The difficulty of mining slides up and down depending on the block rate.

As the profitability drops, some miners will stop, the block rate will drop and the difficulty will drop until things balance again.

But I wonder if there is some kind of minimum amount of mining required to verify X number of transactions. If there are many transactions, but few miners, then would transactions begin taking too long to become verified?

Yes, there is a byte limit to the size of a block. If blocks become infrequent enough due to decreased mining power, it's conceivable that a backlog of transactions would build up. At the next difficulty adjustment, though, speed would pick back up again.

Geoffrey Hinton "Next Generation Neural Networks"

http://www.youtube.com/watch?v=AyzOUbkUf3M

-It is more biologically plausible then any other NN algorithm I've seen

-It results in creativity (in the video he has the computer "imagine the number 2")

-It pretty much explains why we need to sleep/dream. The network has to be run both forward (accepting sensory input) and backwards (generating simulated sensory input) in order to learn

-It emphasizes the point that the brain is NOT trying to do matrix multiply (or any other deterministic calculation) with random elements (if it was trying to be an analog computer it would be). The randomness is an essential part of the algorithm.

I agree. Hopfield networks, of which Hinton's Boltzmann machines are substantial elaborations, have many human-like properties:

-can fill-in details as a result of noisy or missing input -can sometimes "see" patterns in random noise