  Understanding the innovation process, that is the underlying mechanisms
through which novelties emerge, diffuse and trigger further novelties is
undoubtedly of fundamental importance in many areas (biology, linguistics,
social science and others). The models introduced so far satisfy the Heaps'
law, regarding the rate at which novelties appear, and the Zipf's law, that
states a power law behavior for the frequency distribution of the elements.
However, there are empirical cases far from showing a pure power law behavior
and such a deviation is present for elements with high frequencies. We explain
this phenomenon by means of a suitable "damping" effect in the probability of a
repetition of an old element. While the proposed model is extremely general and
may be also employed in other contexts, it has been tested on some Twitter data
sets and demonstrated great performances with respect to Heaps' law and, above
all, with respect to the fitting of the frequency-rank plots for low and high
frequencies.
