nd ed.). Cambridge: Cambridge University Press.
28. Ricciardi, L. M., & Sato, S. (1988). First-passage-time density and moments of the Orstein-Uhlenbeck process. Journal of Applied Probability, 25, 43-57.
29. Rice, S. O. (1944). Mathematical analysis of random noise. Bell System Technical Journal, 23, 282-332.
30. Riehle, A., Grün, S., Diesmann, M., & Aertsen, A. (1997). Spike synchronization and rate modulation differentially involved in motor cortical function. Science, 278, 1950-1953.
31. Shadlen, M. N., & Newsome, W. T. (1994). Noise, neural codes and cortical organization. Current Opinion in Neurobiology, 4, 569-579.
32. Shadlen, M. N., & Newsome, W. T. (1998). The variable discharge of cortical neurons: Implications for connectivity, computation, and information coding. Journal of Neuroscience, 18, 3870-3896.
33. Shidara, M., Kawano, K., Gomi, H., & Kawato, M. (1993). Inverse-dynamics encoding of eye movement by Purkinje cells in the cerebellum. Nature, 365, 50-52.
34. Softky, W. R., & Koch, C. (1993). The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs. Journal of Neuroscience, 13, 334-350.
35. Stein, R. B. (1967). Some models of neuronal variability. Biophysics Journal, 7, 37-68.
36. Thorpe, S., Fize, D., & Marlot, C. (1996). Speed of processing in the human visual system. Nature, 381, 520-522.
37. Troyer, T. W., & Miller, K. D. (1997). Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Computation, 9, 971-983.
38. Tsodyks, M., & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences U.S.A., 94, 719-723.
39. Tsodyks, M., & Sejnowski, T. (1995). Rapid state switching in balanced cortical network models. Network: Computation in Neural Systems, 6, 111-124.
40. Tuckwell, H. C. (1988). Introduction to theoretical neurobiology: Volume 2, Nonlinear and stochastic theories. Cambridge: Cambridge University Press.
41. Tuckwell, H. C. (1989). Stochastic processes in the neurosciences. Philadelphia: Society for Industrial and Applied Mathematics.
42. Tuckwell, H. C., & Cope, D. K. (1980). Accuracy of neuronal interspike times calculated from a diffusion approximation. Journal of Theoretical Biology, 83, 377-387.
43. van Kampen, N. G. (1992). Stochastic processes in physics and chemistry (2nd ed.). Amsterdam: North-Holland.
44. van Vreeswijk, C., & Sompolinsky, H. (1996). Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science, 274, 1724-1726.
45. van Vreeswijk, C., & Sompolinsky, H. (1998). Chaotic balanced state in a model of cortical circuits. Neural Computation, 10, 1321-1371.