Generalized rate-code model for neuron ensembles with finite populations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 5, 2007, Pages

  Hasegawa, Hideo ^a  

^a TOKYO GAKUGEI UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; FOKKER PLANCK EQUATION; GAUSSIAN DISTRIBUTION; GAUSSIAN NOISE (ELECTRONIC); RANDOM PROCESSES; SYNCHRONIZATION;

AUGMENTED MOMENT METHOD (AMM); NEURONAL ENSEMBLES; SINUSOIDAL INPUTS;

NEURONS;

EID: 34347348912     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.051904     Document Type: Article

References (64)

1. F. Rieke, D. Warland, R. Steveninck, and W. Bialek, Spikes-Exploring the Neural Code (MIT Press, Cambridge, MA, 1996).
2. W. M. Ursey and R. C. Reid, Annu. Rev. Physiol. ARPHAD 0066-4278 10.1146/annurev.physiol.61.1.435 61, 435 (1999).
3. R. C. deCharms and A. Zador, Annu. Rev. Neurosci. ARNSD5 0147-006X 10.1146/annurev.neuro.23.1.613 23, 613 (2000).
4. R. A. Anderson, S. Musallam, and B. Pesaran, Curr. Opin. Neurobiol. COPUEN 0959-4388 14, 720 (2004).
5. J. K. Chapin, K. A. Moxon, R. S. Markowitz, and M. A. L. Nicolelis, Nat. Neurosci. NANEFN 1097-6256 10.1038/10223 2, 664 (1999).
6. V. B. Mountcasle, J. Neurophysiol. JONEA4 0022-3077 20, 408 (1957).
7. W. Gerstner and W. Kistler, Spiking Neuron Models (Cambridge University Press, Cambridge, U.K., 2002).
8. A. L. Hodgkin and A. F. Huxley, J. Physiol. (London) JPHYA7 0022-3751 117, 500 (1952).
9. L. F. Abbott and C. van Vreeswijk, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.48.1483 48, 1483 (1993).
10. A. Treves, Network NWRKEA 0269-3089 4, 259 (1993).
11. W. Gerstner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.51.738 51, 738 (1995).
12. H. R. Wilson and J. D. Cowan, Biophys. J. BIOJAU 0006-3495 12, 1 (1972).
13. B. W. Knight, Neural Comput. NEUCEB 0899-7667 10.1162/089976600300015673 12, 473 (2000).
14. A. Omurtag, B. W. Knight, and L. Sirovich, J. Comput. Neurosci. JCNEFR 0923-5313 10.1023/A:1008964915724 8, 51 (2000).
15. E. Haskell, D. Q. Nykamp, and D. Tranchina, Network NWRKEA 0269-3089 12, 141 (2000).
16. J. Eggert and J. L. van Hemmen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.1855 61, 1855 (2000).
17. R. Rodriguez and H. C. Tuckwell, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.54.5585 54, 5585 (1996).
18. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.041903 67, 041903 (2003).
19. D. J. Amit and M. V. Tsodyks, Network NWRKEA 0269-3089 2, 259 (1991).
20. B. Ermentrout, Neural Comput. NEUCEB 0899-7667 6, 679 (1994).
21. O. Shriki, D. Hansel, and H. Sompolinsky, Neural Comput. NEUCEB 0899-7667 10.1162/08997660360675053 15, 1809 (2003).
22. N. Brunel, J. Comput. Neurosci. JCNEFR 0923-5313 10.1023/A:1008925309027 8, 183 (2000).
23. Z. F. Mainen and T. J. Sejnowski, Science SCIEAS 0036-8075 10.1126/science.7770778 268, 1503 (1995).
24. M. A. Muñoz, in Advances in Condensed Matter and Statistical Mechanics, edited by, E. Korutcheva, and, R. Cuerno, (Nova Science Publishers, New York, 2004), p. 34.
25. M. A. Muñoz, F. Colaiori, and C. Castellano, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.056102 72, 056102 (2005).
26. C. Van den Broeck, J. M. R. Parrondo, and R. Toral, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.73.3395 73, 3395 (1994).
27. C. Tsallis, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01016429 52, 479 (1988).
28. C. Tsallis, R. S. Mendes, and A. R. Plastino, Physica A PHYADX 0378-4371 10.1016/S0378-4371(98)00437-3 261, 534 (1998).
