deletions | additions       diff --git a/subsection_Image_analysis_Pharyngeal_pumping__.tex b/subsection_Image_analysis_Pharyngeal_pumping__.tex  index 52dbf91..1be77ce 100644  --- a/subsection_Image_analysis_Pharyngeal_pumping__.tex  +++ b/subsection_Image_analysis_Pharyngeal_pumping__.tex 
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Pharyngeal pumping motion is most easily detected through the motion of the grinder -- a cuticle region of the pharynx inside the terminal bulb that is used to crush bacteria to aid digestion \cite{avery199724}. At low magnifications, directly tracking the position of the grinder is ineffective: the amplitude of grinder motion is small and any translation or deformation of the head will compromise the data. Therefore, our approach relied on intensity differences between consecutive images and on the separation of timescales between head motion and pumping (Fig. \ref{fig:entropy}A-B). Key to this approach is a high imaging rate, 60 fps, as compared with the maximal instantaneous rate of pumping, 6 Hz. The position if the head is maintained by mounting the animals into the WormSpa microfluidic device such that tracking a moving animal is not required and the motion of the head is dampened without a major impact on feeding \cite{kopito2014durable}.   Subtracting consecutive frames that were captured 16ms apart isolates fast-changing features, i.e., the motion of the grinder. Examples of distributions of intensity differences in the presence or absence of a pump are shown in Fig. \ref{fig:entropy}C. Notably, rapid motion affects the tail of this distribution. Therefore, a measure that preferentially weighs the tail would enhance the signal to noise ratio of motion detection. Using the entropy, $\sum_i p_i \log p_i$ (where $p_i$ is the probability of observing intensity $i$ in the difference image), to enhance the significance of motion achieves this goal \cite{jing2004foreground}. An additional advantage of this method as compared to background subtraction is that no model of the background needs to be calculated. When calculated for In  a high frame-rate movie of grinder motion, this the  entropy of intensity differences  peaks sharply when pumpingmotion  occurs while the effect contributions  of slower head motion is motions are  minor. In our hands, imaging conditions did not require fine tuning in order to maintain a signal to noise ratio that exceeded $200\%$ (\ref{fig:entropy}D-E). %Since the distribution of intensity values is approximately exponential, the entropy for a single frame is   %\begin{equation}  %S \simeq 1 + \log \mu,