As stated previously, the electrical example, though different from most usage, makes an easier case for distinction. A transformer only changes one attribute, so that the result is the same basic type, but of a different capacity or intensity (voltage for example). A converter, on the other hand makes the resulting object different in type from then initial condition, for example changing alternating current to direct current.
If we could apply this in general, then most of us would be in error in our usage of the two words. Convert would mean something's natural attributes were changed, transform would mean the the size, shape, color, or some other attribute was changed, but the root nature of the item (or attitude or belief) was not changed.
Infamous is strictly negative. Even if it is about fame, this is always negative fame. It's almost never used figuratively, or tongue-in-cheek. It's negative fame, be it due to bad failures, or due to evil conduct.
Notorious is more often than not used as a more neutral "famous" - used in contexts, where you want to limit the positive connotation be it not to sound overly flattering or as tongue-in-cheek expression of limited praise. You can be a DJ notorious in clubs of your city, a notorious speaker at Sci-Fi conventions, a notorious hacker with three hundred security advisories published to your name. These don't strictly imply what you do is wrong, they just say you are widely recognized, and simultaneously don't try to trump up your achievements.
Notoriety is more about insistence, being known for repeating your activity, without actually creating anything very notable, while fame or infamy may be about popularity possible to gain with a single truly spectacular performance. Notorious is often used humorously, due to lack of inherent positivity (presenting a positive fame in mock sinister light) and implied insistence, stubbornness (becoming known despite failure to achieve genuine fame, implying poor quality of "production", insufficient to be called "famous".)
As result, fame and infamy are "stronger" than notoriety, and notoriety is more neutral.
Edit: an example of this usage for Mary-Lou.
The notorious Robert Downey Jr. known for his role of Iron Man, takes the character of Tony Stark, the incorrigible playboy genius philantropist billionaire out of the stage and adopts it as his own. Asked by a reporter, "Tony, could you... sorry, Robert..." - answers, oozing humility, "No, Tony is fine. Tony is perfectly fine." He hides snacks all over the movie stage and pulls them out during filming, taking wild liberties with the script and causing woe both to other actors and the director (and allegedly not just for "artistic license", but simply because he doesn't bother to learn his proper script!) Take the scene from "Avengers" when he serves peanuts to other members of the team, it's completely spontaneous.
[now, there is no doubt Robert Downey Jr. is simply a famous actor, but his antics, ego, and style make the word 'famous' simply miss the point - he's not loved for being a famous actor, but for being the notorious Tony Stark.]
Best Answer
The main nuance is that using "on" makes the cases the subjects of the experiment; they are the things upon which you are experimenting. Using "with" makes the cases instrumental; they are the things you are using to conduct the experiment. From a literal standpoint they pretty much mean the same thing, but there's a subtly different emphasis on the role the cases are playing in the experiment.
Consider the following:
This implies a less consensual situation where the people didn't really have much say in whether the experiment happened or not. They're subjects rather than being involved directly.
This gives a connotation of mutual interest in the experiment; the people were willing participants.