Microscopic structural damage, such as lesions in neural systems or disruptions in urban transportation networks, can impair the dynamics crucial for systems' functionality, such as electrochemical signals or human flows, or any other type of information exchange, respectively, at larger topological scales. Damage is usually modeled by progressive removal of components or connections and, consequently, systems' robustness is assessed in terms of how fast their structure fragments into disconnected subsystems. Yet, this approach fails to capture how damage hinders the propagation of information across scales, since system function can be degraded even in absence of fragmentation—e.g., pathological yet structurally integrated human brain. Here, we probe the response to damage of dynamical processes on the top of complex networks, to study how such an information flow is affected. We find that removal of nodes central for network connectivity might have insignificant effects, challenging the traditional assumption that structural metrics alone are sufficient to gain insights about how complex systems operate. Using a damaging protocol explicitly accounting for flow dynamics, we analyze synthetic and empirical systems, from biological to infrastructural ones, and show that it is possible to drive the system towards functional fragmentation before full structural disintegration.

The infection caused by SARS-CoV-2, responsible for the COVID-19 pandemic, is characterized by an infectious period with either asymptomatic or pre-symptomatic phases, leading to a rapid surge of mild and severe cases putting national health systems under serious stress. To avoid their collapse, and in the absence of pharmacological treatments, during the early pandemic phase countries worldwide were forced to adopt strategies, from elimination to mitigation, based on non-pharmacological interventions which, in turn, overloaded social, educational and economic systems. To date, the heterogeneity and incompleteness of data sources does not allow to quantify the multifaceted impact of the pandemic at country level and, consequently, to compare the effectiveness of country responses. Here, we tackle this challenge from a complex systems perspective, proposing a model to evaluate the impact of systemic failures in response to the pandemic shock. We use health, behavioral and economic indicators for 44 countries to build a shock index quantifying responses in terms of robustness and resilience, highlighting the crucial advantage of proactive policy and decision making styles over reactive ones, which can be game-changing during the emerging of a new variant of concern.

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The governance of the political and economic world order builds on a complex architecture of international treaties at various geographical scales. In a historical phase of high institutional turbulence, assessing the stability of such architecture with respect to the unilateral defection of single countries and the breakdown of single treaties is important. We carry out this analysis on the whole global architecture and find that the countries with the highest disruption potential are mostly medium-small and micro countries. Political stability is highly dependent on many former colonial overseas territories that are today part of the global network of fiscal havens, as well as on emerging economies, mostly from South-East Asia. Economic stability depends on medium-sized European and African countries. Single global treaties have surprisingly less disruptive potential, with the major exception of the WTO. Our results suggest that the potential fragility of the world order seems to be more directly related to global inequality and fiscal injustice than commonly believed and that the legacy of the colonial world order is still strong in the current international relations scenario. In particular, vested interests related to tax avoidance seem to have a structural role in the political architecture of global governance.

After the leak of 11.5 million documents from the Panamanian corporation Mossack Fonseca, an intricate network of offshore business entities has been revealed. The emerging picture is that of legal entities, either individuals or companies, involved in offshore activities and transactions with several tax havens simultaneously which establish, indirectly, an effective network of countries acting on tax evasion. The analysis of this network quantitatively uncovers a strongly connected core (a rich-club) of countries whose indirect interactions, mediated by legal entities, form the skeleton for tax evasion worldwide. Intriguingly, the rich-club mainly consists of well-known tax havens such as British Virgin Islands and Hong Kong, and major global powers such as China, Russia, United Kingdom and United States of America. Our findings build a ground for better understanding phenomena where the erosion of public trust may spark emergent social dynamics, such as social conflicts and political polarization, that are driven by the complex interconnected structure of tax evaders in a globalized economy.

The description of complex human mobility patterns is at the core of many important applications ranging from urbanism and transportation to epidemics containment. Data about collective human movements, once scarce, has become widely available thanks to new sources such as Phone CDR, GPS devices, or Smartphone apps. Nevertheless, it is still common to rely on a single dataset by implicitly assuming that it is a valid instance of universal dynamics, regardless of factors such as data gathering and processing techniques. Here, we test such an overarching assumption on an unprecedented scale by comparing human mobility datasets obtained from 7 different data-sources, tracing over 500 millions individuals in 145 countries. We report wide quantifiable differences in the resulting mobility networks and, in particular, in the displacement distribution previously thought to be universal. These variations -- that do not necessarily imply that the human mobility is not universal -- also impact processes taking place on these networks, as we show for the specific case of epidemic spreading. Our results point to the crucial need for disclosing the data processing and, overall, to follow good practices to ensure the robustness and the reproducibility of the results.

Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct microstates compatible with given topology and dynamical evolution. In this Letter, we propose a maximum entropy principle to characterize network states for systems with heterogeneous, generally correlated, connectivity patterns and non-trivial dynamics. We focus on three distinct coalescence processes, widely encountered in the analysis of empirical interconnected systems, and characterize their entropy and transitions between distinct dynamical regimes across distinct temporal scales. Our framework allows one to study the statistical physics of systems that aggregate, such as in transportation infrastructures serving the same geographic area, or correlate, such as inter-brain synchrony arising in organisms that socially interact, and active matter that swarm or synchronize.

The number of network science applications across many different fields has been rapidly increasing. Surprisingly, the development of theory and domainspecific applications often occur in isolation, risking an effective disconnect between theoretical and methodological advances and the way network science is employed in practice. Here we address this risk constructively, discussing good practices to guarantee more successful applications and reproducible results. We endorse designing statistically grounded methodologies to address challenges in network science. This approach allows one to explain observational data in terms of generative models, naturally deal with intrinsic uncertainties, and strengthen the link between theory and applications.

Recurrent networks are a special class of artificial neural systems that use their internal states to perform computing tasks for machine learning. One of its state-of-the-art developments, i.e. reservoir computing (RC), uses the internal structure -- usually a static network with random structure -- to map an input signal into a nonlinear dynamical system defined in a higher dimensional space. Reservoirs are characterized by nonlinear interactions among their units and their ability to store information through recurrent loops, allowing to train artificial systems to learn task-specific dynamics. However, it is fundamentally unknown how the random topology of the reservoir affects the learning performance. Here, we fill this gap by considering a battery of synthetic networks -- characterized by different topological features -- and 45 empirical connectomes -- sampled from brain regions of organisms belonging to 8 different species -- to build the reservoir and testing the learning performance against a prediction task with a variety of complex input signals. We find nontrivial correlations between RC performances and both the number of nodes and rank of the covariance matrix of activation states, with performance depending on the nature -- stochastic or deterministic -- of input signals. Remarkably, the modularity and the link density of the reservoir are found to affect RC performances: these results cannot be predicted by models only accounting for simple topological features of the reservoir. Overall, our findings highlight that the complex topological features characterizing biophysical computing systems such as connectomes can be used to design efficient bio-inspired artificial neural networks.

The network density matrix formalism allows for describing the dynamics of information on top of complex structures and it has been successfully used to analyze from system's robustness to perturbations to coarse graining multilayer networks from characterizing emergent network states to performing multiscale analysis. However, this framework is usually limited to diffusion dynamics on undirected networks. Here, to overcome some limitations, we propose an approach to derive density matrices based on dynamical systems and information theory, that allows for encapsulating a much wider range of linear and non-linear dynamics and richer classes of structure, such as directed and signed ones. We use our framework to study the response to local stochastic perturbations of synthetic and empirical networks, including neural systems consisting of excitatory and inhibitory links and gene-regulatory interactions. Our findings demonstrate that topological complexity does not lead, necessarily, to functional diversity -- i.e., complex and heterogeneous response to stimuli or perturbations. Instead, functional diversity is a genuine emergent property which cannot be deduced from the knowledge of topological features such as heterogeneity, modularity, presence of asymmetries or dynamical properties of a system.

In recent years, statistical physics' methodologies have proven extremely successful in offering insights into the mechanisms that govern social interactions. However, the question of whether these models are able to capture trends observed in real-world datasets is hardly addressed in the current literature. With this work we aim at bridging the gap between theoretical modeling and validation with data. In particular, we propose a model for opinion dynamics on a social network in the presence of external triggers, framing the interpretation of the model in the context of misbehavior spreading. We divide our population in aware, unaware and zealot/educated agents. Individuals change their status according to two competing dynamics, referred to as behavioral dynamics and broadcasting. The former accounts for information spreading through contact among individuals whereas broadcasting plays the role of an external agent, modeling the effect of mainstream media outlets. Through both simulations and analytical computations we find that the stationary distribution of the fraction of unaware agents in the system undergoes a phase transition when an all-to-all approximation is considered. Surprisingly, such a phase transition disappears in the presence of a minimum fraction of educated agents. Finally, we validate our model using data collected from the public discussion on Twitter, including millions of posts, about the potential adverse effects of the AstraZeneca vaccine against COVID-19. We show that the intervention of external agents, as accounted for in our model, is able to reproduce some key features that are found in this real-world dataset.

Online platforms play a relevant role in the creation and diffusion of false or misleading news. Concerningly, the COVID-19 pandemic is shaping a communication network which reflects the emergence of collective attention towards a topic that rapidly gained universal interest. Here, we characterize the dynamics of this network on Twitter, analysing how unreliable content distributes among its users. We find that a minority of accounts is responsible for the majority of the misinformation circulating online, and identify two categories of users: a few active ones, playing the role of ‘creators’, and a majority playing the role of ‘consumers’. The relative proportion of these groups (approx. 14% creators—86% consumers) appears stable over time: consumers are mostly exposed to the opinions of a vocal minority of creators (which are the origin of 82% of fake content in our data), that could be mistakenly understood as representative of the majority of users. The corresponding pressure from a perceived majority is identified as a potential driver of the ongoing COVID-19 infodemic.

