A great variety of scales across the world differ in the way they go up and down. Some examples that come to mind are the Melodic minor that has A and B natural going up but Bb and Ab going down. A similar phenomenon can be observed in the Desh raga and Maqam Rast (see example below).
Notably, all three scales use "sharper" or "raised" pitches going up, and "flattened" or "lowered" pitches going down.
Has this topic been studied? I am especially interested in the ubiquity of this phenomenon across cultural boundaries.