29. G. Wilk and Z. Wlodarczyk, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2770 84, 2770 (2000).
30. H. Sakaguchi, J. Phys. Soc. Jpn. JUPSAU 0031-9015 10.1143/JPSJ.70.3247 70, 3247 (2001).
31. C. Anteneodo and C. Tsallis, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1617365 44, 5194 (2003).
32. H. Hasegawa, Physica A PHYADX 0378-4371 365, 383 (2006).
33. H. Hasegawa, J. Phys. Soc. Jpn. JUPSAU 0031-9015 75, 033001 (2006).
34. S. Amari, IEEE Trans. Syst. Man Cybern. ISYMAW 0018-9472 2, 643 (1972).
35. J. J. Hopfield, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 10.1073/pnas.79.8.2554 79, 2554 (1982).
36. G. L. Gerstein and B. Mandelbrot, Biophys. J. BIOJAU 0006-3495 4, 41 (1964).
37. H. C. Tuckwell, Introduction to Theoretical Neurobiology and Stochastic Theories (Cambridge University Press, New York, 1988).
38. D. E. F. McKeegan, Brain Res. BRREAP 0006-8993 929, 48 (2002).
39. R. E. Kass, V. Ventura, and E. N. Brown, Neurophysiology NPHYBI 0090-2977 94, 8 (2005).
40. T. P. Vogels, K. Rajan, and L. F. Abbott, Annu. Rev. Neurosci. ARNSD5 0147-006X 10.1146/annurev.neuro.28.061604.135637 28, 357 (2005).
41. H. Hasegawa, Physica A PHYADX 0378-4371 374, 585 (2007).
42. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.68.041909 68, 041909 (2003).
43. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.021911 70, 021911 (2004).
44. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.021912 70, 021912 (2004).
45. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.066107 70, 066107 (2004).
46. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.72.056139 72, 056139 (2005).
47. H. Hasegawa, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.61.718 61, 718 (2000).
48. S. Wang, W. Wang, and F. Liu, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.018103 96, 018103 (2006).
49. Y. Hayashi, Neural Comput. NEUCEB 0899-7667 6, 658 (1994).
50. L. H. A. Monteiro, M. A. Bussab, and J. G. C. Berlinck, J. Theor. Biol. JTBIAP 0022-5193 219, 83 (2002).
51. S. Abe and A. K. Rajagopal, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/33/48/310 33, 8723 (2000).
52. K. D. Harrris, Nat. Rev. Neurosci. NRNAAN 1471-003X 6, 399 (2005).
53. A. A. Fenton and R. U. Muller, Proc. Natl. Acad. Sci. U.S.A. PNASA6 0027-8424 95, 3182 (1998).
54. W. R. Softky and C. Koch, Neural Comput. NEUCEB 0899-7667 4, 643 (1992).
55. W. Calvin and C. Stevens, J. Neurophysiol. JONEA4 0022-3077 31, 574 (1968).
56. M. Shadlen and W. T. Newsome, Curr. Opin. Neurobiol. COPUEN 0959-4388 10.1016/0959-4388(94)90059-0 4, 569 (1994).
57. T. W. Troyer and K. D. Miller, Neural Comput. NEUCEB 0899-7667 10.1162/089976698300017331 10, 1047 (1098).
58. M. Usher, M. Stemmer, C. Koch, and Z. Olami, Neural Comput. NEUCEB 0899-7667 6, 795 (1994).
59. W. R. Softky, Curr. Opin. Neurobiol. COPUEN 0959-4388 10.1016/0959-4388(95)80032-8 5, 239 (1995).
60. J. Feng and D. Brown, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/31/4/ 013 31, 1239 (1998).
61. M. Enculescu and M. M. Bestehorn, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.041904 67, 041904 (2003);
62. A. Tonneilier, Physica D PDNPDT 0167-2789 210, 118 (2005);
63. M. Stetter, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.73.031903 73, 031903 (2006).
64. H. Hasegawa, in Neuronal Network Horizons, edited by, M. L. Weiss, (Nova Science Publishers, New York, 2007).