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The solid squares represent constituents of a sentence (usually words) that have already been parsed. They are connected by a solid line, which suggests that they have been assigned a (syntactic) structure.

On the other hand, the square on the right side represents a sentence constituent that was just encountered. It still has to be integrated into the sentence structure, which is represented by the dashed line. Notice that the line connects to the leftmost constituent. This represents a long-distance integration into the already existing sentence structure, across the constituent in the middle. These long-distance integrations are what a lot of work in our lab is about (see projects).