Despite the numerous ways now available to quantify which parts or subsystems of a network are most important, there remains a lack of centrality measures that are related to the complexity of information flows and are derived directly from entropy measures. Here, we introduce a ranking of edges based on how each edge's removal would change a system's von Neumann entropy (VNE), which is a spectral-entropy measure that has been adapted from quantum information theory to quantify the complexity of information dynamics over networks. We show that a direct calculation of such rankings is computationally inefficient (or unfeasible) for large networks: e.g.\ the scaling is (N3) per edge for networks with N nodes. To overcome this limitation, we employ spectral perturbation theory to estimate VNE perturbations and derive an approximate edge-ranking algorithm that is accurate and fast to compute, scaling as (N) per edge. Focusing on a form of VNE that is associated with a transport operator e−βL, where L is a graph Laplacian matrix and β>0 is a diffusion timescale parameter, we apply this approach to diverse applications including a network encoding polarized voting patterns of the 117th U.S. Senate, a multimodal transportation system including roads and metro lines in London, and a multiplex brain network encoding correlated human brain activity. Our experiments highlight situations where the edges that are considered to be most important for information diffusion complexity can dramatically change as one considers short, intermediate and long timescales β for diffusion.

As the coronavirus disease 2019 (COVID-19) spread globally, emerging variants such as B.1.1.529 quickly became dominant worldwide. Sustained community transmission favors the proliferation of mutated sub-lineages with pandemic potential, due to cross-national mobility flows, which are responsible for consecutive cases surge worldwide. We show that, in the early stages of an emerging variant, integrating data from national genomic surveillance and global human mobility with large-scale epidemic modeling allows to quantify its pandemic potential, providing quantifiable indicators for pro-active policy interventions. We validate our framework on worldwide spreading variants and gain insights about the pandemic potential of BA.5 and BA.2.75 sub-lineages. Country-level epidemic intelligence is not enough to contrast the pandemic of respiratory pathogens such as SARS-CoV-2 and a scalable integrated approach, i.e. pandemic intelligence, is required to enhance global preparedness.

We analyze social media activity during one of the largest protest mobilizations in US history to examine ideological asymmetries in the posting of news content. Using an unprecedented combination of four datasets (tracking offline protests, social media activity, web browsing, and the reliability of news sources), we show that there is no evidence of unreliable sources having any prominent visibility during the protest period, but we do identify asymmetries in the ideological slant of the sources shared on social media, with a clear bias towards right-leaning domains. These results support the “amplification of the right” thesis, which points to the structural conditions (social and technological) that lead to higher visibility of content with a partisan bent towards the right. Our findings provide evidence that right-leaning sources gain more visibility on social media and reveal that ideological asymmetries manifest themselves even in the context of movements with progressive goals.

Real systems are characterized by complex patterns of interactions between their units, by dynamical processes on them, and by the interplay of the two. It is well known that particular structures affect dynamical processes at different scales. Sometimes richly connected units are connected by costly, long-range links. In the brain, hubs form rich clubs for integrating information between different brain regions, and many biological and social networks show this same structural organization. It remains, however, unclear whether this structural organization alone enables a rapid communication between highly connected nodes or whether a functional rich club may emerge as a combination of direct links and longer paths between rich nodes. Here, we identify functional rich clubs through the diffusion geometry, providing a perspective on rich-club phenomena in complex networks. We show that weak structural rich clubs may be functionally stronger, thanks to bridge nodes, while diffusion inside strong structural rich clubs may be damped in modular networks.

When a large number of similar entities interact among each other and with their environment at a low scale, unexpected outcomes at higher spatio-temporal scales might spontaneously arise. This nontrivial phenomenon, known as emergence, characterizes a broad range of distinct complex systems -- from physical to biological and social ones -- and is often related to collective behavior. It is ubiquitous, from non-living entities such as oscillators that under specific conditions synchronize, to living ones, such as birds flocking or fish schooling. Despite the ample phenomenological evidence of the existence of systems' emergent properties, central theoretical questions to the study of emergence remain still unanswered, such as the lack of a widely accepted, rigorous definition of the phenomenon or the identification of the essential physical conditions that favour emergence. We offer here a general overview of the phenomenon of emergence and sketch current and future challenges on the topic. Our short review also serves as an introduction to the Theme Issue "Emergent phenomena in complex physical and socio-technical systems: from cells to societies", where we provide a synthesis of the contents tackled in the Issue and outline how they relate to these challenges, spanning from current advances in our understanding on the origin of life to the large-scale propagation of infectious diseases.

