A network representation is useful for describing the structure of a large variety of complex systems. However, most real and engineered systems have multiple subsystems and layers of connectivity, and the data produced by such systems is very rich. Achieving a deep understanding of such systems necessitates generalizing "traditional" network theory, and the newfound deluge of data now makes it possible to test increasingly general frameworks for the study of networks. In particular, although adjacency matrices are useful to describe traditional single-layer networks, such a representation is insufficient for the analysis and description of multiplex and time-dependent networks. One must therefore develop a more general mathematical framework to cope with the challenges posed by multi-layer complex systems. In this paper, we introduce a tensorial framework to study multi-layer networks, and we discuss the generalization of several important network descriptors and dynamical processes-including degree centrality, clustering coefficients, eigenvector centrality, modularity, Von Neumann entropy, and diffusion-for this framework. We examine the impact of different choices in constructing these generalizations, and we illustrate how to obtain known results for the special cases of single-layer and multiplex networks. Our tensorial approach will be helpful for tackling pressing problems in multi-layer complex systems, such as inferring who is influencing whom (and by which media) in multichannel social networks and developing routing techniques for multimodal transportation systems.
Many complex systems can be represented as networks consisting of distinct types of interactions, which can be categorized as links belonging to different layers. For example, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, accounting for different genetic and physical interactions, each containing thousands of protein-protein relationships. A fundamental open question is then how many layers are indeed necessary to accurately represent the structure of a multilayered complex system. Here we introduce a method based on quantum theory to reduce the number of layers to a minimum while maximizing the distinguishability between the multilayer network and the corresponding aggregated graph. We validate our approach on synthetic benchmarks and we show that the number of informative layers in some real multilayer networks of protein-genetic interactions, social, economical and transportation systems can be reduced by up to 75%.
Assessing the navigability of interconnected networks (transporting information, people, or goods) under eventual random failures is of utmost importance to design and protect critical infrastructures. Random walks are a good proxy to determine this navigability, specifically the coverage time of random walks, which is a measure of the dynamical functionality of the network. Here, we introduce the theoretical tools required to describe random walks in interconnected networks accounting for structure and dynamics inherent to real systems. We develop an analytical approach for the covering time of random walks in interconnected networks and compare it with extensive Monte Carlo simulations. Generally speaking, interconnected networks are more resilient to random failures than their individual layers per se, and we are able to quantify this effect. As an application--which we illustrate by considering the public transport of London--we show how the efficiency in exploring the multiplex critically depends on layers' topology, interconnection strengths, and walk strategy. Our findings are corroborated by data-driven simulations, where the empirical distribution of check-ins and checksout is considered and passengers travel along fastest paths in a network affected by real disruptions. These findings are fundamental for further development of searching and navigability strategies in real interconnected systems.N etwork theory has been revealed to be a perfect instrument to model the structure of complex systems and the dynamical process in which they are involved. However, the classical approach does not take into account the possibility that agents can be networked in different ways, and with different intensity, on multiple layers simultaneously. As an example, in the case of social sciences the same user might choose to subscribe to two or more online social networks and to build different social relationships with different users on each social platform (e.g., LinkedIn for the network of professional contacts, Facebook for the network of friends, etc.). Another example is represented by transportation networks in a city: the network of bus stops, the first layer, is different from the tube network, the second layer, but people make use of both by combining paths to move from one place to another within the city. The cases where one vertex is not present in the full multiplex can be accounted for by including it as an isolated vertex in the layers where it is missing, without altering either topological or dynamical properties of the interconnected network.The existence of such multiple connections on different layers invites a generalization of the theory of complex networks to cope with multilayer interconnected networked systems. More specifically, very recent studies focused on a particular type of multilayer network, the multiplex, where each agent participates in different layers simultaneously, like our previous example in the case of online social networks. Indeed, the actors (vertices) in every layer are t...
