The Krause-Hegselmann Consensus Model with Discrete Opinions

The consensus model of Krause and Hegselmann can be naturally extended to the case in which opinions are integer instead of real numbers. Our algorithm is much faster than the original version and thus more suitable for applications. For the case of a society in which everybody can talk to everybody else, we find that the chance to reach consensus is much higher as compared to other models; if the number of possible opinions Q<=7, in fact, consensus is always reached, which might explain the stability of political coalitions with more than three or four parties. For Q>7 the number S of surviving opinions is approximately the same independently of the size N of the population, as long as Q<N. We considered as well the more realistic case of a society structured like a Barabasi-Albert network; here the consensus threshold depends on the outdegree of the nodes and we find a simple scaling law for S, as observed for the discretized Deffuant model.Comment: 12 pages, 6 figure

The Sznajd Consensus Model with Continuous Opinions

In the consensus model of Sznajd, opinions are integers and a randomly chosen pair of neighbouring agents with the same opinion forces all their neighbours to share that opinion. We propose a simple extension of the model to continuous opinions, based on the criterion of bounded confidence which is at the basis of other popular consensus models. Here the opinion s is a real number between 0 and 1, and a parameter \epsilon is introduced such that two agents are compatible if their opinions differ from each other by less than \epsilon. If two neighbouring agents are compatible, they take the mean s_m of their opinions and try to impose this value to their neighbours. We find that if all neighbours take the average opinion s_m the system reaches complete consensus for any value of the confidence bound \epsilon. We propose as well a weaker prescription for the dynamics and discuss the corresponding results.Comment: 11 pages, 4 figures. To appear in International Journal of Modern Physics

On the Consensus Threshold for the Opinion Dynamics of Krause-Hegselmann

In the consensus model of Krause-Hegselmann, opinions are real numbers between 0 and 1 and two agents are compatible if the difference of their opinions is smaller than the confidence bound parameter \epsilon. A randomly chosen agent takes the average of the opinions of all neighbouring agents which are compatible with it. We propose a conjecture, based on numerical evidence, on the value of the consensus threshold \epsilon_c of this model. We claim that \epsilon_c can take only two possible values, depending on the behaviour of the average degree d of the graph representing the social relationships, when the population N goes to infinity: if d diverges when N goes to infinity, \epsilon_c equals the consensus threshold \epsilon_i ~ 0.2 on the complete graph; if instead d stays finite when N goes to infinity, \epsilon_c=1/2 as for the model of Deffuant et al.Comment: 15 pages, 7 figures, to appear in International Journal of Modern Physics C 16, issue 2 (2005

Distributed Graph Clustering using Modularity and Map Equation

We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other clusters. In the context of a social network, a cluster could be a group of friends. Modularity and map equation are established formalizations of this internally-dense-externally-sparse principle. We present two versions of a simple distributed algorithm to optimize both measures. They are based on Thrill, a distributed big data processing framework that implements an extended MapReduce model. The algorithms for the two measures, DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality measures is straight-forward. We conduct an extensive experimental study on real-world graphs and on synthetic benchmark graphs with up to 68 billion edges. Our algorithms are fast while detecting clusterings similar to those detected by other sequential, parallel and distributed clustering algorithms. Compared to the distributed GossipMap algorithm, DSLM-Map needs less memory, is up to an order of magnitude faster and achieves better quality.Comment: 14 pages, 3 figures; v3: Camera ready for Euro-Par 2018, more details, more results; v2: extended experiments to include comparison with competing algorithms, shortened for submission to Euro-Par 201

An NMR Analog of the Quantum Disentanglement Eraser

We report the implementation of a three-spin quantum disentanglement eraser on a liquid-state NMR quantum information processor. A key feature of this experiment was its use of pulsed magnetic field gradients to mimic projective measurements. This ability is an important step towards the development of an experimentally controllable system which can simulate any quantum dynamics, both coherent and decoherent.Comment: Four pages, one figure (RevTeX 2.1), to appear in Physics Review Letter

Evidential Communities for Complex Networks

Community detection is of great importance for understand-ing graph structure in social networks. The communities in real-world networks are often overlapped, i.e. some nodes may be a member of multiple clusters. How to uncover the overlapping communities/clusters in a complex network is a general problem in data mining of network data sets. In this paper, a novel algorithm to identify overlapping communi-ties in complex networks by a combination of an evidential modularity function, a spectral mapping method and evidential c-means clustering is devised. Experimental results indicate that this detection approach can take advantage of the theory of belief functions, and preforms good both at detecting community structure and determining the appropri-ate number of clusters. Moreover, the credal partition obtained by the proposed method could give us a deeper insight into the graph structure

Time-resolved monitoring of biofouling development on a fat sheet membrane using optical coherence tomography

© The Author(s) 2017. Biofouling on a membrane leads to significant performance decrease in filtration processes. In this study, an optical coherence tomography (OCT) was used to perform a time-resolved analysis of dynamic biofouling development on a submerged membrane under continuous operation. A real-time change in the biofouling morphology was calculated through the image analysis of OCT scans. Three videos were generated through the acquisition of serial static images. This is the first study that displays the dynamic biofouling formation process as a video. The acquisition of OCT cross-sectional scans of the biofouling allowed to evaluate the time-lapsed evolution for three different time periods (early stage, double layers and long-term). Firstly, at the early filtration stage, membrane coverage and average biofouling layer thickness were found to be linearly correlated with the permeate flux pattern. Secondly, after 3 d of operation, an anomalous morphology was observed, constituted by a double-layered biofouling structure: denser on the bottom and looser on the top. In a long-term operation, the biofouling structure underwent a dynamic evolution over time, resulting in a multi-layered structure. The biofouling formation information was closely associated with filtration performance (i.e. flux) indicating the suitability of OCT as real-time and in-situ biofouling monitoring technique

The macro-behavior of agents' opinion under the influence of an external field

In this paper, a model about the evolution of opinion on small world networks is proposed. We studied the macro-behavior of the agents' opinion and the relative change rate as time elapses. The external field was found to play an important role in making the opinion $s(t)$ balance or increase, and without the influence of the external field, the relative change rate $\gamma(t)$ shows a nonlinear increasing behavior as time runs. What's more, this nonlinear increasing behavior is independent of the initial condition, the strength of the external field and the time that we cancel the external field. Maybe the results can reflect some phenomenon in our society, such as the function of the macro-control in China or the Mass Media in our society.Comment: 8 pages, 3 figure

Outflow Dynamics in Modeling Oligopoly Markets: The Case of the Mobile Telecommunications Market in Poland

In this paper we introduce two models of opinion dynamics in oligopoly markets and apply them to a situation, where a new entrant challenges two incumbents of the same size. The models differ in the way the two forces influencing consumer choice -- (local) social interactions and (global) advertising -- interact. We study the general behavior of the models using the Mean Field Approach and Monte Carlo simulations and calibrate the models to data from the Polish telecommunications market. For one of the models criticality is observed -- below a certain critical level of advertising the market approaches a lock-in situation, where one market leader dominates the market and all other brands disappear. Interestingly, for both models the best fits to real data are obtained for conformity level $p \in (0.3,0.4)$. This agrees very well with the conformity level found by Solomon Asch in his famous social experiment