Abstract. 
I will start with reminding the audience of my earlier work on the vanishing 
noise limit of diffusions in noisy heteroclinic networks based on sequential 
analysis of exit locations and exit times for neighborhoods of unstable 
equilibria. After that I will talk about extending these results to longer time
scales and the emergent hierarchical structures based on polynomial transition 
rates (rather than exponential ones of the Freidlin--Wentzell metastability).
 This is joint work with Zsolt Pajor-Gyulai and Hong-Bin Chen. If time permits, 
I will also talk about using exit times to model decision times in psychology 
and incubation periods in medicine.