Localized perturbations in a real-world network have the potential to trigger cascade failures at the whole system level, hindering its operations and functions. Standard approaches analytically tackling this problem are mostly based either on static descriptions, such as percolation, or on models where the failure evolves through first-neighbor connections, crucially failing to capture the nonlocal behavior typical of real cascades. We introduce a dynamical model that maps the failure propagation across the network to a self-avoiding random walk that, at each step, has a probability to perform nonlocal jumps toward operational systems' units. Despite the inherent non-Markovian nature of the process, we are able to characterize the critical behavior of the system out of equilibrium, as well as the stopping time distribution of the cascades. Our numerical experiments on synthetic and empirical biological and transportation networks are in excellent agreement with theoretical expectation, demonstrating the ability of our framework to quantify the vulnerability to nonlocal cascade failures of complex systems with interconnected structure.

During the COVID-19 epidemic, draconian countermeasures forbidding nonessential human activities have been adopted in several countries worldwide, providing an unprecedented setup for testing and quantifying the current impact of humankind on climate and for driving potential sustainability policies in the postpandemic era from a perspective of complex systems. In this study, we consider heterogeneous sources of environmental and human activity observables, considered as components of a complex socioenvironmental system, and apply information theory, network science, and Bayesian inference to analyze their structural relations and nonlinear dynamics between January 2019 and August 2020 in northern Italy, i.e., before, during, and after the national lockdown. The topological structure of a complex system strongly impacts its collective behavior; therefore, mapping this structure is essential to fully understand the functions of the system as a whole and its fragility to unexpected disruptions or shocks. To this aim, we unravel the causal relationships between the 16 environmental conditions and human activity variables, mapping the backbone of the complex interplay between intervening physical observables—such as NO2 emissions, energy consumption, intervening climate variables, and different flavors of human mobility flows—to a causal network model. To identify a tipping point during the period of observation, denoting the presence of a regime shift between distinct network states (i.e., before and during the shock), we introduce a novel information-theoretic method based on statistical divergence widely used in statistical physics. We find that despite a measurable decrease in NO2 concentration, due to an overall decrease in human activities, locking down a region as a climate change mitigation is an insufficient remedy to reduce emissions. Our results provide a functional characterization of socioenvironmental interdependent systems, and our analytical framework can be used, more generally, to characterize environmental changes and their interdependencies using statistical physics.

Networks are a powerful tool to model complex systems, and the definition of many Graph Neural Networks (GNN), Deep Learning algorithms that can handle networks, has opened a new way to approach many real-world problems that would be hardly or even untractable. In this paper, we propose mGNN, a framework meant to generalize GNNs to the case of multi-layer networks, i.e., networks that can model multiple kinds of interactions and relations between nodes. Our approach is general (i.e., not task specific) and has the advantage of extending any type of GNN without any computational overhead. We test the framework into three different tasks (node and network classification, link prediction) to validate it.

The dynamics of a spreading disease and individual behavioral changes are entangled processes that have to be addressed together in order to effectively manage an outbreak. Here, we relate individual risk perception to the adoption of a specific set of control measures, as obtained from an extensive large-scale survey performed via Facebook—involving more than 500,000 respondents from 64 countries—showing that there is a “one-to-one” relationship between perceived epidemic risk and compliance with a set of mitigation rules. We then develop a mathematical model for the spreading of a disease—sharing epidemiological features with COVID-19—that explicitly takes into account non-compliant individual behaviors and evaluates the impact of a population fraction of infectious risk-deniers on the epidemic dynamics. Our modeling study grounds on a wide set of structures, including both synthetic and more than 180 real-world contact patterns, to evaluate, in realistic scenarios, how network features typical of human interaction patterns impact the spread of a disease. In both synthetic and real contact patterns we find that epidemic spreading is hindered for decreasing population fractions of risk-denier individuals. From empirical contact patterns we demonstrate that connectivity heterogeneity and group structure significantly affect the peak of hospitalized population: higher modularity and heterogeneity of social contacts are linked to lower peaks at a fixed fraction of risk-denier individuals while, at the same time, such features increase the relative impact on hospitalizations with respect to the case where everyone correctly perceive the risks.

In the last two decades, network science has proven to be an invaluable tool for the analysis of empirical systems across a wide spectrum of disciplines, with applications to data structures admitting a representation in terms of complex networks. On the one hand, especially in the last decade, an increasing number of applications based on geometric deep learning have been developed to exploit, at the same time, the rich information content of a complex network and the learning power of deep architectures, highlighting the potential of techniques at the edge between applied math and computer science. On the other hand, studies at the edge of network science and quantum physics are gaining increasing attention, e.g., because of the potential applications to quantum networks for communications, such as the quantum Internet. In this work, we briefly review a novel framework grounded on statistical physics and techniques inspired by quantum statistical mechanics which have been successfully used for the analysis of a variety of complex systems. The advantage of this framework is that it allows one to define a set of information-theoretic tools which find widely used counterparts in machine learning and quantum information science, while providing a grounded physical interpretation in terms of a statistical field theory of information dynamics. We discuss the most salient theoretical features of this framework and selected applications to protein–protein interaction networks, neuronal systems, social and transportation networks, as well as potential novel applications for quantum network science and machine learning.

