The Up/Down

When you're seated or on your back and your opponent is standing above you, this is what I call the up/down position. I'm not sure where I got that from, I know it's not something I created, but I don't hear it that much, so sorry to whoever I coopted that from. Anyway, this is a strange position, because it's used across all facets of the Jiu Jitsu spectrum, but not really the same way across any of them.
Sport BJJ- if you wind up in this position in sport BJJ or pure grappling situations a sit up guard is usually the best course of action without established grips, then once you establish grips, you can return to a supine position to launch attacks or continue forward to wrestle up. Remaining on the ground without grips leaves easier avenues for both leg locks and passing as far as your opponent is concerned.
MMA- When we look at the up down position in MMA, it would be unwise to approach the situation by sitting up as there is a high risk of being struck. It is unlikely that the upright person will dive on a leglock as the consequences of giving up top position are greater, allowing us to protect ourselves by keeping our feet in the air, you must continue to fight for the whole round, and usually there is a limit on how much time the referee will allow this position to go on as oftentimes it creates a stalemate. I feel like this unique set of constraints almost negates this position in MMA, although being able to do it well would definitely be an ace in the sleeve of a BJJ based MMA fighter.

Self-Defense- This is an interesting one because if you find yourself on top, you no longer need to engage, but if you are on bottom, it is imperative that you act swiftly and violently. In a setting devoid of rules, if I end up on the ground, my immediate goal is to get back up by any means necessary. That could be strikes, submissions, sweeps, whatever gets me off the floor and able to disengage most quickly is what I need to do. 
*LEO's exist in this area, but in an even more unique situation, because you need to apprehend the other party in this scenario. If you'd like to discuss this further, I welcome you to my cop class at 3pm every Friday.