ArticleFrontiers in computational neuroscience2014
The neuronal response at extended timescales: a linearized spiking input-output relation.
Article in Frontiers in computational neuroscience, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 1 paper.
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1 citing paper in PubMed.
- The neuronal response at extended timescales: long-term correlations without long-term memory.Frontiers in computational neuroscience · 2014Article
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Abstract
Many biological systems are modulated by unknown slow processes. This can severely hinder analysis - especially in excitable neurons, which are highly non-linear and stochastic systems. We show the analysis simplifies considerably if the input matches the sparse "spiky" nature of the output. In this case, a linearized spiking Input-Output (I/O) relation can be derived semi-analytically, relating input spike trains to output spikes based on known biophysical properties. Using this I/O relation we obtain closed-form expressions for all second order statistics (input - internal state - output correlations and spectra), construct optimal linear estimators for the neuronal response and internal state and perform parameter identification. These results are guaranteed to hold, for a general stochastic biophysical neuron model, with only a few assumptions (mainly, timescale separation). We numerically test the resulting expressions for various models, and show that they hold well, even in cases where our assumptions fail to hold. In a companion paper we demonstrate how this approach enables us to fit a biophysical neuron model so it reproduces experimentally observed temporal firing statistics on days-long experiments.
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