An infodemic—an outpouring of information, including misleading and also fake news—is accompanying the current pandemic caused by SARS-CoV-2. In the absence of valid therapeutic approaches, behavioral responses may seriously affect the social dynamics of contagion, so the infodemic may cause confusion and disorientation in the public, leading to possible individually and socially harmful choices. This new phenomenon requires specific modeling efforts to better understand the complex intertwining of the epidemic and infodemic components of a pandemic crisis, with a view to building an integrative public health approach. We propose three models, from epidemiology to game theory, as potential candidates for the onset of the infodemics and statistically assess their accuracy in reproducing real infodemic waves observed in a data set of 390 million tweets collected worldwide. Our results show that evolutionary game-theory models are the most suitable ones to reproduce the observed infodemic modulations around the onset of the local epidemic wave. Furthermore, we find that the number of confirmed COVID-19 reported cases in each country and worldwide are driving the modeling dynamics with opposite effects.

A look at the Nobel laurate’s ground-breaking early work, and the academic environment that made it possible.

Complex biological systems consist of large numbers of interconnected units, characterized by emergent properties such as collective computation. In spite of all the progress in the last decade, we still lack a deep understanding of how these properties arise from the coupling between the structure and dynamics. Here, we introduce the multiscale emergent functional state, which can be represented as a network where links encode the flow exchange between the nodes, calculated using diffusion processes on top of the network. We analyze the emergent functional state to study the distribution of the flow among components of 92 fungal networks, identifying their functional modules at different scales and, more importantly, demonstrating the importance of functional modules for information content of networks, quantified in terms of network spectral entropy. Our results suggest that the topological complexity of fungal networks guarantees the existence of functional modules at different scales keeping the information entropy, and functional diversity, high.

For decades, from design theory to urban planning and management, from social sciences to urban environmental science, cities have been probed and analyzed from the partial perspective of single disciplines. The digital era, with its unprecedented data availability, is allowing for testing old theories and developing new ones, ultimately challenging relatively partial models. Our community has been in the last years providing more and more compelling evidence that cities are complex systems with emergent phenomena characterized by the collective behavior of their citizens who are themselves complex systems. However, more recently, it has also been shown that such multiscale complexity alone is not enough to describe some salient features of urban systems. Multilayer network modeling, accounting for both multiplexity of relationships and interdependencies among the city’s subsystems, is indeed providing a novel integrated framework to study urban backbones, their resilience to unexpected perturbations due to internal or external factors, and their human flows. In this paper, we first offer an overview of the transdisciplinary efforts made to cope with the three dimensions of complexity of the city: the complexity of the urban environment, the complexity of human cognition about the city, and the complexity of city planning. In particular, we discuss how the most recent findings, for example, relating the health and wellbeing of communities to urban structure and function, from traffic congestion to distinct types of pollution, can be better understood considering a city as a multiscale and multilayer complex system. The new challenges posed by the postpandemic scenario give to this perspective an unprecedented relevance, with the necessity to address issues of reconstruction of the social fabric, recovery from prolonged psychological, social and economic stress with the ensuing mental health and wellbeing issues, and repurposing of urban organization as a consequence of new emerging practices such as massive remote working. By rethinking cities as large-scale active matter systems far from equilibrium which consume energy, process information, and adapt to the environment, we argue that enhancing social engagement, for example, involving citizens in codesigning the city and its changes in this critical postpandemic phase, can trigger widespread adoption of good practices leading to emergent effects with collective benefits which can be directly measured.

From physics to engineering, biology and social science, natural and artificial systems are characterized by interconnected topologies whose features – e.g., heterogeneous connectivity, mesoscale organization, hierarchy – affect their robustness to external perturbations, such as targeted attacks to their units. Identifying the minimal set of units to attack to disintegrate a complex network, i.e. network dismantling, is a computationally challenging (NP-hard) problem which is usually attacked with heuristics. Here, we show that a machine trained to dismantle relatively small systems is able to identify higher-order topological patterns, allowing to disintegrate large-scale social, infrastructural and technological networks more efficiently than human-based heuristics. Remarkably, the machine assesses the probability that next attacks will disintegrate the system, providing a quantitative method to quantify systemic risk and detect early-warning signals of system’s collapse. This demonstrates that machine-assisted analysis can be effectively used for policy and decision-making to better quantify the fragility of complex systems and their response to shocks.

