Efficient population coding depends on stimulus convergence and source of noise
Fig 5
Threshold differences as phase transitions with respect to both noise sources.
A. Optimal thresholds for the independent-coding channel depending on output noise R. Insets: The first derivative of the mutual information as a function of noise is continuous, while the second derivative is discontinuous at the critical noise values where the thresholds separate, implying a second-order phase transition. B. As in A, but with respect to input noise σ. C. Optimal thresholds as in A but for the lumped-coding channel. The first derivative is discontinuous at the critical noise values where the thresholds separate, implying a first-order phase transition. D. As in C but with respect to input noise σ.