Cascade-induced synchrony in stochastically driven neuronal networks

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

Volumn 82, Issue 4, 2010, Pages

  Newhall, Katherine A ^a   Kovačič, Gregor ^a   Kramer, Peter R ^a   Cai, David ^b,c  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b SHANGHAI JIAO TONG UNIVERSITY   (China)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CENTRAL LIMIT; COMBINATORIAL ANALYSIS; COUPLED NETWORKS; COUPLING CURRENTS; CUMULANTS; EIGENFUNCTION EXPANSIONS; FIRST-PASSAGE; INTEGRATE-AND-FIRE NEURONS; MEMBRANE POTENTIALS; NEURONAL NETWORKS; PERIODIC DYNAMICS; PHYSIOLOGICAL EFFECTS; SUBTHRESHOLD;

EIGENVALUES AND EIGENFUNCTIONS; FOKKER PLANCK EQUATION; PROBABILITY DISTRIBUTIONS;

NEURAL NETWORKS;

EID: 78651264671     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.82.041903     Document Type: Article

References (78)

1. R. Traub, J. Jeffreys, and M. Whittington, Fast Oscillations in Cortical Circuits (MIT Press, Cambridge, MA, 1999).
2. G. Buzsaki and A. Draguhn, Science 304, 1926 (2004). 10.1126/science. 1099745
3. T. J. Sejnowski and O. Paulsen, J. Neurosci. 26, 1673 (2006). 10.1523/JNEUROSCI.3737-05d.2006
4. M. Steriade, Neuroscience 137, 1087 (2006). 10.1016/j.neuroscience.2005. 10.029
5. A. K. Roopun, M. A. Kramer, L. M. Carracedo, M. Kaiser, C. H. Davies, R. D. Traub, N. J. Kopell, and M. A. Whittington, Front Neurosci. 2, 145 (2008). 10.3389/neuro.01.034.2008
6. P. Fries, Annu. Rev. Neurosci. 32, 209 (2009). 10.1146/annurev.neuro. 051508.135603
7. W. Singer, Neuron 24, 49 (1999). 10.1016/S0896-6273(00)80821-1
8. E. H. Buhl, G. Tamas, and A. Fisahn, J. Physiol. 513, 117 (1998). 10.1111/j.1469-7793.1998.117by.x
9. A. Fisahn, F. G. Pike, E. H. Buhl, and O. Paulsen, Nature (London) 394, 186 (1998). 10.1038/28179
10. J. M. Fellous and T. J. Sejnowski, Hippocampus 10, 187 (2000). 10.1002/(SICI)1098-1063(2000)10:2<187::AID-HIPO8>3.0.CO;2-M
11. N. K. Logothetis, J. Pauls, M. Augath, T. Trinath, and A. Oeltermann, Nature (London) 412, 150 (2001). 10.1038/35084005
12. P. Fries, J. H. Reynolds, A. E. Rorie, and R. Desimone, Science 291, 1560 (2001). 10.1126/science.1055465
13. N. Brunel and X.-J. Wang, J. Neurophysiol. 90, 415 (2003). 10.1152/jn.01095.2002
14. G. Buzsaki, Z. Horvath, R. Urioste, J. Hetke, and K. Wise, Science 256, 1025 (1992). 10.1126/science.1589772
15. A. Bragin, G. Jando, Z. Nadasdy, J. Hetke, K. Wise, and G. Buzsaki, J. Neurosci. 15, 47 (1995).
16. J. Csicsvari, H. Hirase, A. Czurko, and G. Buzsaki, Neuron 21, 179 (1998). 10.1016/S0896-6273(00)80525-5
17. J. Csicsvari, H. Hirase, A. Czurko, A. Mamiya, and G. Buzsaki, J. Neurosci. 19, 274 (1999).
18. J. A. Henrie and R. Shapley, J. Neurophysiol. 94, 479 (2005). 10.1152/jn.00919.2004
19. M. B. Feller, Neuron 22, 653 (1999). 10.1016/S0896-6273(00)80724-2
20. M. J. O'Donovan, Curr. Opin. Neurobiol. 9, 94 (1999). 10.1016/S0959-4388(99)80012-9
21. C. van Vreeswijk and D. Hansel, Neural Comput. 13, 959 (2001). 10.1162/08997660151134280
