Table 1.
List of symbols
| Symbol | Meaning |
|---|---|
| n | Number of neurons |
| θ | Stimulus direction |
| fk(θ) | Tuning function of neuron k (average spike count) |
| f | Vector of tuning functions (for θ = 0; n × 1) |
| f̃ | Discrete Fourier transform of f |
| y | Vector of spike counts |
| φk | Preferred direction of neuron k |
| σk(θ) | SD of spike counts of neuron k |
| σ | Vector of SDs (for θ = 0; n × 1) |
| S = Diag (σ) | Diagonal matrix of SDs |
| gk=f′k/σk | Normalized tuning curve derivatives |
| c(⊖φj ⊖ φk⊖) | Spatial structure of correlation coefficients (⊖ is the angular difference) |
| c0 = c(0) | Correlation coefficient of two neurons with identical preferred directions |
| R | Matrix of correlation coefficients (n × n) |
| rjk | Correlation coefficient of neurons j and k |
| 〈r〉 | Average correlation coefficient of the population, 〈r〉 ≈ 0.3 c0. |
| r | First column of R, rk = ck, except for r0 = 1 |
| Q | Covariance matrix (for θ = 0; n × n) |
| U | Fourier basis, ujk = exp(−iωjk)/ |
| R̃ | Diagonal matrix containing eigenvalues of R. Diagonal elements are r̃ |
| J | Fisher information |
| Jmean | Linear part of Fisher information (Eq. 8) |
| Jcov | Non-linear part of Fisher information (Eq. 9) |
| Jmeanhom | Jmean of a homogeneous population of neurons |
| Jindep | Fisher information of an independent population of neurons |
| κ | Degree of amplitude variability, κ=Var[ ]. |
| ak | Amplitude of tuning function of neuron k |
| F | Fano factor (variance/mean) |
We use boldface lowercase letters to denote (column) vectors (e.g., v) and boldface uppercase letters for matrices (e.g., M). Scalars or scalar elements of vectors and matrices are set in italics (e.g., a, vj, or Mjk). The jth column of M is referred to as mj.