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Coding of Time-Varying Signals in Spike Trains of Integrate-and-Fire Neurons with Random Threshold

Gabbiani, Fabrizio and Koch, Christof (1996) Coding of Time-Varying Signals in Spike Trains of Integrate-and-Fire Neurons with Random Threshold. Neural Computation, 8 (1). pp. 44-66. ISSN 0899-7667. doi:10.1162/neco.1996.8.1.44.

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Recently, methods of statistical estimation theory have been applied by Bialek and collaborators (1991) to reconstruct time-varying velocity signals and to investigate the processing of visual information by a directionally selective motion detector in the fly's visual system, the H1 cell. We summarize here our theoretical results obtained by studying these reconstructions starting from a simple model of H1 based on experimental data. Under additional technical assumptions, we derive a closed expression for the Fourier transform of the optimal reconstruction filter in terms of the statistics of the stimulus and the characteristics of the model neuron, such as its firing rate. It is shown that linear reconstruction filters will change in a nontrivial way if the statistics of the signal or the mean firing rate of the cell changes. Analytical expressions are then derived for the mean square error in the reconstructions and the lower bound on the rate of information transmission that was estimated experimentally by Bialek et al. (1991). For plausible values of the parameters, the model is in qualitative agreement with experimental data. We show that the rate of information transmission and mean square error represent different measures of the reconstructions: in particular, satisfactory reconstructions in terms of the mean square error can be achieved only using stimuli that are matched to the properties of the recorded cell. Finally, it is shown that at least for the class of models presented here, reconstruction methods can be understood as a generalization of the more familiar reverse-correlation technique.

Item Type:Article
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Gabbiani, Fabrizio0000-0003-4966-3027
Koch, Christof0000-0001-6482-8067
Additional Information:© 1995 Massachusetts Institute of Technology. Received August 2, 1994; accepted March 31, 1995. Posted Online April 4, 2008. We would like to thank J. Fröhlich and K. Hepp for very useful discussions on the subject treated here. The comments given by W. Bialek and R. de Ruyter van Steveninck on this manuscript are also gratefully acknowledged. This work was supported by a grant of the Roche Research Foundation and in part by the Center for Neuromorphic Systems Engineering as a part of the National Science Foundation Engineering Research Center Program, and by the California Trade and Commerce Agency, Office of Strategic Technology.
Group:Koch Laboratory (KLAB)
Funding AgencyGrant Number
Roche Research FoundationUNSPECIFIED
Center for Neuromorphic Systems Engineering, CaltechUNSPECIFIED
California Trade and Commerce Agency, Office of Strategic TechnologyUNSPECIFIED
Issue or Number:1
Record Number:CaltechAUTHORS:20120201-093250840
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:29058
Deposited By: Tony Diaz
Deposited On:24 Feb 2012 23:22
Last Modified:26 Apr 2023 16:19

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