little things

nonlinearbaseline.tex

@@ -540,10 +540,12 @@ Estimating second-order susceptibilities reliably requires large numbers (millio
 
 The second-order susceptibility matrices that are based on only 100 segments look flat and noisy, lacking the triangular structure (\subfigref{fig:modelsusceptlown}{B}). The anti-diagonal ridge, however, where the sum of the stimulus frequencies matches the neuron's baseline firing rate, seems to be present whenever the converged estimate shows a clear triangular structure (compare \subfigref{fig:modelsusceptlown}{B} and \subfigref{fig:modelsusceptlown}{A}). The SI($r$) characterizes the height of the ridge in the second-oder susceptibility plane at the neuron's baseline firing rate $r$. Comparing SI($r$) values based on 100 FFT segements to the ones based on one or ten million segments for all 39 model cells (\subfigrefb{fig:modelsusceptlown}{C}) supports this impression. They correlate quite well at contrasts of 1\,\% and 3\,\% ($r=0.9$, $p\ll 0.001$). At a contrast of 10\,\% this correlation is weaker ($r=0.38$, $p<0.05$), because there are only three cells left with SI($r$) values greater than 1.2. Despite the good correlations, care has to be taken to set a threshold on the SI($r$) values for deciding whether a triangular structure would emerge for a much higher number of segments. Because at low number of segments the estimates are noisier, there could be false positives for a too low threshold. Setting the threshold to 1.8 avoids false positives for the price of a few false negatives.
 
-Overall, observing SI($r$) values greater than about 1.8, even for a number of FFT segments as low as one hundred, seems to be a reliable indication for a triangular structure in the second-order susceptibility at the corresponding stimulus contrast. Small stimulus contrasts of 1\,\% are less informative, because of their bad signal-to-noise ratio. Intermediate stimulus contrasts around 3\,\% seem to be optimal, because there, most cells still have a triangular structure in their susceptibility and the signal-to-noise ratio is better. At RAM stimulus contrasts of 10\,\% or higher the signal-to-noise ratio is even better, but only few cells remain with weak triangularly shaped susceptibilities that might be missed as a false positives.
+Overall, observing SI($r$) values greater than about 1.8, even for a number of FFT segments as low as one hundred, seems to be a reliable indication for a triangular structure in the second-order susceptibility at the corresponding stimulus contrast. Small stimulus contrasts of 1\,\% are less informative, because of their bad signal-to-noise ratio. \notejb{Explain what we can read off from n=100} Intermediate stimulus contrasts around 3\,\% seem to be optimal, because there, most cells still have a triangular structure in their susceptibility and the signal-to-noise ratio is better. At RAM stimulus contrasts of 10\,\% or higher the signal-to-noise ratio is even better, but only few cells remain with weak triangularly shaped susceptibilities that might be missed as a false positives.
 
 \begin{figure*}[tp]
   \includegraphics[width=\columnwidth]{dataoverview}
+  \notejb{use color code for contrasts}
+  \notejb{add inset wih distribution of contrasts}
   \caption{\label{fig:dataoverview} Nonlinear responses in P-units and
     ampullary afferents. The second-order susceptibility is condensed
     into the susceptibility index, SI($r$) \eqnref{eq:nli_equation},
@@ -592,9 +594,9 @@ Overall, observing SI($r$) values greater than about 1.8, even for a number of F
 \end{figure*}
 
 \subsection{Low CVs and weak stimuli are associated with distinct nonlinearity in recorded electroreceptive neurons}
-Now we are prepared to evaluate our pool of 39 P-unit model cells, 159 P-units, and 30 ampullary afferents recorded in 75 specimen of \textit{Apteronotus leptorhynchus}. For comparison across cells we condensed the structure of the second-order susceptibilities into SI($r$) values, \eqnref{eq:nli_equation}, computed from FFTs based on 100 segments of 512 samples at a temporal resolution of 0.5\,ms.
+Now we are prepared to evaluate our pool of 39 P-unit model cells, 166 P-units, and 30 ampullary afferents recorded in 76 specimen of \textit{Apteronotus leptorhynchus}. For comparison across cells we condensed the structure of the second-order susceptibilities into SI($r$) values, \eqnref{eq:nli_equation}.
 
