Figure 1.
Three visualizations of the same sparsely sampled cortical map data.
The perceived orderliness of a topographic map can vary depending on how the data is presented. This figure shows identical mapping data (an azimuth map in pallid bat A1) plotted in three ways: (A) no interpolation, (B) Voronoi tessellation (nearest neighbor interpolation), and (C) linear interpolation. Color indicates the value of the mapped tuning parameter and color scaling is continuous and consistent across panels. Scale bar is approximately 0.5 mm. Analysis results for this map (measure values and Benjamini-Hochberg corrected -values; see Results):
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Figure 2.
Elements of a topographic map.
Fundamental elements of a map from a 1-dimensional feature space to a 2-dimensional map space. Dashed lines represent the link between the positions of neurons in feature space with their positions in map space. Here two neurons and
are shown together with their map space (anatomical) and feature space (characteristic stimulus) coordinates.
Figure 3.
Map models and spatial sampling.
Three map models were used to investigate the sensitivity of map measures to different forms of topography: (A) linear map, (B) angle map and (C) clusters (latter two with scale parameter ). The sampling process is illustrated in the lower three panels: (D) raw angle map (scale parameter
) with quasi-random sample locations marked (number of points
), and sampled ‘neurons’ before (E) and after (F) noise was added (SNR = 3).
Figure 4.
Tuning functions and characteristic stimuli.
Examples of typical tuning functions of (A) EI cells and (B) peaked cells in pallid bat primary auditory cortex. Parametric tuning functions (solid lines) were fitted to the measured responses. EI neurons were assigned characteristic azimuth labels (indicated by dashed lines) where the fitted tuning function was equal to 50% of the maximum response. For Peaked neurons, the characteristic azimuth was defined as the peak of the fitted tuning function. IID tuning functions and characteristic stimuli were determined similarly.
Figure 5.
Comparison of the statistical power of seven map measures
(PC: Pearson distance correlation, SC: Spearman distance correlation, ZM: Zrehen measure, WL: wiring length, PL: path length, TP: topographic product, TC: topological correlation) when detecting (A) linear maps, (C) angle maps and (D) clusters. Power is summarized by the quantity , the mean number of points (e.g. neurons, voxels) required to achieve a statistical power of 80%; this is shown as a function of the SNR. Panel B shows the relative powers of the measures for linear map detection; here
is normalized by
, the
of the most powerful measure for a given map type and SNR. For the angle maps and clusters the scale parameter
and the insets show examples of the corresponding map type and scale. All axes have logarithmic scales. Missing data indicate that
is outside the range
. Uncertainty is depicted by shaded regions of
StdErr.
Figure 6.
Relative power of measures for detecting maps of various scales and types.
For each map measure, the plots show the number of data needed for reliable detection of angle maps (A, C, E) and clusters (B, D, F). To show the relative power more clearly, is normalized by
, the
of the most powerful measure for a given map type and SNR. The more powerful the measure, the lower it appears on the plots. It can be seen that the map type i.e. angle map vs. clusters, has little effect upon the relative powers of the measures; the ordering of the measures in terms of power is similar for both forms of map. All axes have logarithmic scales. Missing data indicate that
is outside the range
. Uncertainty is depicted by shaded regions of
StdErr.
Figure 7.
The effect of map scale on nonlinear map detection.
Larger scale maps can be detected with fewer data. Panel A shows (
of the most powerful measure) for angle maps and clusters at three different scales:
. Panel B shows the detectability of each type and scale of nonlinear map relative to a linear map with the same SNR i.e.
normalized by
for a linear map. All axes have logarithmic scales. Missing data indicate that
is outside the range
. Uncertainty is depicted by shaded regions of
StdErr.
Table 1.
Proportion of bats with significant tonotopic, IID and azimuth maps.
Table 2.
Map detection analysis of combined map data from all 8 bats.