Before revision:  We discuss the key differences between URLanization mechanisms with or without conservation and separated timescales, and in particular, we  scrutinize the implications of our findings in neuroscience, hopefully shedding new light into the problem of scale invariance  in cortical dynamics.
After revision:  We discuss the key differences between URLanization mechanisms with or without conservation and separated timescales, and in particular, we introduce the concept of URLanized collective oscillations' and scrutinize the implications of our findings in neuroscience, hopefully shedding new light into the problem of scale invariance in cortical dynamics.