Structural Balance via Gradient Flows over Signed Graphs

Structural balance is a classic property of signed graphs satisfying Heider's seminal axioms. Mathematical sociologists have studied balance theory since its inception in the 1940s. Recent research has focused on the development of dynamic models explaining the emergence of structural balance. In this paper, we introduce a novel class of parsimonious dynamic models for structural balance based on an interpersonal influence process. Our proposed models are gradient flows of an energy function, called the dissonance function, which captures the cognitive dissonance arising from violations of Heider's axioms. Thus, we build a new connection with the literature on energy landscape minimization. This gradient flow characterization allows us to study the transient and asymptotic behaviors of our model. We provide mathematical and numerical results describing the critical points of the dissonance function

Analysis of weighted networks

The connections in many networks are not merely binary entities, either present or not, but have associated weights that record their strengths relative to one another. Recent studies of networks have, by and large, steered clear of such weighted networks, which are often perceived as being harder to analyze than their unweighted counterparts. Here we point out that weighted networks can in many cases be analyzed using a simple mapping from a weighted network to an unweighted multigraph, allowing us to apply standard techniques for unweighted graphs to weighted ones as well. We give a number of examples of the method, including an algorithm for detecting community structure in weighted networks and a new and simple proof of the max-flow/min-cut theorem.Comment: 9 pages, 3 figure

Phase transitions in social sciences: two-populations mean field theory

A new mean field statistical mechanics model of two interacting groups of spins is introduced and the phase transition studied in terms of their relative size. A jump of the average magnetization is found for large values of the mutual interaction when the relative percentage of the two populations crosses a critical threshold. It is shown how the critical percentage depends on internal interactions and on the initial magnetizations. The model is interpreted as a prototype of resident-immigrant cultural interaction and conclusions from the social sciences perspectives are drawn

Generalized Master Equations for Non-Poisson Dynamics on Networks

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature

Universality in movie rating distributions

In this paper histograms of user ratings for movies (1,...,10) are analysed. The evolving stabilised shapes of histograms follow the rule that all are either double- or triple-peaked. Moreover, at most one peak can be on the central bins 2,...,9 and the distribution in these bins looks smooth `Gaussian-like' while changes at the extremes (1 and 10) often look abrupt. It is shown that this is well approximated under the assumption that histograms are confined and discretised probability density functions of L\'evy skew alpha-stable distributions. These distributions are the only stable distributions which could emerge due to a generalized central limit theorem from averaging of various independent random avriables as which one can see the initial opinions of users. Averaging is also an appropriate assumption about the social process which underlies the process of continuous opinion formation. Surprisingly, not the normal distribution achieves the best fit over histograms obseved on the web, but distributions with fat tails which decay as power-laws with exponent -(1+alpha) (alpha=4/3). The scale and skewness parameters of the Levy skew alpha-stable distributions seem to depend on the deviation from an average movie (with mean about 7.6). The histogram of such an average movie has no skewness and is the most narrow one. If a movie deviates from average the distribution gets broader and skew. The skewness pronounces the deviation. This is used to construct a one parameter fit which gives some evidence of universality in processes of continuous opinion dynamics about taste.Comment: 8 pages, 5 figures, accepted for publicatio

Cascades on clique-based graphs

peer-reviewedWe present an analytical approach to determining the expected cascade size in a broad range of dynamical models on the class of highly clustered random graphs introduced by Gleeson [J. P. Gleeson, Phys. Rev. E 80, 036107 (2009)]. A condition for the existence of global cascades is also derived. Applications of this approach include analyses of percolation, and Watts's model. We show how our techniques can be used to study the effects of in-group bias in cascades on social networks.PUBLISHEDpeer-reviewe

Exploration of 2-deoxy-D-ribose and 17β-Estradiol as alternatives to exogenous VEGF to promote angiogenesis in tissue-engineered constructs

Aim: In this study, we explored the angiogenic potential and proangiogenic concentration ranges of 2-deoxy-D-ribose (2dDR) and 17β-Estradiol (E2) in comparison with VEGF. The 2dDR and E2 were then loaded into tissue engineering (TE) scaffolds to investigate their proangiogenic potential when released from fibers. Materials & methods:Ex ovo chick chorioallantoic membrane (CAM) assay was used to evaluate angiogenic activity of 2dDR and E2. Both factors were then introduced into scaffolds via electrospinning to assess their angiogenic potential when released from fibers. Results: Both factors were approximately 80% as potent as VEGF and showed a dose-dependent angiogenic response. The sustained release of both agents from the scaffolds stimulated neovascularization over 7 days in the chorioallantoic membrane assay. Conclusion: We conclude that both 2dDR and E2 provide attractive alternatives to VEGF for the functionalization of tissue engineering scaffolds to promote angiogenesis in vivo

Attention on Weak Ties in Social and Communication Networks

Granovetter's weak tie theory of social networks is built around two central hypotheses. The first states that strong social ties carry the large majority of interaction events; the second maintains that weak social ties, although less active, are often relevant for the exchange of especially important information (e.g., about potential new jobs in Granovetter's work). While several empirical studies have provided support for the first hypothesis, the second has been the object of far less scrutiny. A possible reason is that it involves notions relative to the nature and importance of the information that are hard to quantify and measure, especially in large scale studies. Here, we search for empirical validation of both Granovetter's hypotheses. We find clear empirical support for the first. We also provide empirical evidence and a quantitative interpretation for the second. We show that attention, measured as the fraction of interactions devoted to a particular social connection, is high on weak ties --- possibly reflecting the postulated informational purposes of such ties --- but also on very strong ties. Data from online social media and mobile communication reveal network-dependent mixtures of these two effects on the basis of a platform's typical usage. Our results establish a clear relationships between attention, importance, and strength of social links, and could lead to improved algorithms to prioritize social media content

Pervasive sensing to model political opinions in face-to-face networks

Exposure and adoption of opinions in social networks are important questions in education, business, and government. We de- scribe a novel application of pervasive computing based on using mobile phone sensors to measure and model the face-to-face interactions and subsequent opinion changes amongst undergraduates, during the 2008 US presidential election campaign. We nd that self-reported political discussants have characteristic interaction patterns and can be predicted from sensor data. Mobile features can be used to estimate unique individ- ual exposure to di erent opinions, and help discover surprising patterns of dynamic homophily related to external political events, such as elec- tion debates and election day. To our knowledge, this is the rst time such dynamic homophily e ects have been measured. Automatically esti- mated exposure explains individual opinions on election day. Finally, we report statistically signi cant di erences in the daily activities of individ- uals that change political opinions versus those that do not, by modeling and discovering dominant activities using topic models. We nd people who decrease their interest in politics are routinely exposed (face-to-face) to friends with little or no interest in politics.U.S. Army Research Laboratory (Cooperative Agreement No. W911NF-09-2-0053)United States. Air Force Office of Scientific Research (Award No. FA9550-10-1-0122)Swiss National Science Foundatio