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Initially designed to predict and explain the economic trajectories of countries, cities, and regions, economic complexity has been found applicable in diverse contexts such as ecology and chess openings. The success of economic complexity stems from its capacity to assess hidden capabilities within a system indirectly. The existing algorithms for economic complexity operate only when the underlying interaction topology conforms to a bipartite graph. A single link disrupting the bipartite structure renders these algorithms inapplicable, even if the weight of that link is tiny compared to others. This paper presents a novel extension of economic complexity to encompass any graph, overcoming the constraints of bipartite structures. Additionally, it introduces fitness centrality and orthofitness centrality as new centrality measures in graphs. Fitness Centrality emerges as a promising metric for assessing node vulnerability, akin to node betweenness centrality. Furthermore, we unveil the cost functions that drive the minimization procedures underlying the economic complexity index and fitness centrality algorithms. This extension broadens the scope of economic complexity analysis, enabling its application in diverse network structures beyond bipartite graphs., Comment: 20 pages, 8 figures, 1 table, 5 appendices

In public railway systems, minor disruptions can trigger cascading events that lead to delays in the entire system. Typically, delays originate and propagate because the equipment is blocking ways, operational units are unavailable, or at the wrong place at the needed time. The specific understanding of the origins and processes involved in delay-spreading is still a challenge, even though large-scale simulations of national railway systems are becoming available on a highly detailed scale. Without this understanding, efficient management of delay propagation, a growing concern in some Western countries, will remain impossible. Here, we present a systemic risk-based approach to manage daily delay cascading on national scales. We compute the {\em systemic impact} of every train as the maximum of all delays it could possibly cause due to its interactions with other trains, infrastructure, and operational units. To compute it, we design an effective impact network where nodes are train services and links represent interactions that could cause delays. Our results are not only consistent with highly detailed and computationally intensive agent-based railway simulations but also allow us to pinpoint and identify the causes of delay cascades in detail. The systemic approach reveals structural weaknesses in railway systems whenever shared resources are involved. We use the systemic impact to optimally allocate additional shared resources to the system to reduce delays with minimal costs and effort. The method offers a practical and intuitive solution for delay management by optimizing the effective impact network through the introduction of new cheap local train services., Comment: 27 pages, 14 figures

Forecasting the popularity of new songs has become a standard practice in the music industry and provides a comparative advantage for those that do it well. Considerable efforts were put into machine learning prediction models for that purpose. It is known that in these models, relevant predictive parameters include intrinsic lyrical and acoustic characteristics, extrinsic factors (e.g., publisher influence and support), and the previous popularity of the artists. Much less attention was given to the social components of the spreading of song popularity. Recently, evidence for musical homophily - the tendency that people who are socially linked also share musical tastes - was reported. Here we determine how musical homophily can be used to predict song popularity. The study is based on an extensive dataset from the last.fm online music platform from which we can extract social links between listeners and their listening patterns. To quantify the importance of networks in the spreading of songs that eventually determines their popularity, we use musical homophily to design a predictive influence parameter and show that its inclusion in state-of-the-art machine learning models enhances predictions of song popularity. The influence parameter improves the prediction precision (TP/(TP+FN)) by about 50% from 0.14 to 0.21, indicating that the social component in the spreading of music plays at least as significant a role as the artist's popularity or the impact of the genre., Comment: 7 pages, 3 figures

Open-source software (OSS) is widely spread in industry, research, and government. OSS represents an effective development model because it harnesses the decentralized efforts of many developers in a way that scales. As OSS developers work independently on interdependent modules, they create a larger cohesive whole in the form of an ecosystem, leaving traces of their contributions and collaborations. Data harvested from these traces enable the study of large-scale decentralized collaborative work. We present curated data on the activity of tens of thousands of developers in the Rust ecosystem and the evolving dependencies between their libraries. The data covers seven years of developer contributions to Rust libraries and can be used to reconstruct the ecosystem's development history, such as growing developer collaboration networks or dependency networks. These are complemented by statistics on downloads and popularity, tracking the dynamics of use and success over time. Altogether the data give a comprehensive view of several dimensions of the ecosystem.

