Slow-down or speed-up of inter- and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network

Abstract

Citation:Ausloos M (2015) Slow-down or speed-up of inter-and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network. Front. Phys. 3:43. doi: 10.3389/fphy.2015.00043 Slow-down or speed-up of inter-and intra-cluster diffusion of controversial knowledge in stubborn communities based on a small world network Diffusion of knowledge is expected to be huge when agents are open minded. The report concerns a more difficult diffusion case when communities are made of stubborn agents. Communities having markedly different opinions are for example the Neocreationist and Intelligent Design Proponents (IDP), on one hand, and the Darwinian Evolution Defenders (DED), on the other hand. The case of knowledge diffusion within such communities is studied here on a network based on an adjacency matrix built from time ordered selected quotations of agents, whence for inter-and intra-communities. The network is intrinsically directed and not necessarily reciprocal. Thus, the adjacency matrices have complex eigenvalues; the eigenvectors present complex components. A quantification of the slow-down or speed-up effects of information diffusion in such temporal networks, with non-Markovian contact sequences, can be made by comparing the real time dependent (directed) network to its counterpart, the time aggregated (undirected) network, -which has real eigenvalues. In order to do so, small world networks which both contain an odd number of nodes are studied and compared to similar networks with an even number of nodes. It is found that (i) the diffusion of knowledge is more difficult on the largest networks; (ii) the network size influences the slowing-down or speeding-up diffusion process. Interestingly, it is observed that (iii) the diffusion of knowledge is slower in IDP and faster in DED communities. It is suggested that the finding can be "rationalized," if some "scientific quality" and "publication habit" is attributed to the agents, as common sense would guess. This finding offers some opening discussion toward tying scientific knowledge to belief.

Activist model of political party growth

“…Multiple susceptible populations with different degrees of susceptibility were proposed by Granovetter [50] and have been used in the diffusion of binge drinking [19], religion [33], terrorist groups [16], riots [14] and knowledge diffusion [51]. The Limited Activist model proposes two such populations, one aligned to the party, S, and one opposed, H. It is assumed that the latter would not change political alignment and join the party on the timescales being considered.…”

Partial balance in social networks with stubborn links

“…There is a growing literature studying opinion dynamics in social systems with stubborn agents (whose opinions are kept constant throughout time) [30,31,32,33]. Therefore, complete balance is rarely achieved in real systems as a consequence of the complexity of interactions [34]. Each individual can decide whether to change his/her relationship with others or not, which describes some dynamical processes occurring in the whole system.…”

Instability of social network dynamics with stubborn links

“…The findings reveal some factors affecting the relationship outside of balance theory in the real world. There is a growing literature studying opinion dynamics in social systems with stubborn agents (whose opinions are kept constant throughout time) [30,31,32,33,34]. Therefore, complete balance is almost never achieved in real systems as a consequence of the complexity of interactions [33].…”

“…There is a growing literature studying opinion dynamics in social systems with stubborn agents (whose opinions are kept constant throughout time) [30,31,32,33,34]. Therefore, complete balance is almost never achieved in real systems as a consequence of the complexity of interactions [33]. As such, the decisions that people make and the beliefs that people hold have profound consequences on the structure of the network.…”