In the case of finding yourself within a few paces and under threat of a predator:
I have one personal experience with a man with malicious sexual intentions following, talking, making body contact, shying away, being told to fuck off, and continuing to follow me while unbuckling his belt (I am a male).
The solution (while I could have ran, I was not content with the chance of being caught off balance or seeing where I live or anything like that) came in holding my ground, raising a clenched fist and very present-mindedly yet firmly agressive, stating "I will fucking hurt you".
It seems likely that making that kind of explicit statement triggers a cost-benefit analysis in a predatory mind who is looking for pleasure (maybe both sexual and sadistic) without physically engaging them: verbally letting them know that you are ready, capable, and that any attempt will involve YOU hurting THEM.
Certainly some relevant information in these recent posts on learned blankness (comments are a goldmine) and building small skills in the right order.
I've experienced a notable increase in acuity of focus, multi-tasking, list-making and avoiding unnecessary mental hiccups through a few things:
practicing mental math on the 3-4 digit arithmetic practice on Khan Academy (which interestingly enough, while I did not consciously define it, taught me to approach learning in a rather similar manner to that described in the two LW posts linked above)
sites like Lumosity, Cognitive Fun, and especially (Brain Workshop's)[http://brainworkshop.sourceforge.net] Dual N-Back Game and another game which I have lost the link to involving visually tracking multiple objects (gems in this game's case) - hopefully someone will come along with the link!
reading papers (articles, lectures, etc) as a group, out loud, slowly, and answering questions as they arise, allowing for as much as several hours over coffee in a quiet room to read even something that's only a handful of pages long. It helps to encourage deep discussion but to have someone around to keep the conversation relevant, as it tends to stray too far off course.
going over a Bach piece as a group with someone who understands, even if vaguely, music theory and counterpoint and following the voices and how they interrelate.
I suppose that's what I've got to contribute for now. Possibly more later. YMMV, this is largely anecdotal aside from the flash games.
Think about things you don't know how to do. :)