On some generalized reinforced random walks on integers
  We consider Reinforced Random Walks where transition probabilities are a function of the proportion of times the walk has traversed an edge. We give conditions for recurrence or transience. A phase transition is observed, similar to Pemantle \cite{Pem000} on trees. 
Olivier Raimond (MODAL'X), Bruno Schapira (LM-Orsay)