It is said that "To give added punch, articles are often dropped in the titles"
Is there any general rule or reference about dropping articles, especially in academic research papers?
Omitting an article (definite or indefinite) in a newspaper title is done for brevity and in order to attract more attention. There are some rules regarding titles (and they basically apply to newspapers and magazines and not to research journals). Firstly, usually Simple Present is used regardless of the time position of the action (which is usually in the past). Elaborating a bit more on the use of tenses, titles like "Egypt and Israel Move to Halt Growth of Crisis" (in The Herald Tribune, International) are quite interesting as the infinitive form "to halt" yields a shorter title.
Regarding articles, you may drop them as soon as the meaning remains clear. An example from "The Times, UK" is the title : "Fees will create class of stay-at-home students" while usually one would say "...a class...". The newspaper "Daily Mail, UK" on the other hand, in which journalists are not sparing with titles' length, you find titles like "How the rebels planned assault on Tripoli: Call to arms for 'sleeper cells' came from mosques". So it is more like a "rule of thumb" rather than a grammar rule.
In scientific papers in particular you can be more explicit and usually articles are not dropped.
The particular context of "To give added punch" is about movie/book titles. That's really an aspect of marketese, which probably has little to do with OP's question.
In general, I think this question (about in [the] hospital) shows that there are no hard-and-fast rules, but sometimes there are cases where standard usage differs between US and UK.
I am not a native speaker, but my teachers have taught me not to use any articles in titles. However, I am not completely sure that this is a general rule. I am translating a text about a faculty now and I feel that articles are just needed...if we speak about fees, professors, etc. I feel like putting THE over and over again, because we think of a specific faculty.. What is more, I believe it is okay to omit articles in newspapers, because we want the news to be short and shocking, but in some other places, a word more or less does not make a big deal.