22. B. B. Vladimirski, J. Tabak, M. J. O'Donovan, and J. Rinzel, J. Comput. Neurosci. 25, 39 (2008). 10.1007/s10827-007-0064-4
23. W. H. Nesse, A. Borisyuk, and P. C. Bressloff, J. Comput. Neurosci. 25, 317 (2008). 10.1007/s10827-008-0081-y
24. R. E. Mirollo and S. H. Strogatz, SIAM J. Appl. Math. 50, 1645 (1990). 10.1137/0150098
25. N. Brunel and V. Hakim, Neural Comput. 11, 1621 (1999). 10.1162/089976699300016179
26. C. Borgers and N. Kopell, Neural Comput. 15, 509 (2003). 10.1162/089976603321192059
27. C. Borgers and N. Kopell, Neural Comput. 17, 557 (2005). 10.1162/0899766053019908
28. D. Hansel, G. Mato, and C. Meunier, Neural Comput. 7, 307 (1995). 10.1162/neco.1995.7.2.307
29. W. W. Lytton and T. J. Sejnowski, J. Neurophysiol. 66, 1059 (1991).
30. C. Van Vreeswijk L. F. Abbott, and G. B. Ermentrout, J. Comput. Neurosci. 1, 313 (1994). 10.1007/BF00961879
31. X.-J. Wang and G. Buzsaki, J. Neurosci. 16, 6402 (1996).
32. C. C. Chow, J. A. White, J. Ritt, and N. Kopell, J. Comput. Neurosci. 5, 407 (1998). 10.1023/A:1008889328787
33. P. H. Tiesinga and J. V. Jose, Network 11, 1 (2000). 10.1088/0954-898X/ 11/1/301
34. M. A. Whittington, R. D. Traub, N. Kopell, G. B. Ermentrout, and E. H. Buhl, Int. J. Psychophysiol 38, 315 (2000). 10.1016/S0167-8760(00)00173-2
35. R. Maex and E. D. Schutter, J. Neurosci. 23, 10503 (2003).
36. N. Brunel, J. Comput. Neurosci. 8, 183 (2000). 10.1023/A:1008925309027
37. P. H. E. Tiesinga, J.-M. Fellous, J. V. José, and T. J. Sejnowski, Hippocampus 11, 251 (2001). 10.1002/hipo.1041
38. D. Hansel and G. Mato, Neural Comput. 15, 1 (2003). 10.1162/ 089976603321043685
39. R. D. Traub, A. Bibbig, A. Fisahn, F. E. N. LeBeau, M. A. Whittington, and E. H. Buhl, Eur. J. Neurosci. 12, 4093 (2000). 10.1046/j.1460-9568.2000. 00300.x
40. R. D. Traub, M. O. Cunningham, T. Gloveli, F. E. N. LeBeau, A. Bibbig, E. H. Buhl, and M. A. Whittington, Proc. Natl. Acad. Sci. U.S.A. 100, 11047 (2003). 10.1073/pnas.1934854100
41. R. D. Traub, I. Pais, A. Bibbig, F. E. N. LeBeau, E. H. Buhl, S. G. Hormuzdi, H. Monyer, and M. A. Whittington, Proc. Natl. Acad. Sci. U.S.A. 100, 1370 (2003). 10.1073/pnas.0337529100
42. W. Gerstner, J. L. van Hemmen, and J. D. Cowan, Neural Comput. 8, 1653 (1996). 10.1162/neco.1996.8.8.1653
43. C. C. Chow, Physica D 118, 343 (1998). 10.1016/S0167-2789(98)00082-7
44. J. A. White, C. C. Chow, J. Rit, C. Soto-Trevino, and N. Kopell, J. Comput. Neurosci. 5, 5 (1998). 10.1023/A:1008841325921
45. H. C. Tuckwell, Introduction to Theoretical Neurobiology: Volume 2, Nonlinear and Stochastic Theories, Cambridge Studies in Mathematical Biology (Cambridge University Press, Cambridge, England, 1988).
46. A. N. Burkitt, Biol. Cybern. 95, 1 (2006). 10.1007/s00422-006-0068-6
47. A. N. Burkitt, Biol. Cybern. 95, 97 (2006). 10.1007/s00422-006-0082-8
48. Y. Kuramoto, Physica D 50, 15 (1991). 10.1016/0167-2789(91)90075-K
49. W. Senn and R. Urbanczik, SIAM J. Appl. Math. 61, 1143 (2000).
