86,259 research outputs found
From continuous to discontinuous transitions in social diffusion
Models of social diffusion reflect processes of how new products, ideas or
behaviors are adopted in a population. These models typically lead to a
continuous or a discontinuous phase transition of the number of adopters as a
function of a control parameter. We explore a simple model of social adoption
where the agents can be in two states, either adopters or non-adopters, and can
switch between these two states interacting with other agents through a
network. The probability of an agent to switch from non-adopter to adopter
depends on the number of adopters in her network neighborhood, the adoption
threshold and the adoption coefficient , two parameters defining a Hill
function. In contrast, the transition from adopter to non-adopter is
spontaneous at a certain rate . In a mean-field approach, we derive the
governing ordinary differential equations and show that the nature of the
transition between the global non-adoption and global adoption regimes depends
mostly on the balance between the probability to adopt with one and two
adopters. The transition changes from continuous, via a transcritical
bifurcation, to discontinuous, via a combination of a saddle-node and a
transcritical bifurcation, through a supercritical pitchfork bifurcation. We
characterize the full parameter space. Finally, we compare our analytical
results with Montecarlo simulations on annealed and quenched degree regular
networks, showing a better agreement for the annealed case. Our results show
how a simple model is able to capture two seemingly very different types of
transitions, i.e., continuous and discontinuous and thus unifies underlying
dynamics for different systems. Furthermore the form of the adoption
probability used here is based on empirical measurements.Comment: 7 pages, 3 figure
Influence networks
Some behaviors, ideas or technologies spread and become persistent in society, whereas others vanish. This paper analyzes the role of social influence in determining such distinct collective outcomes. Agents are assumed to acquire information from others through a certain sampling process that generates an influence network, and they use simple rules to decide whether to adopt or not depending on the observed sample. We characterize, as a function of the primitives of the model, the diffusion threshold (i.e., the spreading rate above which the adoption of the new behavior becomes persistent in the population) and the endemic state (i.e., the fraction of adopters in the stationary state of the dynamics). We find that the new behavior will easily spread in the population if there is a high correlation between how influential (visible) and how easily influenced an agent is, which is determined by the sampling process and the adoption rule. We also analyze how the density and variance of the out-degree distribution affect the diffusion threshold and the endemic state.social influence, networks, diffusion threshold, endemic state
SPoT: Representing the Social, Spatial, and Temporal Dimensions of Human Mobility with a Unifying Framework
Modeling human mobility is crucial in the analysis and simulation of opportunistic networks, where contacts are exploited as opportunities for peer-topeer message forwarding. The current approach with human mobility modeling has been based on continuously modifying models, trying to embed in them the mobility properties (e.g., visiting patterns to locations or specific distributions of inter-contact times) as they came up from trace analysis. As
a consequence, with these models it is difficult, if not impossible, to modify the features of mobility or to control the exact shape of mobility metrics (e.g., modifying the distribution of inter-contact times). For these reasons, in this paper we propose a mobility framework rather than a mobility model, with the explicit goal of providing a exible and controllable tool for modeling mathematically and generating simulatively different possible features of human mobility. Our framework, named SPoT, is able to incorporate the three dimensions - spatial, social, and temporal - of human mobility. The way SPoT does it is by mapping the different social communities of the network into different locations, whose members visit with a configurable temporal pattern. In order to characterize the temporal patterns of user visits to locations and the relative positioning of locations based on their shared users, we analyze the traces of real user movements extracted from three location-based online social networks (Gowalla, Foursquare, and Altergeo). We observe that a Bernoulli process effectively approximates user visits to locations in the majority of cases and that locations that share many common users visiting them frequently tend to be located close to each other. In addition, we use these traces to test the exibility of the framework, and we show that SPoT is able to accurately reproduce the mobility behavior observed in traces. Finally, relying on the Bernoulli assumption for arrival processes, we provide a throughout mathematical analysis of the controllability of the framework, deriving the conditions under which heavy-tailed and exponentially-tailed aggregate inter-contact times (often observed in real traces) emerge
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