The subject of this exercise is the arpeggiated version of the Melodic Minor Scale starting on it's 4th scale degree (Lydian Dominant), over a minor ii-V7-i root movement.
A wealth of information on Melodic Minor harmony can be found in previous posts on this blog, together with ii-V7 exercises.
C-D-E-F#-G-A-Bb
This scale goes by the name of C Lydian Dominant, which happens to be the mode built from the 4th scale step of G Melodic Minor (Jazz Minor). If we play this arpeggio over an E bass note, we get the sound and function of an E-7b5, the ii chord in the key of D minor.
The rule to remember here is: All Melodic Minor roots and modes are interchangeable with each other.
In measure #1, you're simply playing the sound of G Melodic Minor over E.
The exact same treatment applies for measure #2.
The arpeggio, in this case Eb7#11 13, moves up a minor 3rd from measure #1, while the bass note moves up a perfect fourth or down a perfect fifth to A, forming an A7alt (V7 chord).
The notes of this arpeggio create an Eb Lydian Dominant scale
Eb-F-G-A-Bb-C-Db
which is the 4th mode of Bb Melodic Minor. We are, therefore, hearing the sound of Bb Melodic Minor over A (aka: A altered, A altered dominant or A half tone / whole tone).
A common device, effective when used sparingly, is to play a Melodic Minor phrase on the ii chord, and repeat that phrase exactly on the V chord, transposed up a minor 3rd.
This is what's been done here fin the first 2 bars.
Measure #3 (i chord) is made up of an A Pentatonic b6, (A-B-C#-E-F, derived from scale steps 5-6-7-2-b3 of D Melodic Minor). Mucho info on Penta b6 is available on these blog pages, as well as in the available books.
Measure #4 continues the D minor, tonic i chord resolution.
Why was the 7#11 13 arpeggio chosen for this exercise?
Because............It sounds good; and `as the Duke of Ellington once proclaimed: "If it sounds good, it is good!"
Diggeth I do, your Dukeness!