Delete a publication from my activity wall

You can delete publications that you don't want to appear on your activity wall. 

You can do this by clicking on the arrow at the top right of the post, as shown below. Then select "delete this news item". 

The deletion is then definitive.

This does not result in the deletion of all the publications of the member concerned, just the publication itself. If you want to block a member's posts, you need to go to your privacy settings, or block the member in question.