deletions | additions       diff --git a/subsubsection_Dendrograms_We_use_Dendrograms__.tex b/subsubsection_Dendrograms_We_use_Dendrograms__.tex  index 6b9033a..20b70a5 100644  --- a/subsubsection_Dendrograms_We_use_Dendrograms__.tex  +++ b/subsubsection_Dendrograms_We_use_Dendrograms__.tex 
...
\subsection{Dendrograms} \subsubsection{Dendrograms}  We use Dendrograms to organize the hierarchical structure of our intensity maps. Figure (the one under the Dendrogram section at the very bottom of this authorea feed) (Basic Dendrogram)  provides a simple 2D depiction of a Dendrogram. We To create one, we  identify the peak intensity value in a data set, classify it as a "leaf", and catalog other local maxima at smaller intensities, intensities  also classified as "leaves". The intensities attached to particular leaves are known as "branches." This technique allows one to visualize local features of intensity levels appearing within our synthetic observations, as visualized in Figure ???. observations.  To account for simulated noise in our data maps, we set a minimum distance between two local maxima, referred to as a  "minimum deltas." delta."  Increasing the minimum delta value decreases the total number of features (necessary?). We refer the reader to Rosolowskly et al. (2008) for a complete description of applying Dendrograms to Molecular Cloud structures. Koch et al. (2015) defines two Dendogram statistics: the Number of Features Statistic and the Histogram Statistic. To compute the Number of Features Statistic, we generate multiple Dendrograms per run, varying the minimum delta parameter, and count the total number of features associated with each minimum delta. We follow the analysis of Koch et al (2015) (I'm using this alot, any other way to word this? Come back to this) and use an array of minimum delta parameters (maybe type this out in symbols similar to how Eric does it?) (symbols instead?)  ranging from 10^-2.5 K to 10^0.5 K in 100 logarithmic steps. Figure 12 depicts our Histogram statistic