For decades the number of scientific publications has been rapidly increasing, effectively out-dating knowledge at a tremendous rate. Only few scientific milestones remain relevant and continuously attract citations. Here we quantify how long scientific work remains being utilized, how long it takes before today's work is forgotten, and how milestone papers differ from those forgotten. To answer these questions, we study the complete temporal citation network of all American Physical Society journals. We quantify the probability of attracting citations for individual publications based on age and the number of citations they have received in the past. We capture both aspects, the forgetting and the tendency to cite already popular works, in a microscopic generative model for the dynamics of scientific citation networks. We find that the probability of citing a specific paper declines with age as a power law with an exponent of $\alpha \sim -1.4$. Whenever a paper in its early years can be characterized by a scaling exponent above a critical value, $\alpha_c$, the paper is likely to become "ever-lasting". We validate the model with out-of-sample predictions, with an accuracy of up to 90% (AUC $\sim 0.9$). The model also allows us to estimate an expected citation landscape of the future, predicting that 95% of papers cited in 2050 have yet to be published. The exponential growth of articles, combined with a power-law type of forgetting and papers receiving fewer and fewer citations on average, suggests a worrying tendency toward information overload and raises concerns about scientific publishing's long-term sustainability., Comment: 11 pages, 4 figures

Rediscovering a new function for something can be just as important as the discovery itself. In 1982, Stephen Jay Gould and Elisabeth Vrba named this phenomenon Exaptation to describe a radical shift in the function of a specific trait during biological evolution. While exaptation is thought to be a fundamental mechanism for generating adaptive innovations, diversity, and sophisticated features, relatively little effort has been made to quantify exaptation outside the topic of biological evolution. We think that this concept provides a useful framework for characterising the emergence of innovations in science. This article explores the notion that exaptation arises from the usage of scientific ideas in domains other than the area that they were originally applied to. In particular, we adopt a normalised entropy and an inverse participation ratio as observables that reveal and quantify the concept of exaptation. We identify distinctive patterns of exaptation and expose specific examples of papers that display those patterns. Our approach represents a first step towards the quantification of exaptation phenomena in the context of scientific evolution., Comment: 14 pages, 6 figures

Zipf's, Heaps' and Taylor's laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the scaling of fluctuations for systems as diverse as written texts and cities, ecological systems and stock markets. Many modeling schemes have been proposed in literature to explain those laws, but only recently a modeling framework has been introduced that accounts for the emergence of those laws without deducing the emergence of one of the laws from the others or without ad hoc assumptions. This modeling framework is based on the concept of adjacent possible space and its key feature of being dynamically restructured while its boundaries get explored, i.e., conditional to the occurrence of novel events. Here, we illustrate this approach and show how this simple modelling framework, instantiated through a modified Polya's urn model, is able reproduce Zipf's, Heaps' and Taylor's laws within a unique self-consistent scheme. In addition the same modelling scheme embraces other less common evolutionary laws (Hoppe's model and Dirichlet processes) as particular cases., Comment: This article belongs to the Special Issue Economic Fitness and Complexity

We present a new metric estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new metric is parameter free. This new map almost reproduces the results of the original homogeneous metrics already defined in literature and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm involved., Comment: 12 pages, 8 figures

Railways are a key infrastructure for any modern country. The reliability and resilience of this peculiar transportation system may be challenged by different shocks such as disruptions, strikes and adverse weather conditions. These events compromise the correct functioning of the system and trigger the spreading of delays into the railway network on a daily basis. Despite their importance, a general theoretical understanding of the underlying causes of these disruptions is still lacking. In this work, we analyse the Italian and German railway networks by leveraging on the train schedules and actual delay data retrieved during the year 2015. We use {these} data to infer simple statistical laws ruling the emergence of localized delays in different areas of the network and we model the spreading of these delays throughout the network by exploiting a framework inspired by epidemic spreading models. Our model offers a fast and easy tool for the preliminary assessment of the {effectiveness of} traffic handling policies, and of the railway {network} criticalities., Comment: 32 pages (with appendix), 28 Figures (with appendix), 2 Tables

Novelties are part of our daily lives. We constantly adopt new technologies, conceive new ideas, meet new people, experiment with new situations. Occasionally, we as individuals, in a complicated cognitive and sometimes fortuitous process, come up with something that is not only new to us, but to our entire society so that what is a personal novelty can turn into an innovation at a global level. Innovations occur throughout social, biological and technological systems and, though we perceive them as a very natural ingredient of our human experience, little is known about the processes determining their emergence. Still the statistical occurrence of innovations shows striking regularities that represent a starting point to get a deeper insight in the whole phenomenology. This paper represents a small step in that direction, focusing on reviewing the scientific attempts to effectively model the emergence of the new and its regularities, with an emphasis on more recent contributions: from the plain Simon's model tracing back to the 1950s, to the newest model of Polya's urn with triggering of one novelty by another. What seems to be key in the successful modelling schemes proposed so far is the idea of looking at evolution as a path in a complex space, physical, conceptual, biological, technological, whose structure and topology get continuously reshaped and expanded by the occurrence of the new. Mathematically it is very interesting to look at the consequences of the interplay between the "actual" and the "possible" and this is the aim of this short review., Comment: 25 pages, 10 figures

