  Often in the setting of human-based interactions, the existence of a temporal
hierarchy of information plays an important role in diffusion and opinion
dynamics within communities. For example at the individual agent level, more
recently acquired information may exert greater influence during
decision-making processes. To facilitate further exploration of this effect, we
introduce an efficient method for modelling temporally asynchronous opinion
updates, where the timing of updates depends on the timing of incoming opinion
states received from neighbours. The framework enables the introduction of
information arrival-time lag by means of lag-vectors. These are used to weight
the relevance of information received by agents, based on the delay between its
receipt and the subsequent opinion update. The temporal dynamics (i.e. the
times at which information is transmitted) are governed by an underlying
algebraic structure called max-plus algebra. We investigate the resulting
continuous opinion dynamics under the max-plus regime using a modified
Hegselmann-Krause model, replacing the conventional confidence-interval based
on the distance between opinions with one based instead on the recency of
information received by agents.
