Depends which of the examples you are looking at, as from my quick look they appearing kind of dated.
Depending what version of Tornado and Python you are running, mostly likely there is newer caller styles that you can look at.
Stop by the
Tornado.org latest documents and look at the sample code Ben has in there as it may give you more ideas.
Beware as there is lots and lots of old sample code floating about on SO and Gist so keep an eye on when it created as lots of new subtle call adjustments have been added in last few years and that old stuff can send you down the rabbits’s hole needlessly.
-Kevin