Universal statistics of terminal dynamics before collapse

Recent biological developments have both drastically increased the precision as well as amount of generated data, allowing for a switching from pure mean value characterization of the process under consideration to an analysis of the whole ensemble, exploiting the stochastic nature of biology. We focus on the general class of non-equilibrium processes with distinguished terminal points as can be found in cell fate decision, check points or cognitive neuroscience. Aligning the data to a terminal point (e.g. represented as an absorbing boundary) allows to device a general methodology to characterize and reverse engineer the terminating history. Using a small noise approximation we derive mean variance and covariance of the aligned data for general finite time singularities.