Testing resonating vector strength: auditory system, electric fish, and noise

Quite often a response to some input with a specific frequency ν(○) can be described through a sequence of discrete events. Here, we study the synchrony vector, whose length stands for the vector strength, and in doing so focus on neuronal response in terms of spike times. The latter are supposed to be given by experiment. Instead of singling out the stimulus frequency ν(○) we study the synchrony vector as a function of the real frequency variable ν. Its length turns out to be a resonating vector strength in that it shows clear maxima in the neighborhood of ν(○) and multiples thereof, hence, allowing an easy way of determining response frequencies. We study this "resonating" vector strength for two concrete but rather different cases, viz., a specific midbrain neuron in the auditory system of cat and a primary detector neuron belonging to the electric sense of the wave-type electric fish Apteronotus leptorhynchus. We show that the resonating vector strength always performs a clear resonance correlated with the phase locking that it quantifies. We analyze the influence of noise and demonstrate how well the resonance associated with maximal vector strength indicates the dominant stimulus frequency. Furthermore, we exhibit how one can obtain a specific phase associated with, for instance, a delay in auditory analysis.