We, myself and Jürgen, have just submitted our paper to Whotopia magazine. They have received it and it's now in review. Hopefully it will make the cut and appear in issue 25 of the magazine.
It's a short little essay, only 1,500 words so it's not a very deep paper. But seeing it's the first one I'm involved with I needed to start somewhere. And everyone involved thinks it went well. Even the proofreader who bleed all over it making sure the grammar was correct and all the commas that should have been there were re-inserted. It's nice to have a grammar-nazi for a friend.
First we did a basic analysis of the Doctor's friends network starting from 1963 when he abducts his first two Earth companions and it goes up to the end of series six. In essence it shows that no matter how long the show has gone on the network of friends stays pretty much in the shape of very tight ball. Almost everything is completely connected. And yes, Sarah Jane had quite a bit to do with that one with her meeting both the Tenth and Eleventh Doctors.
The second part deals with the viewpoint of many fans that the companions are getting younger, especially in the new series. By means of higher maths [that's Jürgen's job] and a hell of a lot of data mining [that's my job] we show that the fact is, No - they've always been that young. And the new companion is right in the middle of the average age.
I enjoyed writing this paper and we plan on doing more in this field. Considering that there's nearly 50 years of data it would take quite a while to run out of things to do.