deletions | additions       diff --git a/subsection_Image_analysis_Pharyngeal_pumping__.tex b/subsection_Image_analysis_Pharyngeal_pumping__.tex  index c787d02..dc0d2ba 100644  --- a/subsection_Image_analysis_Pharyngeal_pumping__.tex  +++ b/subsection_Image_analysis_Pharyngeal_pumping__.tex 
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\subsection{Image analysis}  Pharyngeal pumping motion is readily 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{AveryThomas1997}. 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. 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. ****** got Subtracting consecutive frames that were captured 17ms 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 far as here ************ compared to background subtraction is that no model of the background needs to be calculated. When calculated for a high frame-rate movie of grinder motion, this entropy peaks sharply when pumping motion occurs while the effect of slower head motion is 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,  %\end{equation}  %where $\mu$ is the mean intensity difference. During pumps, this means will be higher than during pauses, such that the time series spikes at each pumping event (Fig. \ref{fig:entropy}D).  Subtracting consecutive frames isolates the fast-changing components in the image, resulting in a marked signal from the terminal bulb. The intensity distribution of difference values during a two frames with or without pumping shows marked differences (Fig. \ref{fig:entropy}B). The most obvious feature is the longer tail in the difference distribution, which comes from the larger number of pixels that experience a large change in value during a pump (Fig. \ref{fig:entropy}C). To get a time series - a temporal representation of this data- we require an order parameter. We calculate the entropy from the pixel distributions \cite{jing2004foreground}. Since the distribution of intensity values is well described by an exponential distribution (\ref{fig:entropy}C), the expected entropy for a single frame is   \begin{equation}  S = 1 + \log \mu,  \end{equation}  where $\mu$ is the mean of the exponential distribution. During pumps, the means is expected to be higher than during pauses, such that the time series spikes at each pumping event (Fig. \ref{fig:entropy}D).  This order parameter results in a good signal- to-noise ratio across different imaging conditions.   We now identify peaks in the difference image entropy, using monotonicity detection after filtering, which correspond to pumping events.  
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  Since the animals are stably confined in a straight posture in the microfluidic devices and locomotion can only occur in the direction of the channel, we can create a kymograph of the pumping motion. The kymographs shows the characteristic triangular shape when a pump occurs. Kymographs enable easy visual inspection of the trajectories; Additionally, the image analysis frame work contains an interactive verification script: The user can manually click on pumps in the kymograph to compare the automatic tracking and the visual inspection. This method was used to assess the tracking accuracy in Fig. \ref{fig:longtimeseries}.     ****** got as far as here ************