Not sure that these are markers of gentrifying neighborhoods -- just as an example, the big red area on your Austin map next to the University of Texas is largely student housing, and has always been this way: students have little to no income, often have roommates, and the parking policies of the university ensure that many students have few options other than to live near campus.

Likewise, the map of Philadelphia misses most of south Philadelphia, an area that is gentrifying extremely quickly with several hundred million dollar condo developments set to go up in the middle of the ghetto.

Interesting statistics, but I don't know that the conclusions that the authors are trying to draw are valid.