Before revision:  Furthermore, for various fictitious present analysis times t_2, positioned in advance to bubble crashes, we employ a clustering method to group  LPPLS fits over different time scales and the predicted critical times t_c (the most probable time for the start of the crash ending the bubble) .
After revision:  Furthermore, for various fictitious present analysis times t_2, positioned in advance to bubble crashes, we employ a clustering method to group LPPLS fits over different time scales , where tc is the most probable time for the start of the crash ending the bubble) .