Mathematical proof that spiking neurons have more computational power than sigmoid functions

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Project Description

We have designed a digital circuit that behaves like an analog neuron. This device learns from incoming sensory streams, like the brain learns. Particularly the synapse function is a very detailed emulation of the biological synapse, supporting different types of neurotransmitters and neuromodulators. In a sigmoid function the synapse is assigned a value, its 'strength', while in biological neurons the synapse function is dynamic, depending on neurotransmitter type, neurotransmitter level, spike interval, spike intensity, synapse type, and depletion factor. These are all part of the computational properties of the neuron.

We need to prove - beyond doubt - that hardware (digital) spiking neurons with realistic synapses have more computational power than sigmoid functions in software.

References are found in papers published online by Wolfgang Maass, Institute for theorethical Computer Science "Noisy Spiking Neurons with temporal coding have more computational power than sigmoidal neurons" and "Computation with Spiking Neurons"

Also, a paper by Xiao-lin Zhang "A Mathematical model of a neuron with synapses based on Physiology". I need to combine the theorems of Maass with the theorems of Xiao-lin Zhang. However, I am a computer scientist and a neurologist, not a mathematician. I need help to put this into a format that makes sense to a mathematician.

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