Citation numbers are extensively used for assessing the quality of scientific research. The use of raw citation counts is generally misleading, especially when applied to cross-disciplinary comparisons, since the average number of citations received is strongly dependent on the scientific discipline of reference of the paper. Measuring and eliminating biases in citation patterns is crucial for a fair use of citation numbers. Several numerical indicators have been introduced with this aim, but...

Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is indeed the case for uncorrelated networks with minimum degree $\ge 3$. Here we focus on real networks, which generally have both structural correlations and low-degree nodes. We show that: (i) the ensemble distribution of the dynamically most important...

Using data from world stock exchange indices prior to and during periods of global financial crises, clusters and networks of indices are built for different thresholds and diverse periods of time, so that it is then possible to analyze how clusters are formed according to correlations among indices and how they 504 evolve in time, particularly during times of financial crises. Further analysis is made on the eigenvectors corresponding to the second highest eigenvalues of the correlation...

We study precursors to the global market crash that occurred on all main stock exchanges throughout the world in October 2008 about three weeks after the bankruptcy of Lehman Brothers Holdings Inc. on 15 September. We examine the collective behavior of stock returns and analyze the market mode, which is a market-wide collective mode, with constituent issues of the FTSE 100 index listed on the London 653 Stock Exchange. Before the market crash, a sharp rise in a measure of the collective...

We study the structure of the social graph of active Facebook users, the largest social network ever analyzed. We compute numerous features of the graph including 998 the number of users and friendships, the degree distribution, path lengths, clustering, and mixing patterns. Our results center around three main observations. First, we characterize the global structure of the graph, determining that the social network is nearly fully connected, with 99.91% of individuals belonging to a single...

The importance of the ability of predict trends in social media has been growing rapidly in the past few years with the growing dominance of social media in our everyday's life. Whereas many works focus on the detection of anomalies in networks, there exis 7f5 t little theoretical work on the prediction of the likelihood of anomalous network pattern to globally spread and become "trends". In this work we present an analytic model the social diffusion dynamics of spreading network patterns. Our...

To investigate the actual phenomena of transport on a complex network, we analysed empirical data for an inter-firm trading network, which consists of about one million Japanese firms and the sales of these firms (a sale corresponds to the total in-flow into a node). First, we analysed the relationships between sales and sales of nearest neighbourhoods from which we obtain a simple linear relationship between sales and the weighted sum of sales of nearest neighbourhoods (i.e., customers). In...

Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and...

The recent wave of mobilizations in the Arab world and across Western countries has generated much discussion on how digital media is connected to the diffusion of protests. We examine that connection using data from the surge of mobilizations that took place in Spain in May 2011. We study recruitment patterns in the Twitter network and find evidence of social influence and complex contagion. We identify the network position of early participants (i.e. the leaders of the recruitment process)...

We constraint on computer the best linear unbiased generalized statis 610 tics of random field for the best linear unbiased generalized statistics of an unknown constant mean of random field and derive the numerical generalized least-squares estimator of an unknown constant mean of random field. We derive the third constraint of spatial statistics and show that the classic generalized least-squares estimator of an unknown constant mean of the field is only an asymptotic disjunction of the...