Dynamic Substrate for the Physical Encoding of Sensory Information in Bat Biosonar

Quantitative approaches to sensory information encoding by bat noseleaves and pinnae

“…Based on this similarity measure, transfer functions can be grouped into a given numbers. Spectral clustering (based on an eigenvector decomposition of a similarity matrix containing the Euclidean distances between all possible transfer function pairs (Luxburg 2007)) has been used successfully for this purpose (Müller et al 2017). The results of this clustering exercises are noteworthy for their own sake, because they have demonstrated that the analyzed beampatterns consist of patches of similar transfer functions (s. Figure 1).…”

“…However, discretization creates its own issues since biased estimates will be obtained if the discrete bins that are used to represent the beampatterns are either too wide (entropy will be underestimated) or too narrow (entropy will be overestimated. An optimal bin width can be determined by testing estimates obtained over a large range of different alphabet lengths against a randomized reference (Müller et al 2017). In this way, the alphabet length can be used a variable that is adjusted to get the best possible estimate for the entropy in the signal.…”

“…One way to estimate how much additional sensory information could be encoded through changes in the noseleaf and pinna shapes during pulse emission and reception is based on the mutual information (Cover and Thomas 1991) between the beampatterns associated with different shape conformation stages of these structures (Müller et al 2017). In this approach, each beampattern is considered as a random function of direction and frequency.…”

“…An analysis of beampatterns obtained through numerical predictions from horseshoe bat noseleaf and ear shapes as well as measurements from physical models of these structures has yielded normalized mutual information estimates that were typically around 20% for pairs of different shape conformations (Müller et al 2017). This indicates that by changing the shapes of their noseleaves and ears bats are able to encode substantial amounts of additional sensory information into the signals that are received at the animals' ear drum.…”

“…Discretization of the beampatterns has been accomplished by using the transfer function (gain as a function of frequency) associated with each direction (Müller et al 2017): Each transfer function (sampled at discrete frequencies) can be represented as a vector for this purpose. The similarity between the vectors associated with different directions is quantified by their Euclidean distance.…”