he Pierre Auger Observatory, located on a vast, high plain in western\ud Argentina, is the world's largest cosmic ray observatory. The objectives\ud of the Observatory are to probe the origin and characteristics of cosmic\ud rays above 10(17) eV and to study the interactions of these, the most\ud energetic particles observed in nature. The Auger design features an\ud array of 1660 water Cherenkov particle detector stations spread over\ud 3000 km(2) overlooked by 24 air fluorescence telescopes. In addition,\ud three high elevation fluorescence telescopes overlook a 23.5 km(2),\ud 61-detector infilled array with 750 in spacing. The Observatory has been\ud in successful operation since completion in 2008 and has recorded data\ud from an exposure exceeding 40,000 km(2) sr yr. This paper describes the\ud design and performance of the detectors, related subsystems and\ud infrastructure that make up the Observatory
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (i.e., "multiplexity") among their constituent components and/or multiple interacting subsystems. Such structural complexity has a significant effect on both dynamics and function. Throwing away or aggregating available structural information can generate misleading results and be a major obstacle towards attempts to understand complex systems. The recent "multilayer" approach for modeling networked systems explicitly allows the incorporation of multiplexity and other features of 1 arXiv:1604.02021v2 [physics.soc-ph] 4 Apr 2017 realistic systems. On one hand, it allows one to couple different structural relationships by encoding them in a convenient mathematical object. On the other hand, it also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping achieve a thorough, accurate understanding of complex systems. The study of multilayer networks has also revealed new physical phenomena that remain hidden when using ordinary graphs, the traditional network representation.Here we survey progress towards attaining a deeper understanding of spreading processes on multilayer networks, and we highlight some of the physical phenomena related to spreading processes that emerge from multilayer structure. IntroductionNetworks provide a powerful representation of interaction patterns in complex systems 1-3 . The structure of social relations among individuals, interactions between proteins, food webs, and many other situations can be represented using networks. Until recently, the vast majority of studies focused on networks that consist of a single type of entity, with different entities connected to each other via a single type of connection. Such networks are now called single-layer (or monolayer) networks. The idea of incorporating additional information -such as multiple types of interactions, subsystems, and time-dependence -has long been pointed out in various fields, such as sociology, anthropology, and engineering, but an effective unified framework for the mathematical treatment of such multidimensional structures, which are usually called multilayer networks, was developed only recently 4, 5 .Multilayer networks can be used to model many complex systems. For example, relationships between humans include different types of interactions -such as relationships between family members, friends, and coworkers -that constitute different layers of a social system. Different layers of connectivity also arise naturally in natural and human-made systems in transportation 6 ,
Editor: S. DodelsonWe report a measurement of the flux of cosmic rays with unprecedented precision and statistics using the Pierre Auger Observatory. Based on fluorescence observations in coincidence with at least one surface detector we derive a spectrum for energies above 10 18 eV. We also update the previously published energy spectrum obtained with the surface detector array. The two spectra are combined addressing the systematic uncertainties and, in particular, the influence of the energy resolution on the spectral shape. 242Pierre Auger Collaboration / Physics Letters B 685 (2010) The spectrum can be described by a broken power law E −γ with index γ = 3.3 below the ankle which is measured at log 10 (E ankle /eV) = 18.6. Above the ankle the spectrum is described by a power law with index 2.6 followed by a flux suppression, above about log 10 (E/eV) = 19.5, detected with high statistical significance.
Background An infodemic is an overabundance of information—some accurate and some not—that occurs during an epidemic. In a similar manner to an epidemic, it spreads between humans via digital and physical information systems. It makes it hard for people to find trustworthy sources and reliable guidance when they need it. Objective A World Health Organization (WHO) technical consultation on responding to the infodemic related to the coronavirus disease (COVID-19) pandemic was held, entirely online, to crowdsource suggested actions for a framework for infodemic management. Methods A group of policy makers, public health professionals, researchers, students, and other concerned stakeholders was joined by representatives of the media, social media platforms, various private sector organizations, and civil society to suggest and discuss actions for all parts of society, and multiple related professional and scientific disciplines, methods, and technologies. A total of 594 ideas for actions were crowdsourced online during the discussions and consolidated into suggestions for an infodemic management framework. Results The analysis team distilled the suggestions into a set of 50 proposed actions for a framework for managing infodemics in health emergencies. The consultation revealed six policy implications to consider. First, interventions and messages must be based on science and evidence, and must reach citizens and enable them to make informed decisions on how to protect themselves and their communities in a health emergency. Second, knowledge should be translated into actionable behavior-change messages, presented in ways that are understood by and accessible to all individuals in all parts of all societies. Third, governments should reach out to key communities to ensure their concerns and information needs are understood, tailoring advice and messages to address the audiences they represent. Fourth, to strengthen the analysis and amplification of information impact, strategic partnerships should be formed across all sectors, including but not limited to the social media and technology sectors, academia, and civil society. Fifth, health authorities should ensure that these actions are informed by reliable information that helps them understand the circulating narratives and changes in the flow of information, questions, and misinformation in communities. Sixth, following experiences to date in responding to the COVID-19 infodemic and the lessons from other disease outbreaks, infodemic management approaches should be further developed to support preparedness and response, and to inform risk mitigation, and be enhanced through data science and sociobehavioral and other research. Conclusions The first version of this framework proposes five action areas in which WHO Member States and actors within society can apply, according to their mandate, an infodemic management approach adapted to national contexts and practices. Responses to the COVID-19 pandemic and the related infodemic require swift, regular, systematic, and coordinated action from multiple sectors of society and government. It remains crucial that we promote trusted information and fight misinformation, thereby helping save lives.
SignificanceSocial media can deeply influence reality perception, affecting millions of people’s voting behavior. Hence, maneuvering opinion dynamics by disseminating forged content over online ecosystems is an effective pathway for social hacking. We propose a framework for discovering such a potentially dangerous behavior promoted by automatic users, also called “bots,” in online social networks. We provide evidence that social bots target mainly human influencers but generate semantic content depending on the polarized stance of their targets. During the 2017 Catalan referendum, used as a case study, social bots generated and promoted violent content aimed at Independentists, ultimately exacerbating social conflict online. Our results open challenges for detecting and controlling the influence of such content on society.
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