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

Process model comparison based on cophenetic distance

The automated comparison of process models has received increasing attention in the last decade, due to the growing existence of process models and repositories, and the consequent need to assess similarities between the underlying processes. Current techniques for process model comparison are either structural (based on graph edit distances), or behavioural (through activity profiles or the analysis of the execution semantics). Accordingly, there is a gap between the quality of the information provided by these two families, i.e., structural techniques may be fast but inaccurate, whilst behavioural are accurate but complex. In this paper we present a novel technique, that is based on a well-known technique to compare labeled trees through the notion of Cophenetic distance. The technique lays between the two families of methods for comparing a process model: it has an structural nature, but can provide accurate information on the differences/similarities of two process models. The experimental evaluation on various benchmarks sets are reported, that position the proposed technique as a valuable tool for process model comparison.Peer ReviewedPostprint (author's final draft

Biological CO2-Methanation: an Approach to Standardization

Power-to-Methane as one part of Power-to-Gas has been recognized globally as one of the key elements for the transition towards a sustainable energy system. While plants that produce methane catalytically have been in operation for a long time, biological methanation has just reached industrial pilot scale and near-term commercial application. The growing importance of the biological method is reflected by an increasing number of scientific articles describing novel approaches to improve this technology. However, these studies are difficult to compare because they lack a coherent nomenclature. In this article, we present a comprehensive set of parameters allowing the characterization and comparison of various biological methanation processes. To identify relevant parameters needed for a proper description of this technology, we summarized existing literature and defined system boundaries for Power-to-Methane process steps. On this basis, we derive system parameters providing information on the methanation system, its performance, the biology and cost aspects. As a result, three different standards are provided as a blueprint matrix for use in academia and industry applicable to both, biological and catalytic methanation. Hence, this review attempts to set the standards for a comprehensive description of biological and chemical methanation processes

Role of social environment and social clustering in spread of opinions in co-evolving networks

Taking a pragmatic approach to the processes involved in the phenomena of collective opinion formation, we investigate two specific modifications to the co-evolving network voter model of opinion formation, studied by Holme and Newman [1]. First, we replace the rewiring probability parameter by a distribution of probability of accepting or rejecting opinions between individuals, accounting for the asymmetric influences in relationships among individuals in a social group. Second, we modify the rewiring step by a path-length-based preference for rewiring that reinforces local clustering. We have investigated the influences of these modifications on the outcomes of the simulations of this model. We found that varying the shape of the distribution of probability of accepting or rejecting opinions can lead to the emergence of two qualitatively distinct final states, one having several isolated connected components each in internal consensus leading to the existence of diverse set of opinions and the other having one single dominant connected component with each node within it having the same opinion. Furthermore, and more importantly, we found that the initial clustering in network can also induce similar transitions. Our investigation also brings forward that these transitions are governed by a weak and complex dependence on system size. We found that the networks in the final states of the model have rich structural properties including the small world property for some parameter regimes. [1] P. Holme and M. Newman, Phys. Rev. E 74, 056108 (2006)

Effects of Mass Media and Cultural Drift in a Model for Social Influence

In the context of an extension of Axelrod's model for social influence, we study the interplay and competition between the cultural drift, represented as random perturbations, and mass media, introduced by means of an external homogeneous field. Unlike previous studies [J. C. Gonz\'alez-Avella {\it et al}, Phys. Rev. E {\bf 72}, 065102(R) (2005)], the mass media coupling proposed here is capable of affecting the cultural traits of any individual in the society, including those who do not share any features with the external message. A noise-driven transition is found: for large noise rates, both the ordered (culturally polarized) phase and the disordered (culturally fragmented) phase are observed, while, for lower noise rates, the ordered phase prevails. In the former case, the external field is found to induce cultural ordering, a behavior opposite to that reported in previous studies using a different prescription for the mass media interaction. We compare the predictions of this model to statistical data measuring the impact of a mass media vasectomy promotion campaign in Brazil.Comment: 10 pages, 3 figures; minor changes; added references. To appear in IJMP

Dynamics of Majority Rule

We introduce a 2-state opinion dynamics model where agents evolve by majority rule. In each update, a group of agents is specified whose members then all adopt the local majority state. In the mean-field limit, where a group consists of randomly-selected agents, consensus is reached in a time that scales ln N, where N is the number of agents. On finite-dimensional lattices, where a group is a contiguous cluster, the consensus time fluctuates strongly between realizations and grows as a dimension-dependent power of N. The upper critical dimension appears to be larger than 4. The final opinion always equals that of the initial majority except in one dimension.Comment: 4 pages, 3 figures, 2-column revtex4 format; annoying typo fixed in Eq.(1); a similar typo fixed in Eq.(6) and some references update