Ron ,
In one of the posts you mentioned :

Quote:
you cannot write "proof of ... fields ... posing". this kind of construction is just wrong.
sorry.
this is going to annoy a lot of people, because this sort of construction is bread and butter in spoken language,
BUT:
if the focus of the construction is the ACTION, then you must use the POSSESSIVE form for the noun/pronoun preceding the "-ing" participle. since that's fatally awkward to say in words, i'll provide an example:
everyone laughed at me accidentally walking into the girls' bathroom --> WRONG. sorry. this sentence would actually mean that everyone laughed at me as they were walking into the girls' bathroom.
everyone laughed at my accidentally walking into the girls' bathroom --> CORRECT, because it's the action (my walking into the bathroom, not really me) that they're laughing at.

so, incredibly enough, the correct version of the sentence here would actually be "the fields' posing ...".
the gmat considers such constructions fatally awkward, and won't include them in correct answers (i believe this has been articulated in the official guide at a couple of different points, so i'm not just making an empirical claim). therefore, you can ignore such constructions outright, and eliminate choices that contain them.

incidentally, if the focus of the construction is the NOUN (or pronoun) itself, then you don't use a possessive. for instance:
i saw him walking down the street --> correct, because it was him i saw, not his walking action. this sentence is, however, ambiguous, because either he or i may have been the one walking down the street.
i saw his walking down the street wouldn't be incorrect, but it would be a bit strange, unless i'm a modeling scout who actually analyzes the gait of random strangers as they walk down the street.
Can you explain me this concept?

Shivani

it's not clear what concept you're asking for help with here, because you have not clearly demarcated Ron's quote and identified what part of it you had trouble with..

_________________
Tim Sanders
Manhattan GMAT Instructor