Table 1.

List of symbols

SymbolMeaning
nNumber of neurons
θStimulus direction
fk(θ)Tuning function of neuron k (average spike count)
fVector of tuning functions (for θ = 0; n × 1)
Discrete Fourier transform of f
yVector of spike counts
φkPreferred direction of neuron k
σk(θ)SD of spike counts of neuron k
σVector of SDs (for θ = 0; n × 1)
S = Diag (σ)Diagonal matrix of SDs
gk=f′kkNormalized 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
RMatrix of correlation coefficients (n × n)
rjkCorrelation coefficient of neurons j and k
rAverage correlation coefficient of the population, 〈r〉 ≈ 0.3 c0.
rFirst column of R, rk = ck, except for r0 = 1
QCovariance matrix (for θ = 0; n × n)
UFourier basis, ujk = exp(−iωjk)/
Diagonal matrix containing eigenvalues of R. Diagonal elements are r̃
JFisher information
JmeanLinear part of Fisher information (Eq. 8)
JcovNon-linear part of Fisher information (Eq. 9)
JmeanhomJmean of a homogeneous population of neurons
JindepFisher information of an independent population of neurons
κDegree of amplitude variability, κ=Var[].
akAmplitude of tuning function of neuron k
FFano 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.