Recently, social phenomena have received a lot of attention not only from social scientists, but also from physicists, mathematicians and computer scientists, in the emerging interdisciplinary field of complex system science. Opinion dynamics is one of the processes studied, since opinions are the drivers of human behaviour, and play a crucial role in many global challenges that our complex world and societies are facing: global financial crises, global pandemics, growth of cities, urbanisation and migration patterns, and last but not least important, climate change and environmental sustainability and protection. Opinion formation is a complex process affected by the interplay of different elements, including the individual predisposition, the influence of positive and negative peer interaction (social networks playing a crucial role in this respect), the information each individual is exposed to, and many others. Several models inspired from those in use in physics have been developed to encompass many of these elements, and to allow for the identification of the mechanisms involved in the opinion formation process and the understanding of their role, with the practical aim of simulating opinion formation and spreading under various conditions. These modelling schemes range from binary simple models such as the voter model, to multi-dimensional continuous approaches. Here, we provide a review of recent methods, focusing on models employing both peer interaction and external information, and emphasising the role that less studied mechanisms, such as disagreement, has in driving the opinion dynamics. [...], Comment: 42 pages, 6 figures

The complex organization of syntax in hierarchical structures is one of the core design features of human language. Duality of patterning refers for instance to the organization of the meaningful elements in a language at two distinct levels: a combinatorial level where meaningless forms are combined into meaningful forms and a compositional level where meaningful forms are composed into larger lexical units. The question remains wide open regarding how such a structure could have emerged. Furthermore a clear mathematical framework to quantify this phenomenon is still lacking. The aim of this paper is that of addressing these two aspects in a self-consistent way. First, we introduce suitable measures to quantify the level of combinatoriality and compositionality in a language, and present a framework to estimate these observables in human natural languages. Second, we show that the theoretical predictions of a multi-agents modeling scheme, namely the Blending Game, are in surprisingly good agreement with empirical data. In the Blending Game a population of individuals plays language games aiming at success in communication. It is remarkable that the two sides of duality of patterning emerge simultaneously as a consequence of a pure cultural dynamics in a simulated environment that contains meaningful relations, provided a simple constraint on message transmission fidelity is also considered., Comment: 11 pages, to appear in the Proceedings of the Workshop on Origins of Communication Systems: Modeling and Ethologically-based Theory, Konrad Lorenz Institute for Evolution and Cognition Research, Altenberg, Austria (2013). Special Issue of topiCS on New frontiers in language evolution and development

The issue of sustainability is at the top of the political and societal agenda, being considered of extreme importance and urgency. Human individual action impacts the environment both locally (e.g., local air/water quality, noise disturbance) and globally (e.g., climate change, resource use). Urban environments represent a crucial example, with an increasing realization that the most effective way of producing a change is involving the citizens themselves in monitoring campaigns (a citizen science bottom-up approach). This is possible by developing novel technologies and IT infrastructures enabling large citizen participation. Here, in the wider framework of one of the first such projects, we show results from an international competition where citizens were involved in mobile air pollution monitoring using low cost sensing devices, combined with a web-based game to monitor perceived levels of pollution. Measures of shift in perceptions over the course of the campaign are provided, together with insights into participatory patterns emerging from this study. Interesting effects related to inertia and to direct involvement in measurement activities rather than indirect information exposure are also highlighted, indicating that direct involvement can enhance learning and environmental awareness. In the future, this could result in better adoption of policies towards decreasing pollution., Comment: 17 pages, 6 figures, 1 supplementary file

In the last few years the Web has progressively acquired the status of an infrastructure for social computation that allows researchers to coordinate the cognitive abilities of human agents in on-line communities so to steer the collective user activity towards predefined goals. This general trend is also triggering the adoption of web-games as a very interesting laboratory to run experiments in the social sciences and whenever the contribution of human beings is crucially required for research purposes. Nowadays, while the number of on-line users has been steadily growing, there is still a need of systematization in the approach to the web as a laboratory. In this paper we present Experimental Tribe (XTribe in short), a novel general purpose web-based platform for web-gaming and social computation. Ready to use and already operational, XTribe aims at drastically reducing the effort required to develop and run web experiments. XTribe has been designed to speed up the implementation of those general aspects of web experiments that are independent of the specific experiment content. For example, XTribe takes care of user management by handling their registration and profiles and in case of multi-player games, it provides the necessary user grouping functionalities. XTribe also provides communication facilities to easily achieve both bidirectional and asynchronous communication. From a practical point of view, researchers are left with the only task of designing and implementing the game interface and logic of their experiment, on which they maintain full control. Moreover, XTribe acts as a repository of different scientific experiments, thus realizing a sort of showcase that stimulates users' curiosity, enhances their participation, and helps researchers in recruiting volunteers., Comment: 11 pages, 2 figures, 1 table, 2013 Third International Conference on Cloud and Green Computing (CGC), Sept. 30 2013-Oct. 2 2013, Karlsruhe, Germany

