Boolean Dynamics with Random Couplings

This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N Boolean elements at a given time is given a value which depends upon K elements in the previous time step. We review the work of many authors on the behavior of the models, looking particularly at the structure and lengths of their cycles, the sizes of their basins of attraction, and the flow of information through the systems. In the limit of infinite N, there is a phase transition between a chaotic and an ordered phase, with a critical phase in between. We argue that the behavior of this system depends significantly on the topology of the network connections. If the elements are placed upon a lattice with dimension d, the system shows correlations related to the standard percolation or directed percolation phase transition on such a lattice. On the other hand, a very different behavior is seen in the Kauffman net in which all spins are equally likely to be coupled to a given spin. In this situation, coupling loops are mostly suppressed, and the behavior of the system is much more like that of a mean field theory. We also describe possible applications of the models to, for example, genetic networks, cell differentiation, evolution, democracy in social systems and neural networks.Comment: 69 pages, 16 figures, Submitted to Springer Applied Mathematical Sciences Serie

Analysing interactions in a teacher network forum: a sociometric approach

This article presents the sociometric analysis of the interactions in a forum of a social network created for the professional development of Portuguese-speaking teachers. The main goal of the forum, which was titled Stricto Sensu, was to discuss the educational value of programmes that joined the distance learning model in Brazil. The empirical study focused on the sociometrie analysis of the social interactions that take place in asynchronous online environments. This approach, according to literature, allows for new means to observe, analyse, and interpret the reality of a new social paradigm. This type of analysis tries to understand the relationship established between the different actors, seeking to verify if the roles they play in both the access to information and the construction of shared knowledge. The data collected allow the researchers to deduce that the indicators used in the analysis are important for understanding and intervening in the dynamics and functioning of the network to propose improvements in its structure and organisation. In the specific case of the aforementioned discussion forum, the results of the sociometrie analysis of the perceived interactions were not surprising, considering that the nature of the topic did not demand deep reflection to contribute to the debate.This work is funded by Portuguese Foundation for Science and Technology under the doctoral grant SFRH/BD/60677/2009

Structure-oriented prediction in complex networks

Complex systems are extremely hard to predict due to its highly nonlinear interactions and rich emergent properties. Thanks to the rapid development of network science, our understanding of the structure of real complex systems and the dynamics on them has been remarkably deepened, which meanwhile largely stimulates the growth of effective prediction approaches on these systems. In this article, we aim to review different network-related prediction problems, summarize and classify relevant prediction methods, analyze their advantages and disadvantages, and point out the forefront as well as critical challenges of the field

Dynamic Centrality for Directed Co-author Network with Context

Part 4: Data Analysis and Information RetrievalInternational audienceCo-author network is a typical example of dynamic complex network, which evolves and changes over time. One of the ways how to capture and describe the dynamics of the network is determination of Stationarity for detected communities in the network. In the paper, we have proposed the modified Stationarity, which is focused only on co-authors of a given author and not on the whole community to which the author belongs. Therefore, this modified Stationarity is defined for each author in the network and is perceived as dynamic centrality. The relations in homogeneous co-author network are not only set by the number of common publications, but are given by a context to terms used by the author extracted from the article titles. This dynamic centrality calculates with the evaluation by context of directed edges in co-author network. Such modified Stationarity gives us information about stability or dynamics of the author’s neighbourhood that influences her/him, or about the stability and dynamics of the author’s neighbourhood, which the author influences in relation to context

Newton’s Gravitational Law for Link Prediction in Social Networks

Link prediction is an important research area in network science due to a wide range of real-world application. There are a number of link prediction methods. In the area of social networks, these methods are mostly inspired by social theory, such as having more mutual friends between two people in a social network platform entails higher probability of those two people becoming friends in the future. In this paper we take our inspiration from a different area, which is Newton’s law of universal gravitation. Although this law deals with physical bodies, based on our intuition and empirical results we found that this could also work in networks, and especially in social networks. In order to apply this law, we had to endow nodes with the notion of mass and distance. While node importance could be considered as mass, the shortest path, path count, or inverse similarity (AdamicAdar, Katz score etc.) could be considered as distance. In our analysis, we have primarily used degree centrality to denote the mass of the nodes, while the lengths of shortest paths between them have been used as distances. In this study we compare the proposed link prediction approach to 7 other methods on 4 datasets from various domains. To this end, we use the ROC curves and the AUC measure to compare the methods. As the results show that our approach outperforms the other 7 methods on 2 out of the 4 datasets, we also discuss the potential reasons of the observed behaviour