Sliding
Exercise A
This exercise is Petrucci-esque, it's a technique he frequently uses when playing the harmonic minor scale as, yet again, it's dirrivative of something very middle-Eastern. The note sequence is a very simplistic descend in E harmonic minor, but the positions shifts while adding "slide-in's" before every note is something to practice. It feels unnatural, but it's a great technique and can be executed in any musical context.
Exercise B
This exercise is very funk-oriented. We're in the key of F#m, playing through some arpeggios (F#m7, Amaj7) and finishing up with some regular old note sequences diatonic to the key.
The slide-in notes, added before some of more "isolated" notes, create a very jazzy "accidental" sound. Some of the notes being executed would not normal work in the given key if they were to be played alone, but by quickly hinting at them, phrases such as this can really come to life and sound a little more refreshing.