  In this work we investigate how future actions are influenced by the previous
ones, in the specific contexts of scientific collaborations and friendships on
social networks. We are not interested in modeling the process of link
formation between the agents themselves, we instead describe the activity of
the agents, providing a model for the formation of the bipartite network of
actions and their features. Therefore we only require to know the chronological
order in which the actions are performed, and not the order in which the agents
are observed. Moreover, the total number of possible features is not specified
a priori but is allowed to increase along time, and new actions can
independently show some new entry features or exhibit some of the old ones. The
choice of the old features is driven by a degree-fitness method. With this term
we mean that the probability that a new action shows one of the old features
does not solely depend on the "popularity" of that feature (i.e. the number of
previous actions showing it), but is also affected by some individual traits of
the agents or the features themselves, synthesized in certain quantities,
called "fitnesses" or "weights", that can have different forms and different
meaning according to the specific setting considered. We show some theoretical
properties of the model and provide statistical tools for the parameters'
estimation. The model has been tested on three different datasets and the
numerical results are provided and discussed.
