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Register a new userInnovation flow through social networks: Productivity distribution
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A detailed empirical analysis of the productivity of non financial firms across several countries and years shows that productivity follows a non-Gaussian distribution with power law tails. We demonstrate that these empirical findings can be interpreted as consequence of a mechanism of exchanges in a social network where firms improve their productivity by direct innovation or/and by imitation of other firms technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we obtain that the expectation values of the productivity level are proportional to the connectivity of the network of links between firms. The comparison with the empirical distributions reveals that such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.
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The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of peoples actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a maximum entropy attachment model - except for its mean value which depends deterministically on the volume of the users activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.
We propose a bare-bones stochastic model that takes into account both the geographical distribution of people within a country and their complex network of connections. The model, which is designed to give rise to a scale-free network of social connections and to visually resemble the geographical spread seen in satellite pictures of the Earth at night, gives rise to a power-law distribution for the ranking of cities by population size (but for the largest cities) and reflects the notion that highly connected individuals tend to live in highly populated areas. It also yields some interesting insights regarding Gibrats law for the rates of city growth (by population size), in partial support of the findings in a recent analysis of real data [Rozenfeld et al., Proc. Natl. Acad. Sci. U.S.A. 105, 18702 (2008)]. The model produces a nontrivial relation between city population and city population density and a superlinear relationship between social connectivity and city population, both of which seem quite in line with real data.
In this work we dig into the process of scientific discovery by looking at a yet unexploited source of information: Polymath projects. Polymath projects are an original attempt to collectively solve mathematical problems in an online collaborative environment. To investigate the Polymath experiment, we analyze all the posts related to the projects that arrived to a peer reviewed publication with a particular attention to the organization of labor and the innovations originating from the author contributions. We observe that a significant presence of sporadic contributor boosts the productivity of the most active users and that productivity, in terms of number of posts, grows super-linearly with the number of contributors. When it comes to innovation in large scale collaborations, there is no exact rule determining, a priori, who the main innovators will be. Sometimes, serendipitous interactions by sporadic contributors can have a large impact on the discovery process and a single post by an occasional participant can steer the work into a new direction.
We show how the prevailing majority opinion in a population can be rapidly reversed by a small fraction p of randomly distributed committed agents who consistently proselytize the opposing opinion and are immune to influence. Specifically, we show that when the committed fraction grows beyond a critical value p_c approx 10%, there is a dramatic decrease in the time, T_c, taken for the entire population to adopt the committed opinion. In particular, for complete graphs we show that when p < p_c, T_c sim exp(alpha(p)N), while for p > p_c, T_c sim ln N. We conclude with simulation results for ErdH{o}s-Renyi random graphs and scale-free networks which show qualitatively similar behavior.
We study the evolutionary Prisoners Dilemma on two social networks obtained from actual relational data. We find very different cooperation levels on each of them that can not be easily understood in terms of global statistical properties of both networks. We claim that the result can be understood at the mesoscopic scale, by studying the community structure of the networks. We explain the dependence of the cooperation level on the temptation parameter in terms of the internal structure of the communities and their interconnections. We then test our results on community-structured, specifically designed artificial networks, finding perfect agreement with the observations in the real networks. Our results support the conclusion that studies of evolutionary games on model networks and their interpretation in terms of global properties may not be sufficient to study specific, real social systems. In addition, the community perspective may be helpful to interpret the origin and behavior of existing networks as well as to design structures that show resilient cooperative behavior.
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