I am confused about when one can omit the article "the"/"a" in front of a noun. Examples are
During (the) observation, it was noticed that ...
The results of (a) quantitative evaluation are listed in table 2.
(A) quantitative analysis shows that ...
(The) execution of the algorithm is very fast.
In all of these, omitting the article feels more natural to me. I tried to verify my gut feeling by comparing the sentences to the rules presented here, but I can't find any rule that justifies the articles' omission.
What is the correct way to formulate the above examples? Is my feeling just wrong? Also, does including/excluding the articles change the sentences' meaning?