Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

This work is motivated by the ongoing open question of how information in the outside world is represented and processed by the brain. Consequently, several novel methods are developed. A new mathematical formulation is proposed for the encoding and decoding of analog signals using integrate-and-fire neuron models. Based on this formulation, a novel algorithm, significantly faster than the state-of-the-art method, is proposed for reconstructing the input of the neuron. Two new identification methods are proposed for neural circuits comprising a filter in series with a spiking neuron model. These methods reduce the number of assumptions made by the state-of-the-art identification framework, allowing for a wider range of models of sensory processing circuits to be inferred directly from input-output observations. A third contribution is an algorithm that computes the spike time sequence generated by an integrate-and-fire neuron model in response to the output of a linear filter, given the input of the filter encoded with the same neuron model.