Statistical Analysis of Neural Data: the Integrate-and-fire Neuron and Other Continuous-time State-space Models *
نویسنده
چکیده
3 The “Fokker-Planck” equation is a partial differential equation that controls the evolution of the forward (and backward) probabilities 9 3.1 Deriving the “free” Fokker-Planck equation (no spike observations) . . . . . . 10 3.1.1 Conductance-based model . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.2 Computing mean firing rates in a network of GLM neurons . . . . . . 13 3.2 Incorporating spike observations into the Fokker-Planck equation . . . . . . . 14 3.2.1 Soft threshold integrate-and-fire model . . . . . . . . . . . . . . . . . . 15 3.2.2 Hard threshold IF model . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2.3 Leaky integrate-and-fire cell driven by white current noise . . . . . . . 17 3.2.4 Noiseless leaky integrate-and-fire cell . . . . . . . . . . . . . . . . . . . 17 3.2.5 Leaky integrate and fire cell with Poisson conductance inputs . . . . . 18 3.3 A similar “backwards” equation holds for the backwards probabilities . . . . 18
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