typo

paper/paper.tex

@@ -78,7 +78,7 @@
 \maketitle
 
 \begin{abstract}
-We use simulations to build an explicit probability distribution for
+We use simulations to build an analytic probability distribution for
 the asphericity in the satellite distribution around Local Group (LG)
 type galaxies in the Lambda Cold Dark Matter (LCDM) paradigm. 
 We use this distribution to estimate the  atypicality
@@ -277,7 +277,7 @@ \section{Introduction}
 distance fixed \citep{2017AN....338..854P}. 
 We characterize the satellites in terms of the scalars describing its
 deviation from the spherical distribution. 
-We then build an explicit analytic probability distribution for the
+We then build an analytic probability distribution for the
 asphericity; this solves the problem of having a common reference
 point to compare simulations.  
 We use a simulation to estimate the parameters in this distribution to
@@ -583,11 +583,11 @@ \subsection{Characterizing Asphericity}
 This allows us to build a normalized version of all quantities of
 interest by subtracting the mean and dividing by the standard
 deviation of the values from randomized samples.
-We use the normalized quantities to build the explicit probability
+We use the normalized quantities to build the analytic probability
 distributions for the scalars describing asphericity. 
 
 
-\subsection{Building an explicit asphericity probability distribution}
+\subsection{Building an analytic asphericity probability distribution}
 
 After building the normalized variables with the simulated data we
 perform a Kolmogorov-Smirnov test with the null hypothesis of belonging
@@ -978,7 +978,7 @@ \section{Conclusions}\label{sec:conclusions}
 multivariate normal distribution.
 
 
-The focus of our approach was building an explicit probability
+The focus of our approach was building an analytic probability
 distribution for the observables of interest, instead of trying to
 find simulated objects that fulfill different observational criteria. 
 This approach is particularly useful in the case of atypical
@@ -989,7 +989,7 @@ \section{Conclusions}\label{sec:conclusions}
 
 An extension of this framework to outliers in higher order deviations
 (i.e. coherent \emph{velocity} structures) should also be possible, 
-provided that an explicit probability distribution for the scalars of
+provided that an analytic probability distribution for the scalars of
 interest can be built.  
 The approach presented here is also useful to gauge the influence of 
 influence of different physical elements includes the simulation. 
@@ -1007,7 +1007,7 @@ \section{Conclusions}\label{sec:conclusions}
 responsible for the extreme features observed in its satellite
 distribution. 
 
-\section*{Acknowledgements} 
+\section*{Acknowledgments} 
 JEFR acknowledges support from COLCIENCIAS Contract No. 287-2016,
 Project 1204-712-50459 and the European Union's Horizon 2020 Research and Innovation
 Programme under the Marie Sk\l{}odowska-Curie grant agreement No 73437