deletions | additions       diff --git a/Sampling Spatial.tex b/Sampling Spatial.tex  index 1618a37..cf41992 100644  --- a/Sampling Spatial.tex  +++ b/Sampling Spatial.tex 
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In prior work and this paper, indicator functions provide the basis to partition the spatial domain into non-overlapping, evenly spaced, cuboidal volumes [ref]; an investigation of other basis functions are currently underway (e.g. wavelets). Equation ~\ref{??} defines the basis for the spatial domain as $\chi_{s}(x)$. $s$ is an index to a unique cuboidal volume $\omega_{s}$ in the spatial domain with the properties   \begin{equation}\label{eq-cubevol} \begin{equation} %\label{eq-cubevol}  \omega_{s} \cap \omega_{t} =   \begin{cases}   \omega_{s}, & \mbox{if } \mbox{s=t} 
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and  \begin{equation}\label{eq-cubevol2} \begin{equation} %\label{eq-cubevol2}  \chi_{s}(x) =   \begin{cases}   1, & \mbox{if } x \in \omega_{s}