The public health research agenda for infodemic management has five workstreams: (1) measuring and continuously monitoring the impact of infodemics during health emergencies; (2) detecting signals and understanding the spread and risk of infodemics; (3) responding and deploying interventions that mitigate and protect against infodemics and their harmful effects; (4) evaluating infodemic interventions and strengthening the resilience of individuals and communities to infodemics; and (5) promoting the development, adaptation, and application of interventions and toolkits for infodemic management. Each workstream identifies research questions and highlights 49 high priority research questions.

As COVID-19 spreads worldwide, an infodemic – i.e., an over-abundance of information, reliable or not – spreads across the physical and the digital worlds, triggering behavioral responses which cause public health concern. We study 200 million interactions captured from Twitter during the early stage of the pandemic, from January to April 2020, to understand its socio-informational structure on a global scale. The COVID-19 global communication network is characterized by knowledge groups, hierarchically organized in sub-groups with well-defined geo-political and ideological characteristics. Communication is mostly segregated within groups and driven by a small number of subjects: 0.1% of users account for up to 45% and 10% of activities and news shared, respectively, centralizing the information flow. Contradicting the idea that digital social media favor active participation and co-creation of online content, our results imply that public health policy strategies to counter the effects of the infodemic must not only focus on information content, but also on the social articulation of its diffusion mechanisms, as a given community tends to be relatively impermeable to news generated by non-aligned sources.

Interconnected systems have to route information to function properly: At the lowest scale neural cells exchange electrochemical signals to communicate, while at larger scales animals and humans move between distinct spatial patches and machines exchange information via the Internet through communication protocols. Nontrivial patterns emerge from the analysis of information flows, which are not captured either by broadcasting, such as in random walks, or by geodesic routing, such as shortest paths. In fact, alternative models between those extreme protocols are still eluding us. Here we propose a class of stochastic processes, based on biased random walks, where agents are driven by a physical potential pervading the underlying network topology. By considering a generalized Coulomb dependence on the distance on destination(s), we show that it is possible to interpolate between random walk and geodesic routing in a simple and effective way. We demonstrate that it is not possible to find a one-size-fit-all solution to efficient navigation and that network heterogeneity or modularity has measurable effects. We illustrate how our framework can describe the movements of animals and humans, capturing with a stylized model some measurable features of the latter. From a methodological perspective, our potential-driven random walks open the doors to a broad spectrum of analytical tools, ranging from random-walk centralities to geometry induced by potential-driven network processes.

With hindsight, the main weakness behind the ineffective response to the coronavirus disease 2019 (COVID-19) pandemic in some countries has been the failure to understand, and take account of, the multilayered systemic interdependencies that spread the effects of the pandemic across social, technological, economic and health-care dimensions. For example, to respond to the COVID-19 pandemic, all people were required to rapidly adjust to social distancing and travel restrictions. Such a complex behavioural response entails adaptation to achieve a full recovery from the systemic shock. To capitalize on the positive effects of disruption to the status quo, much more complex socioeconomic modelling needs to be considered when designing and evaluating possible public health interventions that have major behavioural implications. We provide a simple example of how this reasoning may highlight generally unacknowledged connections and interdependencies and guide the construction of scenarios that can inform policy decisions to enhance the resilience of society and tackle existing societal challenges.

This special theme issue of Big Data & Society presents leading-edge, interdisciplinary research that focuses on examining how health-related (mis-)information is circulating on social media. In particular, we are focusing on how computational and Big Data approaches can help to provide a better understanding of the ongoing COVID-19 infodemic (overexposure to both accurate and misleading information on a health topic) and to develop effective strategies to combat it.

Chapter for the book Coronavirus Disease - COVID-19. Advances in Experimental Medicine and Biology, edited by N. Rezaei

Information exchange in the human brain is crucial for vital tasks and to drive diseases. Neuroimaging techniques allow for the indirect measurement of information flows among brain areas and, consequently, for reconstructing connectomes analyzed through the lens of network science. However, standard analyses usually focus on a small set of network indicators and their joint probability distribution. Here, we propose an information-theoretic approach for the analysis of synthetic brain networks (based on generative models) and empirical brain networks, and to assess connectome's information capacity at different stages of dementia. Remarkably, our framework accounts for the whole network state, overcoming limitations due to limited sets of descriptors, and is used to probe human connectomes at different scales. We find that the spectral entropy of empirical data lies between two generative models, indicating an interpolation between modular and geometry-driven structural features. In fact, we show that the mesoscale is suitable for characterizing the differences between brain networks and their generative models. Finally, from the analysis of connectomes obtained from healthy and unhealthy subjects, we demonstrate that significant differences between healthy individuals and the ones affected by Alzheimer’s disease arise at the microscale (max. posterior probability smaller than 1%) and at the mesoscale (max. posterior probability smaller than 10%).

