deletions | additions       diff --git a/subsubsection_Description_We_used_a__.tex b/subsubsection_Description_We_used_a__.tex  index e7f6eae..05b865a 100644  --- a/subsubsection_Description_We_used_a__.tex  +++ b/subsubsection_Description_We_used_a__.tex 
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Furthermore this dataset provides both positions and accelerations, which are the data we were looking for.  \subsubsection{Extraction of data}  For our experiments we used only data during a restricted period of several minutes beginning at arbitrary time of the play. Computationnalywe defined a  trajectory will be defined  as a set of ordered x and y-axis 2-dimensional  positions and accelerations regularly distributed in time. Furthermore we will handle a set of synchronized trajectories. This synchronization is highly important since we will used it when we will approximate the joint probability distribution of positions or accelerations of two players.  Data are read and extracted with a 25Hz frequency which corresponds to the best frequency we could have if we were extracting the trajectories directly from the videos of the soccer match. As each players is equipped with several sensors we combine their data to have one and only one trajectory per player.