Before revision:  We study a general representational model of path integration in which the self-position is represented by a vector formed by the activities of a population of grid cells , and the  self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.
After revision:  We study a general representational model of path integration by grid cells, where the 2D self-position is represented by a vector formed by the activities of a population of grid cells , and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration.