Fig. 5.

Computation in the LC and NNC. (A) Artificial ORN soma activity patterns ($\{{\mathbf{x}}^{(t)}\}$, $D=2$ ORN somas), generated with two Gaussian clusters of 100 points each centered at (1, 0.3) and (0.3, 1), $=0.17$. This input is fed to the LC-2 (i.e., $K=2$ LNs) (B, D, and F) and the NNC-2 (C, E, and F), $\rho =1$. (B) LN activity, $\{{\mathbf{z}}^{(t)}\}$, in the LC-2. Because of a degree of freedom in LC, LN activity can be any rotation of the activity depicted here, i.e., $\mathbf{Q}·\mathbf{z}$, where $\mathbf{Q}$ is a rotation (orthogonal) matrix. (C) LN activity, $\{{\mathbf{z}}^{(t)}\}$, in the NNC-2. LNs encode cluster memberships. (D) Scatter plot of the activity patterns in ORN somas ($\{{\mathbf{x}}^{(t)}\}$, black, from (A) and in ORN axons in the LC-2 ($\{{\mathbf{y}}^{(t)}\}$, magenta). ${\sigma }_{X,i}{\mathbf{u}}_{X,i}$, ${\sigma }_{Y,i}{\mathbf{u}}_{Y,i}$: vectors of the PCA directions of uncentered $\{{\mathbf{x}}^{(t)}\}$ and $\{{\mathbf{y}}^{(t)}\}$ scaled by the SD of that direction. ${\mathbf{w}}_k$ (green): direction of an ORNs $\to$ LN synaptic weight vector in the LC-2 from (B). Rotating the LN output $\{{\mathbf{z}}^{(t)}\}$ would alter the ${\mathbf{w}}_k$s, but not the $\{{\mathbf{y}}^{(t)}\}$. (E) Scatter plot of the activity patterns in ORN somas ($\{{\mathbf{x}}^{(t)}\}$, black, from (A) and in ORN axons in the NNC-2 ($\{{\mathbf{y}}^{(t)}\}$, blue). All activities are nonnegative and the ${\mathbf{w}}_k$s point toward the cluster locations, enabling the clustering observed in (C). (F) The PCA variances of the activity are less dispersed in ORN axons (output, $\{{\mathbf{y}}^{(t)}\}$) than in ORN somas (input, $\{{\mathbf{x}}^{(t)}\}$) for the LC and NNC. The output representation is thus partially whitened. The LC and NNC are similar in terms of their PCA variances. (G and H) Transformation of the SD (${\sigma }_X$, ${\sigma }_Y$) of PCA directions from ORN somas ($\{{\mathbf{x}}^{(t)}\}$) to ORN axons ($\{{\mathbf{y}}^{(t)}\}$) in the LC model on linear and logarithmic scales, for different values of $\rho$ (different line colors), encoding inhibition strength. When $\rho =0$, the output equals the input. The higher the $\rho$, the smaller the PCA variances in the ORN axon.