I often use the pattern 'I appreciate your noticing this' but recently decided it sounds strange, and switched to 'you'. (I do this with different verbs; this is just an example.) Are they both valid?
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POSS_-ing_gerund complement), or in an objective (originally accusative) form (you, him, Mr. Smith -- this is called anACC_-ing_gerund complement). There is no grammatical difference. – John Lawler Apr 30 '14 at 18:37