  Many complex systems find a convenient representation in terms of networks:
structures made by pairwise interactions (links) of elements (nodes). For many
biological and social systems, elementary interactions involve however more
than two elements, and simplicial complexes are more adequate to describe such
phenomena. Moreover, these interactions often change over time. Here, we
propose a framework to model such an evolution: the Simplicial Activity Driven
(SAD) model, in which the building block is a simplex of nodes representing a
multi-agent interaction. We show analytically and numerically that the use of
simplicial structures leads to crucial differences in the outcome of
paradigmatic processes modelling disease propagation or social contagion, with
respect to the activity-driven (AD) model, a paradigmatic temporal network
model involving only binary interactions. In particular, fluctuations in the
number of nodes involved in the interactions can affect the outcome of models
of simple contagion processes, contrarily to what happens in the AD model.
Moreover, social contagion models such as cascading processes present a much
richer phenomenology and can become extremely slow when occurring on evolving
simplicial complexes.