50. N. Brunel and S. Sergi, J. Theor. Biol. 195, 87 (1998). 10.1006/jtbi.1998.0782
51. R. M. Capocelli and L. M. Ricciardi, Biol. Cybern. 8, 214 (1971). 10.1007/BF00288750
52. P. Diţǎ, J. Phys. A 18, 2685 (1985). 10.1088/0305-4470/18/ 14/019
53. S. Sato, Math. Biosci. 39, 53 (1978). 10.1016/0025-5564(78)90027-5
54. T. Shimokawa, K. Pakdaman, T. Takahata, S. Tanabe, and S. Sata, Biol. Cybern. 83, 327 (2000). 10.1007/s004220000156
55. V. Lánská, P. Lánský, and C. Smith, J. Theor. Biol. 166, 393 (1994). 10.1006/jtbi.1994.1035
56. R. Brette, M. Rudolph, T. Carnevale, M. Hines, D. Beeman, J. M. Bower, M. Diesmann, A. Morrison, P. H. Goodman, F. C. Harris, Jr., J. Comput. Neurosci. 23, 349 (2007). 10.1007/s10827-007-0038-6
57. D. P. Bertsekas and J. N. Tsitsiklis, Introduction to Probability, 2nd ed. (Athena Scientific, Nashua, NH, 2008), Sec. 4.1
58. K. A. Newhall, G. Kovačič, P. R. Kramer, D. Zhou, A. V. Rangan, and D. Cai, Commun. Math. Sci. 8, 541 (2010).
59. S. Sato, J. Appl. Probab. 14, 850 (1977). 10.2307/3213358
60. D. Cai, L. Tao, A. V. Rangan, and D. W. McLaughlin, Commun. Math. Sci. 4, 97 (2006).
61. A. V. Rangan, G. Kovačič, and D. Cai, Phys. Rev. E 77, 041915 (2008). 10.1103/PhysRevE.77.041915
62. L. E. Reichl, A Modern Course in Statistical Physics, 2nd ed. (Wiley-Interscience, 1998).
63. D. Nykamp and D. Tranchina, J. Comput. Neurosci. 8, 19 (2000). 10.1023/A:1008912914816
64. C. W. Gardiner, Handbook of Stochastic Methods, 3rd ed. (Springer, 2004).
65. J. Thomas, Numerical Partial Differential Equations: Finite Difference Methods (Springer, New York, 1998).
66. R. E. L. DeVille and C. S. Peskin, Bull. Math. Biol. 70, 1608 (2008). 10.1007/s11538-008-9311-8
67. P. L. Nunez, Neocortical Dynamics and Human EEG Rhythms (Oxford University Press, New York, Oxford, 1995).
68. V. Bringuier, F. Chavane, L. Glaeser, and Y. Fregnac, Science 283, 695 (1999). 10.1126/science.283.5402.695
69. R. Eckhorn, A. M. Gail, A. Bruns, A. Gabriel, B. Al-Shaikhli, and M. Saam, IEEE Trans. Neural Netw. 15, 1039 (2004). 10.1109/TNN.2004.833130
70. M. Shelley and L. Tao, J. Comput. Neurosci. 11, 111 (2001). 10.1023/A:1012885314187
71. G. Kovačič, L. Tao, A. V. Rangan, and D. Cai, Phys. Rev. E 80, 021904 (2009). 10.1103/PhysRevE.80.021904
72. D. Zhou, Y. Sun, A. V. Rangan, and D. Cai, J. Comput. Neurosci. 28, 229 (2010). 10.1007/s10827-009-0201-3
73. Y. Sun, D. Zhou, A. V. Rangan, and D. Cai, J. Comput. Neurosci. 28, 247 (2010). 10.1007/s10827-009-0202-2
74. D. Zhou, A. V. Rangan, Y. Sun, and D. Cai, Phys. Rev. E 80, 031918 (2009). 10.1103/PhysRevE.80.031918
75. K. A. Newhall, M. Shkarayev, P. Kramer, G. Kovačič, and D. Cai, Phys. Rev. E (to be published).
76. Handbook of Mathematical Functions, 9th ed., edited by, M. Abramowitz, and, I. A. Stegun, (Dover Publications, Inc., New York, 1972).
77. L. J. Slater, Confluent Hypergeometric Functions (Cambridge University Press, New York, 1960).
78. S. Karlin and H. M. Taylor, A First Course in Stochastic Processes, 2nd ed. (Academic, Boston, 1975).