Multiplicatively interacting point processes and applications to neural modeling

Journal of Computational Neuroscience

Volumn 28, Issue 2, 2010, Pages 267-284

  Cardanobile, Stefano ^a   Rotter, Stefan ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Generalised linear model; Interacting random process; Poisson process; Recurrent network dynamics; Spiking neuron; Winner takes all

Indexed keywords

FUNCTIONS; NEURAL NETWORKS; NEURONS;

GENERALIZED LINEAR MODEL; INTERACTING RANDOM PROCESS; NETWORK DYNAMICS; NEURAL MODELLING; POINT PROCESS; POISSON PROCESS; RECURRENT NETWORK DYNAMIC; RECURRENT NETWORKS; SPIKING NEURONES; WINNER-TAKE-ALL;

RANDOM PROCESSES;

ARTICLE; ARTIFICIAL NEURAL NETWORK; LINEAR SYSTEM; MATHEMATICAL MODEL; MONTE CARLO METHOD; NONLINEAR SYSTEM; PRIORITY JOURNAL; SPIKE; STATISTICAL ANALYSIS;

EID: 77953323110     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-009-0204-0     Document Type: Article

References (28)

1. Amit, D. J., & Brunel, N. (1997). Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex. Cerebral Cortex, 7, 237-252.
2. Benci, V., & Di Nasso, M. (2003). Alpha-theory: An elementary axiomatics for nonstandard analysis. Expositiones Mathematicae, 21(4), 355-386.
3. Benci, V., Galatolo, S., & Ghimenti, M. (2008). An elementary approach to stochastic differential equations using the infinitesimals. In V. Bergelson, A. Blass, M. D. Nasso, & R. Jin (Eds.), Ultrafilters across mathematics, Cont. Math. AMS. http://arxiv.org/abs/0807.3477.
4. Blake, R. (1989). A neural theory of binocular rivalry. Psychological Review, 96, 145-167.
5. Carandini, M. (2004). Amplification of trial-to-trial response variability by neurons in visual cortex. PLoS Biology, 2, 1483-1493.
6. Destexhe, A., Rudolph, M., & Pare, D. (2003). The highconductance state of neocortical neurons in vivo. Nature Reviews. Neuroscience, 4(9), 739-751 (2003). doi:10.1038/nrn1198. (Pubitemid 37280153)
7. Fahle, M., & Palm, G. (1991). Perceptual rivalry between illusory and real contours. Biological Cybernetics, 66(1), 1-8.
8. Fukai, T., & Tanaka, S. (1997). A simple neural network exhibiting selective activation of neuronal ensembles: From winnertake-all to winners-share-all. Neural Computation, 9(1), 77-97.
9. Gerstner, W., & Kistler, W. M. (2002). Spiking neuron models. Single neurons, populations, plasticity. Cambridge: Cambridge University Press.
10. Hawkes, A. G. (1971a). Point spectra of some mutually exciting point processes. Journal of the Royal Statistical Society. Series B, 33, 438-443.
11. Hawkes, A. G. (1971b). Spectra of some self-exciting and mutually exciting point processes. Biometrika, 58, 83-90.
12. Ilyashenko, Y. (2002). Centennial history of Hilbert's 16th problem. Bulletin of the American Mathematical Society (New Series), 39(3), 301-354 (electronic).
13. Johnson, D. H. (1996). Point process models of single-neuron discharges. Journal of Computational Neuroscience, 3, 275-299.
14. Jolivet, R., Rauch, A., Lüscher, H., & Gerstner, W. (2006). Predicting spike timing of neocortical pyramidal neurons by simple threshold models. Journal of Computational Neuroscience, 21(1), 35-49. doi:10.1007/s10827-006-7074-5. (Pubitemid 44028469)
15. Kriener, B., Tetzlaff, T., Aertsen, A., Diesmann, M., & Rotter, S. (2008). Correlations and population dynamics in cortical networks. Neural Computation, 20(9), 2185-2226.
16. Muller, E., Buesing, L., Schemmel, J., & Meier, K. (2007). Spike-frequency adapting neural ensembles: Beyond mean adaptation and renewal theories. Neural Computation, 19(11), 2958-3010. doi:10.1162/neco.2007.19.11. 2958. PMID: 17883347.
17. Nelson, E. (1977). Internal set theory: A new approach to nonstandard analysis. Bulletin of the American Mathematical Society, 83(6), 1165-1198.
18. Nelson, E. (1987). Radically elementary probability theory. In Annals of mathematics studies (Vol. 117). Princeton: Princeton University Press.
19. Ogata, Y. (1999). Seismicity analysis through point-process modeling: A review. Pure and Applied Geophysics, 155, 471-507.
20. Paninski, L. (2004). Maximum likelihood estimation of cascade point-process neural encoding models. Network: Comput. Neural Syst., 15, 243-262. (Pubitemid 39586479)
21. Pillow, J. W., Shlens, J., Paninski, L., Sher, A., Litke, A. M., Chichilnisky, E. J., et al. (2008). Spatio-temporal correlations and visual signalling in a complete neuronal population. Nature, 454(7207), 995-999. doi:10.1038/nature07140.
22. Rotter, S. (1994). Wechselwirkende stochastische Punktprozesse als Modell für neuronale Aktivität im Neocortex der Säugetiere. In Reihe physik (Vol. 21). Harri Deutsch Verlag.
23. Rotter, S., Heck, D., & Aertsen, A. (1996). Spatio-temporal patterns of activity in cortical networks. In J. Bower (Ed.), Computational neuroscience: Trends in research 1995 (p. 261). London: Academic Press.
24. Toyoizumi, T., Rad, K. R., & Paninski, L. (2009). Mean-field approximations for coupled populations of generalized linear model spiking neurons with Markov refractoriness. Neural Computation, 21, 1-41.
25. Truccolo, W., Eden, U. T., Fellows, M. R., Donoghue, J. P., & Brown, E. D. (2005). A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. Journal of Neurophysiology, 93, 1074-1089.
26. van den Boogaard, H. (1988). System identification based on point processes and correlation densities. II: The refractory neuron model. Mathematical Biosciences, 91(1), 35-65.
27. van den Boogaard, H., Hesselmans, G., & Johannesma, P. (1986). System identification based on point processes and correlation densities. I: The nonrefractory neuron model. Mathematical Biosciences, 80(2), 143-171.
28. Wiener, N. (1958). Nonlinear problems in random theory. Cambridge: MIT.