Towards real-world complexity: an introduction to multiplex networks

Many real-world complex systems are best modeled by multiplex networks of interacting network layers. The multiplex network study is one of the newest and hottest themes in the statistical physics of complex networks. Pioneering studies have proven that the multiplexity has broad impact on the system's structure and function. In this Colloquium paper, we present an organized review of the growing body of current literature on multiplex networks by categorizing existing studies broadly according to the type of layer coupling in the problem. Major recent advances in the field are surveyed and some outstanding open challenges and future perspectives will be proposed.Comment: 20 pages, 10 figure

Growing Hypergraphs with Preferential Linking

A family of models of growing hypergraphs with preferential rules of new linking is introduced and studied. The model hypergraphs evolve via the hyperedge-based growth as well as the node-based one, thus generalizing the preferential-attachment models of scale-free networks. We obtain the degree distribution and hyperedge size distribution for various combinations of node- and hyperedge-based growth modes. We find that the introduction of hyperedge-based growth can give rise to power-law degree distribution $P(k)\sim k^{-\gamma}$ even without node-wise preferential-attachments. The hyperedge size distribution $P(s)$ can take diverse functional forms, ranging from exponential to power-law to a nonstationary one, depending on the specific hyperedge-based growth rule. Numerical simulations support the mean-field theoretical analytical predictions

Structure and evolution of online social relationships: heterogeneity in unrestricted discussions

With the advancement in the information age, people are using electronic media more frequently for communications, and social relationships are also increasingly resorting to online channels. While extensive studies on traditional social networks have been carried out, little has been done on online social networks. Here we analyze the structure and evolution of online social relationships by examining the temporal records of a bulletin board system (BBS) in a university. The BBS dataset comprises of 1908 boards, in which a total of 7446 students participate. An edge is assigned to each dialogue between two students, and it is defined as the appearance of the name of a student in the from- and to-field in each message. This yields a weighted network between the communicating students with an unambiguous group association of individuals. In contrast to a typical community network, where intracommunities (intercommunities) are strongly (weakly) tied, the BBS network contains hub members who participate in many boards simultaneously but are strongly tied, that is, they have a large degree and betweenness centrality and provide communication channels between communities. On the other hand, intracommunities are rather homogeneously and weakly connected. Such a structure, which has never been empirically characterized in the past, might provide a new perspective on the social opinion formation in this digital era

Degree distributions under general node removal: Power-law or Poisson?

Perturbations made to networked systems may result in partial structural loss, such as a blackout in a power-grid system. Investigating the resultant disturbance in network properties is quintessential to understand real networks in action. The removal of nodes is a representative disturbance, but previous studies are seemingly contrasting about its effect on arguably the most fundamental network statistic, the degree distribution. The key question is about the functional form of the degree distributions that can be altered during node removal or sampling, which is decisive in the remaining subnetwork's static and dynamical properties. In this work, we clarify the situation by utilizing the relative entropies with respect to the reference distributions in the Poisson and power-law form. Introducing general sequential node removal processes with continuously different levels of hub protection to encompass a series of scenarios including random removal and preferred or protective removal of the hub, we classify the altered degree distributions starting from various power-law forms by comparing two relative entropy values. From the extensive investigation in various scenarios based on direct node-removal simulations and by solving the rate equation of degree distributions, we discover in the parameter space two distinct regimes, one where the degree distribution is closer to the power-law reference distribution and the other closer to the Poisson distribution.Comment: 12 pages, 7 figure

Modeling bursts and heavy tails in human dynamics

Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human activity patterns the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. We discuss two queueing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution with exponent alpha=3/2. The second model imposes limitations on the queue length, resulting in alpha=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns. Finally, we discuss possible extension of the proposed queueing models and outline some future challenges in exploring the statistical mechanisms of human dynamics.Comment: RevTex, 19 pages, 8 figure

Impact of the Topology of Global Macroeconomic Network on the Spreading of Economic Crises

Throughout economic history, the global economy has experienced recurring crises. The persistent recurrence of such economic crises calls for an understanding of their generic features rather than treating them as singular events. The global economic system is a highly complex system and can best be viewed in terms of a network of interacting macroeconomic agents. In this regard, from the perspective of collective network dynamics, here we explore how the topology of the global macroeconomic network affects the patterns of spreading of economic crises. Using a simple toy model of crisis spreading, we demonstrate that an individual country's role in crisis spreading is not only dependent on its gross macroeconomic capacities, but also on its local and global connectivity profile in the context of the world economic network. We find that on one hand clustering of weak links at the regional scale can significantly aggravate the spread of crises, but on the other hand the current network structure at the global scale harbors higher tolerance of extreme crises compared to more “globalized” random networks. These results suggest that there can be a potential hidden cost in the ongoing globalization movement towards establishing less-constrained, trans-regional economic links between countries, by increasing vulnerability of the global economic system to extreme crises

Discutindo a educação ambiental no cotidiano escolar: desenvolvimento de projetos na escola formação inicial e continuada de professores

A presente pesquisa buscou discutir como a Educação Ambiental (EA) vem sendo trabalhada, no Ensino Fundamental e como os docentes desta escola compreendem e vem inserindo a EA no cotidiano escolar., em uma escola estadual do município de Tangará da Serra/MT, Brasil. Para tanto, realizou-se entrevistas com os professores que fazem parte de um projeto interdisciplinar de EA na escola pesquisada. Verificou-se que o projeto da escola não vem conseguindo alcançar os objetivos propostos por: desconhecimento do mesmo, pelos professores; formação deficiente dos professores, não entendimento da EA como processo de ensino-aprendizagem, falta de recursos didáticos, planejamento inadequado das atividades. A partir dessa constatação, procurou-se debater a impossibilidade de tratar do tema fora do trabalho interdisciplinar, bem como, e principalmente, a importância de um estudo mais aprofundado de EA, vinculando teoria e prática, tanto na formação docente, como em projetos escolares, a fim de fugir do tradicional vínculo “EA e ecologia, lixo e horta”.Facultad de Humanidades y Ciencias de la Educació