Hypergraphs offer an explicit formalism to describe multibody interactions in complex systems. To connect dynamics and function in systems with these higher-order interactions, network scientists have generalised random-walk models to hypergraphs and studied the multibody effects on flow-based centrality measures. Mapping the large-scale structure of those flows requires effective community detection methods applied to cogent network representations. For different hypergraph data and research questions, which combination of random-walk model and network representation is best? We define unipartite, bipartite, and multilayer network representations of hypergraph flows and explore how they and the underlying random-walk model change the number, size, depth, and overlap of identified multilevel communities. These results help researchers choose the appropriate modelling approach when mapping flows on hypergraphs.

The spread of an infectious disease is well approximated by metapopulation networks connected by human mobility flow and upon which an epidemiological model is defined. In order to account for travel restrictions or cancellation we introduce a model with a parameter that explicitly indicates the ratio between the time scales of the intervening processes. We study the critical properties of the epidemic process and its dependence on such a parameter. We find that the critical threshold separating the absorbing state from the active state depends on the scale parameter and exhibits a critical behavior itself: a metacritical point – a critical value in the curve of critical points – reflected in the behavior of the attack rate measured for a wide range of empirical metapopulation systems. Our results have potential policy implications, since they establish a non-trivial critical behavior between temporal scales of reaction (epidemic spread) and diffusion (human mobility) processes.

Complex systems are large collections of entities that organize themselves into non-trivial structures, represented as networks. One of their key emergent properties is robustness against random failures or targeted attacks —i.e., the networks maintain their integrity under removal of nodes or links. Here, we introduce network entanglement to study network robustness through a multiscale lens, encoded by the time required for information diffusion through the system. Our measure’s foundation lies upon a recently developed statistical field theory for information dynamics within interconnected systems. We show that at the smallest temporal scales, the node-network entanglement reduces to degree, whereas at extremely large scales, it measures the direct role played by each node in keeping the network connected. At the meso-scale, entanglement plays a more important role, measuring the importance of nodes for the transport properties of the system. We use entanglement as a centrality measure capturing the role played by nodes in keeping the overall diversity of the information flow. As an application, we study the disintegration of empirical social, biological and transportation systems, showing that the nodes central for information dynamics are also responsible for keeping the network integrated.

Network science enables the effective analysis of real interconnected systems, characterized by a complex interplay between topology and network flows. It is well-known that the topology of a network affects its resilience to failures or attacks, as well as its functions. Many real systems—such as the Internet, transportation networks and the brain—exchange information, so it is crucial to quantify how efficiently system’s units communicate. Measures of parallel communication efficiency for weighted networks rely on the identification of an ideal version of the system, which currently lacks a universal definition. Consequently, an inattentive choice might hinder a rigorous comparison of network flows across scales or might lead to a descriptor not robust to fluctuations in the topology or the flows. We propose a physically-grounded estimator of flow efficiency valid for any weighted network, regardless of scale, nature of weights and (missing) metadata, allowing for comparison across disparate systems. Our estimator captures the effect of flows heterogeneity along with topological differences of both synthetic and empirical systems. We also show that cutting the heaviest connections may increase the average efficiency of the system and hence, counterintuively, a sparser network is not necessarily less efficient.

Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat them independently. Recent evidence suggests that this separation may be inadequate, as there can be significant coupling between frequency bands (interlayer connectivity). A multilayer network approach offers a solution to analyze frequency-specific networks in one framework. We propose to use a recently developed network reconstruction method in conjunction with phase oscillator models to estimate interlayer connectivity that optimally fits the empirical data. This approach determines interlayer connectivity based on observed frequency-specific time series of the phase and a connectome derived from diffusion weighted imaging. The performance of this interlayer reconstruction method was evaluated in-silico. Our reconstruction of the underlying interlayer connectivity agreed to very high degree with the ground truth. Subsequently, we applied our method to empirical resting-state MEG data obtained from healthy subjects and reconstructed two-layered networks consisting of either alpha-to-beta or theta-to-gamma band connectivity. Our analysis revealed that interlayer connectivity is dominated by a multiplex structure, i.e. by one-to-one interactions for both alpha-to-beta band and theta-to-gamma band networks. For theta–gamma band networks, we also found a plenitude of interlayer connections between distant nodes, though weaker connectivity relative to the one-to-one connections. Our work is an stepping stone towards the identification of interdependencies across frequency-specific networks. Our results lay the ground for the use of the promising multilayer framework in this field with more-informed and justified interlayer connections.

Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system’s units in random order, or sequentially ordered by specific topological descriptors. However, in the vast majority of empirical applications, it is required to dismantle the network following more sophisticated protocols, for instance, by combining topological properties and non-topological node metadata. We propose a novel mathematical framework to fill this gap: networks are enriched with features and their nodes are removed according to the importance in the feature space. We consider features of different nature, from ones related to the network construction to ones related to dynamical processes such as epidemic spreading. Our framework not only provides a natural generalization of percolation but, more importantly, offers an accurate way to test the robustness of networks in realistic scenarios.

