Dynamics of neuronal populations: the equilibrium solution
SIAM Journal on Applied Mathematics
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems
Unfolding an electronic integrate-and-fire circuit
Biological Cybernetics
Spiking neurons and the first passage problem
Neural Computation
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Theoretical and experimental evidence is presented for the presence in nervous tissue of neurons whose firing rate faithfully follow their input stimulus. Such neurons are shown to deliver their spikes with minimum dissipation per spike. This optimal performance is likely accomplished by use of local circuitry that adjusts conductances to match input currents so that the neuron operates near the threshold for firing. This results in an unusual mechanism for neuronal firing that uses background noise to achieve the desired firing rate. This framework takes place dynamically, and the present deliberations apply under time varying conditions. It is shown that an analytically explicit probability distribution function, which depends on one dimensionless parameter, can account for the interspike interval statistics under general time varying conditions. An innovative analysis based on the unsteady firing rate fits data to the appropriate probability distribution function.