deletions | additions       diff --git a/subsubsection_Description_We_used_a__.tex b/subsubsection_Description_We_used_a__.tex  index 05b865a..f4f7f52 100644  --- a/subsubsection_Description_We_used_a__.tex  +++ b/subsubsection_Description_We_used_a__.tex 
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For our experiments we used only data during a restricted period of several minutes beginning at arbitrary time of the play. Computationnaly trajectory will be defined as a set of 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 player  is equipped with several sensors we combine their data to have one and only one trajectory per player. Sometimes some data have been missed, we but one can  cope with this problem interpolating data so as to maintain synchronization between the different trajectories. When a player goes out of the field we can't neither treat it as usual with positions out of the field because it would be non sense nor stop extracting the data because it would break the continuity of extracted player's position. Whereas the displacement of a player going and fetching the ball out of the field is non sense, the paths of other players at this while bring relevant information. Thus in this case we just consider that the outside player remain at the last read position on the field with a null acceleration.