Erratum: Propagation of chaos in neural fields (Annals of Applied Probability (2014) 24 (1298-1328) DOI: 10.1214/13-AAP950);Propagation of chaos in neural fields

Annals of Applied Probability

Volumn 24, Issue 3, 2014, Pages 1298-1328

  Touboul, Jonathan ^a  

^a Centre de Recherche Interdisciplinaire en Biologie   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84899512305     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/18-AAP1393     Document Type: Erratum

References (35)

1. AMARI, S. (1972). Characteristics of random nets of analog neuron-like elements. IEEE Trans. Syst. Man Cybern. 2 643-657.
2. BOSKING, W. H., ZHANG, Y., SCHOFIELD, B. and FITZPATRICK, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. J. Comput. Neurosci. 17 2112-2127.
3. BRESSLOFF, P. C. (2012). Spatiotemporal dynamics of continuum neural fields. J. Phys. A 45 033001, 109. MR2871421
4. BUZSÁKI, G. (2006). Rhythms of the Brain. Oxford Univ. Press, Oxford. MR2270828
5. COOMBES, S. and LAING, C. (2009). Delays in activity-based neural networks. Philos. Trans. R. Soc. A Math. Phys. Eng. Sci. 367 1117-1129. MR2481263
6. COOMBES, S. and OWEN, M. R. (2005). Bumps, breathers, and waves in a neural network with spike frequency adaptation. Phys. Rev. Lett. 94 148102.
7. DA PRATO, G. and ZABCZYK, J. (1992). Stochastic Equations in Infinite Dimensions. Cambridge Univ. Press, Cambridge. MR1207136
8. DESTEXHE, A.,MAINEN, Z. F. and SEJNOWSKI, T. J. (1994). An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Comput. 6 14-18.
9. DOBRUSHIN, R. L. (1970). Prescribing a System of Random Variables by Conditional Distributions. Theory of Probability and Its Applications 15.
10. ECKER, A. S., BERENS, P., KELIRIS, G. A., BETHGE, M., LOGOTHETIS, N. K. and TOLIAS, A. S. (2010). Decorrelated neuronal firing in cortical microcircuits. Science 327 584-587.
11. ERMENTROUT, G. B. and COWAN, J. D. (1979). Temporal oscillations in neuronal nets. J. Math. Biol. 7 265-280. MR0648852
12. ERMENTROUT, G. B. and COWAN, J. D. (1980). Large scale spatially organized activity in neural nets. SIAM J. Appl. Math. 38 1-21. MR0559077
13. ERMENTROUT, G. B. and TERMAN, D. H. (2010). Mathematical Foundations of Neuroscience. Springer, New York. MR2674516
14. FITZHUGH, R. (1969). Mathematical Models of Excitation and Propagation in Nerve. McGraw-Hill, New York.
15. FREGNAC, Y., BLATOW, M., CHANGEUX, J. P., DE FELIPE, J., LANSNER, A.,MAASS, W., MC CORMICK, D. A.,MICHEL, C. M.,MONYER, H., SZATHMÁRY, E. and R., YUSTE (2006). Ups and downs in cortical computation. In Microcircuits: The Interface Between Neurons and Global Brain Function 393-433. MIT Press, Cambridge, MA.
16. GOLDWYN, J. H., IMENNOV, N. S., FAMULARE, M. and SHEA-BROWN, E. (2011). Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons. Phys. Rev. E (3) 83 041908.
17. HODGKIN, A. L. and HUXLEY, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117 500-544.
18. HUBEL, D. H., WIESEL, T. N. and STRYKER, M. P. (1978). Anatomical demonstration of orientation columns in macaque monkey. J. Comput. Neurosci. 177 361-380.
19. IZHIKEVICH, E. M. (2006). Polychronization: Computation with spikes. Neural Comput. 18 245-282. MR2188057
20. KANDEL, E. R., SCHWARTZ, J. H. and JESSEL, T. M. (2000). Principles of Neural Science, 4th ed. McGraw-Hill, New York.
21. LAING, C. R., TROY, W. C., GUTKIN, B. and ERMENTROUT, G. B. (2002). Multiple bumps in a neuronal model of working memory. SIAM J. Appl. Math. 63 62-97 (electronic). MR1952887
22. MAO, X. (2002). A note on the LaSalle-type theorems for stochastic differential delay equations. J. Math. Anal. Appl. 268 125-142. MR1893197
23. MCKEAN, H. P. JR. (1966). A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl. Acad. Sci. USA 56 1907-1911. MR0221595
24. MOUNTCASTLE, V. B. (1997). The columnar organization of the neocortex. Brain 120 701-722.
25. RENART, A., DE LA ROCHA, J., BARTHO, P., HOLLENDER, L., PARGA, N., REYES, A. and HARRIS, K. D. (2010). The asynchronous state in cortical circuits. Science 327 587-590.
26. REVUZ, D. and YOR, M. (1999). Continuous Martingales and Brownian Motion, 3rd ed. Springer, Berlin. MR1725357
27. SERIES, P., GEORGES, S., LORENCEAU, J. and FRÉGNAC, Y. (2002). Orientation dependent modulation of apparent speed: A model based on the dynamics of feed-forward and horizontal connectivity in v1 cortex. Vision Research 42 2781-2797.
28. SZNITMAN, A.-S. (1984). Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56 311-336. MR0743844
29. SZNITMAN, A.-S. (1991). Topics in propagation of chaos. In École D'Été de Probabilités de Saint-Flour XIX 165-251. Springer, Berlin. MR1108185
30. TANAKA, H. (1983). Some probabilistic problems in the spatially homogeneous Boltzmann equation. In Theory and Application of Random Fields (Bangalore, 1982) 258-267. Springer, Berlin. MR0799949
31. THORPE, S., DELORME, A. and VANRULLEN, R. (2001). Spike based strategies for rapid processing. Neural Netw. 14 715-726.
32. TOUBOUL, J. (2012). Mean-field equations for stochastic firing-rate neural fields with delays: Derivation and noise-induced transitions. Phys. D 241 1223-1244. MR2930724
33. VILLANI, C. (2002). A review of mathematical topics in collisional kinetic theory. In Handbook of Mathematical Fluid Dynamics, Vol. I 71-305. North-Holland, Amsterdam. MR1942465
34. WILSON, H. R. and COWAN, J. D. (1972). Excitatory and inhibitory interactions in localized populations of model neurons. Biophys. J. 12 1-24.
35. WILSON, H. R. and COWAN, J. D. (1973). A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Biol. Cybernet. 13 55-80.