Are there interesting cycles (other then the famous ones such as: Harris and Mumford's gonality divisor, the Gieseker-Petri divisor [which can be realized as the branch locus of a forgetful map from the space of admissible covers], and the Hain-Pixton double ramification locus) in $A^*(\overline{M}_{g,n})$ coming from Hurwitz theory?