deletions | additions       diff --git a/subsubsection_Genus_Statistic_Genus_statistic__.tex b/subsubsection_Genus_Statistic_Genus_statistic__.tex  index 4d6c3f1..d72c78d 100644  --- a/subsubsection_Genus_Statistic_Genus_statistic__.tex  +++ b/subsubsection_Genus_Statistic_Genus_statistic__.tex 
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\subsubsection{Genus Statistic}  Genus statistic statistics  characterize spatial information in a data map by assigning a topology. identifying and counting minima and maxima.  They essentially compute the difference between the number of isolated features, or peaks, and holes, or voids, above and below a given threshold. threshold, respectively.  Beginning with the work of \citet{gott86}, genus statistics have been frequently used in cosmological studies to characterize the distribution of mass in the universe. \citet{kowal07} were the first to adopt genus statistics to study interstellar turbulence. They analyzed density and column density maps produced by MHD simulations and found that the shape of the distribution correlates with the sonic Mach number. This analysis was extended to observational data of the Small Magellenic Cloud (SMC) by \citet{chepurnov08}. To compute the genus statistic for each output, we normalize the integrated intensity map and convolve it with a 2D Gaussian kernel with width of 1 pixel. This smooths the map so that small scale variations and noise do not contribute to the number of features.  %(of width 1--don't know where to put this, also just writing it to not forget - need check unit for the width of 1).