Omit colons and full stops after headings in research papers
Headings or headlines are a special kind of text and are not as rigidly governed by conventions of punctuation. In particular, whenever a heading is on a separate line (the text that follows the heading starts on the next line below the heading), it is pointless to end it with a colon or a full stop. The Publications Office of the European Union  puts the matter succinctly: "Do not use colons at the end of headings or to introduce a table or graph set in text matter."
Such punctuation does not help readers; in fact, it has been shown to affect comprehension. A study that specifically addressed this point found that headlines that ended in a full stop lowered comprehension . As Darren Rowse puts it , "Full stops, like their name suggests, are something that halts the eye of your reader. . . . [whereas] titles are all about leading your reader into your post."
However, minor headings are sometimes followed by full stops or colons, but only when they are "run on" (text continues on the same line immediately after the heading). Even then, the punctuation can be dispensed with if the headings are set in bold or italics. This, however, is a matter of style: if your target journal uses colons or full stops after such headings, you should do the same.
 Publications Office, European Union. [no date]. House rules for the preparation of the text. <http://publications.europa.eu/ code/en/en-4100100en.htm>
 Harrison K. [no date]. Bringing a headline to a full stop. <www.cuttingedgepr.com/ article/coreprskills_headline_to_full_stop.asp>
 Rowse D. 2006. Full stops (periods) in titles. <www.problogger.net/ archives/2006/09/26/full-stops-periods-in-titles>
Another comma-related question that eludes many authors has been discussed in this post: Research paper: Comma after "etc." at the end of a sentence.
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