When to omit the article before a noun?

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.

Are there other rules that apply regarding the omission of articles before nouns? What is the correct way to formulate the above examples? Does including/excluding the article change the sentences meaning?

Related questions:
Why do people omit the definite article?, Omitting article before "evaluation"