Optimising threshold levels for information transmission in binary threshold networks: Independent multiplicative noise on each threshold

• We have found the optimal threshold levels in a multilevel binary threshold system with multiplicative and additive noise.
• This mode is relevant to sensor network design and understanding neurobiological sensory neurons such as in the peripheral auditory system.
• The optimal thresholds for multiplicative noise exhibit bifurcations.
• The optimal thresholds are all unique when the additive noise intensity is fixed.
• The optimal thresholds are identical for large additive noise.

The problem of optimising the threshold levels in multilevel threshold system subject to multiplicative Gaussian and uniform noise is considered. Similar to previous results for additive noise, we find a bifurcation phenomenon in the optimal threshold values, as the noise intensity changes. This occurs when the number of threshold units is greater than one. We also study the optimal thresholds for combined additive and multiplicative Gaussian noise, and find that all threshold levels need to be identical to optimise the system when the additive noise intensity is a constant. However, this identical value is not equal to the signal mean, unlike the case of additive noise. When the multiplicative noise intensity is instead held constant, the optimal threshold levels are not all identical for small additive noise intensity but are all equal to zero for large additive noise intensity. The model and our results are potentially relevant for sensor network design and understanding neurobiological sensory neurons such as in the peripheral auditory system.