HR is "Heart Rate" and AF is "Atrial Fibrillation". "Heart Rate" is just how many times the heart beats in a minute. "Atrial Fibrillation" is an abnormal rhythm of the heart beat and the rate at which the heart beats in AFib can be normal or fast.

Would the reverse be to use the anal-log?

i choose to believe it means rhythmic sneezes

I thought hearts went 'lub dub' instead of 'wee woo' - I would've said it's more tangent or some transformed Gaussian at best?

You recall incorrectly. It was a check for GI bleed prior to anticoagulant administration prior to cardioversion. They were literally running through pre-procedure tests in order to do the standard treatment for AF.

Source: The paper itself