Opinion formation is an important element of social dynamics. It has been widely studied in the last years with tools from physics, mathematics and computer science. Here, a continuous model of opinion dynamics for multiple possible choices is analysed. Its main features are the inclusion of disagreement and possibility of modulating information, both from one and multiple sources. The interest is in identifying the effect of the initial cohesion of the population, the interplay between cohesion and information extremism, and the effect of using multiple sources of information that can influence the system. Final consensus, especially with external information, depends highly on these factors, as numerical simulations show. When no information is present, consensus or segregation is determined by the initial cohesion of the population. Interestingly, when only one source of information is present, consensus can be obtained, in general, only when this is extremely mild, i.e. there is not a single opinion strongly promoted, or in the special case of a large initial cohesion and low information exposure. On the contrary, when multiple information sources are allowed, consensus can emerge with an information source even when this is not extremely mild, i.e. it carries a strong message, for a large range of initial conditions., Comment: 20 pages, 11 figures

Opinion dynamics concerns social processes through which populations or groups of individuals agree or disagree on specific issues. As such, modelling opinion dynamics represents an important research area that has been progressively acquiring relevance in many different domains. Existing approaches have mostly represented opinions through discrete binary or continuous variables by exploring a whole panoply of cases: e.g. independence, noise, external effects, multiple issues. In most of these cases the crucial ingredient is an attractive dynamics through which similar or similar enough agents get closer. Only rarely the possibility of explicit disagreement has been taken into account (i.e., the possibility for a repulsive interaction among individuals' opinions), and mostly for discrete or 1-dimensional opinions, through the introduction of additional model parameters. Here we introduce a new model of opinion formation, which focuses on the interplay between the possibility of explicit disagreement, modulated in a self-consistent way by the existing opinions' overlaps between the interacting individuals, and the effect of external information on the system. Opinions are modelled as a vector of continuous variables related to multiple possible choices for an issue. Information can be modulated to account for promoting multiple possible choices. Numerical results show that extreme information results in segregation and has a limited effect on the population, while milder messages have better success and a cohesion effect. Additionally, the initial condition plays an important role, with the population forming one or multiple clusters based on the initial average similarity between individuals, with a transition point depending on the number of opinion choices.

Folksonomies provide a rich source of data to study social patterns taking place on the World Wide Web. Here we study the temporal patterns of users' tagging activity. We show that the statistical properties of inter-arrival times between subsequent tagging events cannot be explained without taking into account correlation in users' behaviors. This shows that social interaction in collaborative tagging communities shapes the evolution of folksonomies. A consensus formation process involving the usage of a small number of tags for a given resources is observed through a numerical and analytical analysis of some well-known folksonomy datasets., Comment: 6 pages, 10 figures; Proceedings of the 20th ACM conference on Hypertext and hypermedia, 2009

A distributed classification paradigm known as collaborative tagging has been widely adopted in new Web applications designed to manage and share online resources. Users of these applications organize resources (Web pages, digital photographs, academic papers) by associating with them freely chosen text labels, or tags. Here we leverage the social aspects of collaborative tagging and introduce a notion of resource distance based on the collective tagging activity of users. We collect data from a popular system and perform experiments showing that our definition of distance can be used to build a weighted network of resources with a detectable community structure. We show that this community structure clearly exposes the semantic relations among resources. The communities of resources that we observe are a genuinely emergent feature, resulting from the uncoordinated activity of a large number of users, and their detection paves the way for mapping emergent semantics in social tagging systems., Comment: 14 pages, 8 figures

Endothelial cells are responsible for the formation of the capillary blood vessel network. We describe a system of endothelial cells by means of two-dimensional molecular dynamics simulations of point-like particles. Cells' motion is governed by the gradient of the concentration of a chemical substance that they produce (chemotaxis). The typical time of degradation of the chemical substance introduces a characteristic length in the system. We show that point-like model cells form network resembling structures tuned by this characteristic length, before collapsing altogether. Successively, we improve the non-realistic point-like model cells by introducing an isotropic strong repulsive force between them and a velocity dependent force mimicking the observed peculiarity of endothelial cells to preserve the direction of their motion (persistence). This more realistic model does not show a clear network formation. We ascribe this partial fault in reproducing the experiments to the static geometry of our model cells that, in reality, change their shapes by elongating toward neighboring cells., Comment: 10 pages, 3 figures, 2 of which composite with 8 pictures each. Accepted on J.Stat.Mech. (2009). Appeared at the poster session of StatPhys23, Genoa, Italy, July 13 (2007)