-In the P-unit models, each model cell contributed with three RAM stimulus presentations with contrasts of 1, 3, and 10\,\%, resulting in $n=117$ data points. 19 (16\,\%) had SI($r$) values larger than 1.8, indicating the expected ridges at the baseline firing rate in their second-order susceptiility . The lower the cell's baseline CV, i.e. the less intrinsic noise, the higher the SI($r$) (\figrefb{fig:dataoverview}\,\pane[i]{A}). Also, the lower the response modulation, i.e. the weaker the effective stimulus, the higher the S($r$) (\figrefb{fig:dataoverview}\,\pane[ii]{A}). Cells with high SI($r$) values are the ones with baseline firing rate below 200\,Hz (\figrefb{fig:dataoverview}\,\pane[iii]{A}). In comparison to the experimentally measured P-unit recordings, the model cells are skewed to lower baseline CVs (Mann-Whitney $U=12924$, $p=1.3\times 10^{-7}$), because the models are not able to reproduce bursting, which we observe in many P-units and which leads to high CVs. Also the response modulation of the models is skewed to lower values (Mann-Whitney $U=12846$, $p=9.1\times 10^{-8}$), because in the measured cells, response modulation is positively correlated with baseline CV \notejb{(XXX)}, i.e. bursting cells are more sensitive. \notejb{cehck baseline firing rate differences.}
+In the P-unit models, each model cell contributed with three RAM stimulus presentations with contrasts of 1, 3, and 10\,\%, resulting in $n=117$ data points. 19 (16\,\%) had SI($r$) values larger than 1.8, indicating the expected ridges at the baseline firing rate in their second-order susceptiility . The lower the cell's baseline CV, i.e. the less intrinsic noise, the higher the SI($r$) (\figrefb{fig:dataoverview}\,\panel[i]{A}). Also, the lower the response modulation, i.e. the weaker the effective stimulus, the higher the S($r$) (\figrefb{fig:dataoverview}\,\panel[ii]{A}). Cells with high SI($r$) values are the ones with baseline firing rate below 200\,Hz (\figrefb{fig:dataoverview}\,\panel[iii]{A}). In comparison to the experimentally measured P-unit recordings, the model cells are skewed to lower baseline CVs (Mann-Whitney $U=12924$, $p=1.3\times 10^{-7}$), because the models are not able to reproduce bursting, which we observe in many P-units and which leads to high CVs. Also the response modulation of the models is skewed to lower values (Mann-Whitney $U=12846$, $p=9.1\times 10^{-8}$), because in the measured cells, response modulation is positively correlated with baseline CV \notejb{(XXX)}, i.e. bursting cells are more sensitive. \notejb{check baseline firing rate differences.}
 
 
 \notejb{We need to know which contrasts}
@@ -789,6 +791,8 @@ We expected to see elevated values in the second-order susceptibility at $\omega
 \end{equation}
 from the second-order susceptibilities estimated from experimental data. $D(f)$ is the projection of the absolute values of the second-order susceptibility matrix onto the diagonal, calculated by taking the mean of the anti-diagonal elements. The peak of $D(f)$ at the neuron's baseline firing rate $\fbase$ was found by finding the maximum of $D(f)$ in the range $\fbase \pm 5$\,Hz. This peak was then normalized by the median of $D(f)$ (\subfigrefb{fig:punit}{G}). Since in most experimentally measured cells the second-order susceptibilities was more or less flat, normalizing by the median is working well. If the same RAM was recorded several times in a cell, each trial resulted in a separate second-order susceptibility matrix. For the population statistics in \figref{fig:dataoverview} the mean of the resulting \nli{} values is used.
 
+\notejb{computed from FFTs based on 100 segments of 512 samples at a temporal resolution of 0.5\,ms}
+
 For the model simulations, the second-order susceptibilities where not flat but often showed a broader bump on which the peak at the neuron's baseline firing rate occured (see, for example, \figrefb{fig:modelsusceptcontrasts}, panels \panel[i]{B}, \panel[iii]{C}, and \panel[iv]{D}). Instead of normalizing by the median, we normalized the model simulations by the mean values of the projection $D(f)$ in small ranges close to the left and right of the neuron's baseline firing rate:
 \begin{equation}
   \label{eq:nli_equation2}