Dr. Gerardo Iñiguez from Institute for Research in Applied Mathematics and Systems, National Autonomous University of Mexico. He is going to talk about:
Modelling complex contagion with tie heterogeneities
Social influence, the effect that the past behaviour of acquaintances has on
our daily decisions, is arguably the main driving mechanism of many complex collective
phenomena in society, including the spreading of innovations, ideas and fads,
or the growth of political and social movements. Many of these processes have
been studied empirically in the past, particularly with regards to the
existence of so-called adoption cascades, where large number of people adopt
the same behaviour in a relatively short time. Moreover, they have been
modelled either as simple contagion (where adoption is driven by independent
contagion stimuli, like the Bass model of innovation diffusion), or as complex
contagion (where a threshold on the number of adopting neighbours in a
network determines spreading, like the Watts model of adoption cascades).
However, it is still unclear whether real spreading phenomena is regulated by
simple or complex contagion (or a combination of both), which makes it difficult to identify
cognitive and social mechanisms that may control the collective action of
large groups of people. Furthermore, most spreading models disregard one relevant
property of real social networks, namely tie heterogeneities in terms of social influence.
Influence arriving on social ties may vary from neighbour to neighbour, as it largely depends
on the nature and frequency of interaction with a given friend.
Here we close this gap on the understanding of social contagion by extending
the conventional Watts cascade model to account for tie heterogeneities. We focus on the case of a
bimodal weight distribution, such that spreading is determined by the adoption
threshold of nodes and the standard deviation of tie weights. We find that the
presence of tie heterogeneities induce unexpected dynamical behaviour, as
they either speed up or slow down contagion with respect to the unweighted
case, depending on the adoption threshold and weight standard
deviation. We found this effect to be present in both synthetic and real social networks,
which we verify via numerical simulations and an analytical approach based on
approximate master equations. Moreover, we find that our model with tie heterogeneities
bridges the theoretical descriptions of simple and complex contagion, and
thus hints at the existence of a single mechanism driving social spreading, regardless of the initial
hypotheses used to describe contagion stimuli between individuals. These
results may be instrumental in developing more accurate spreading models that manage to
gauge the rise and extent of real behavioural cascades in society.
Date: 10th January 2017, at 15:00
Place: Amphi J (ENS Lyon, site Monod).