Protein–protein interaction networks have been used to investigate the influence of SARS-CoV-2 viral proteins on the function of human cells, laying out a deeper understanding of COVID–19 and providing ground for applications, such as drug repurposing. Characterizing molecular (dis)similarities between SARS-CoV-2 and other viral agents allows one to exploit existing information about the alteration of key biological processes due to known viruses for predicting the potential effects of this new virus. Here, we compare the novel coronavirus network against 92 known viruses, from the perspective of statistical physics and computational biology. We show that regulatory spreading patterns, physical features and enriched biological pathways in targeted proteins lead, overall, to meaningful clusters of viruses which, across scales, provide complementary perspectives to better characterize SARS-CoV-2 and its effects on humans. Our results indicate that the virus responsible for COVID–19 exhibits expected similarities, such as to Influenza A and Human Respiratory Syncytial viruses, and unexpected ones with different infection types and from distant viral families, like HIV1 and Human Herpes virus. Taken together, our findings indicate that COVID–19 is a systemic disease with potential effects on the function of multiple organs and human body sub-systems.

Complex networks are characterized by latent geometries induced by their topology or by the dynamics on the top of them. In the latter case, different network-driven processes induce distinct geometric features that can be captured by adequate metrics. Random walks, a proxy for a broad spectrum of processes, from simple contagion to metastable synchronization and consensus, have been recently used in [Phys. Rev. Lett. 118, 168301 (2017)] to define the class of diffusion geometry and pinpoint the functional mesoscale organization of complex networks from a genuine geometric perspective. Here, we firstly extend this class to families of distinct random walk dynamics -- including local and non-local information -- on the top of multilayer networks -- a paradigm for biological, neural, social, transportation, biological and financial systems -- overcoming limitations such as the presence of isolated nodes and disconnected components, typical of real-world networks. Secondly, we characterize the multilayer diffusion geometry of synthetic and empirical systems, highlighting the role played by different random search dynamics in shaping the geometric features of the corresponding diffusion manifolds.

Networks are finite metric spaces, with distances defined by the shortest paths between nodes. However, this is not the only form of network geometry: two others are the geometry of latent spaces underlying many networks and the effective geometry induced by dynamical processes in networks. These three approaches to network geometry are intimately related, and all three of them have been found to be exceptionally efficient in discovering fractality, scale invariance, self-similarity and other forms of fundamental symmetries in networks. Network geometry is also of great use in a variety of practical applications, from understanding how the brain works to routing in the Internet. We review the most important theoretical and practical developments dealing with these approaches to network geometry and offer perspectives on future research directions and challenges in this frontier in the study of complexity.

Information manipulation is widespread in today’s media environment. Online networks have disrupted the gatekeeping role of traditional media by allowing various actors to influence the public agenda; they have also allowed automated accounts (or bots) to blend with human activity in the flow of information. Here, we assess the impact that bots had on the dissemination of content during two contentious political events that evolved in real time on social media. We focus on events of heightened political tension because they are particularly susceptible to information campaigns designed to mislead or exacerbate conflict. We compare the visibility of bots with human accounts, verified accounts, and mainstream news outlets. Our analyses combine millions of posts from a popular microblogging platform with web-tracking data collected from two different countries and timeframes. We employ tools from network science, natural language processing, and machine learning to analyze the diffusion structure, the content of the messages diffused, and the actors behind those messages as the political events unfolded. We show that verified accounts are significantly more visible than unverified bots in the coverage of the events but also that bots attract more attention than human accounts. Our findings highlight that social media and the web are very different news ecosystems in terms of prevalent news sources and that both humans and bots contribute to generate discrepancy in news visibility with their activity.

A volunteer effort by Artificial Intelligence (AI) researchers has shown it can deliver significant research outcomes rapidly to help tackle COVID-19. Within two months, CLAIRE’s self-organising volunteers delivered the World’s first comprehensive curated repository of COVID-19-related datasets useful for drug-repurposing, drafted review papers on the role CT/X-ray scan analysis and robotics could play, and progressed research in other areas. Given the pace required and nature of voluntary efforts, the teams faced a number of challenges. These offer insights in how better to prepare for future volunteer scientific efforts and large scale, data-dependent AI collaborations in general. We offer seven recommendations on how to best leverage such efforts and collaborations in the context of managing future crises.

Revealing the structural features of a complex system from the observed collective dynamics is a fundamental problem in network science. To compute the various topological descriptors commonly used to characterize the structure of a complex system (e.g., the degree, the clustering coefficient, etc.), it is usually necessary to completely reconstruct the network of relations between the subsystems. Several methods are available to detect the existence of interactions between the nodes of a network. By observing some physical quantities through time, the structural relationships are inferred using various discriminating statistics (e.g., correlations, mutual information, etc.). In this setting, the uncertainty about the existence of the edges is reflected in the uncertainty about the topological descriptors. In this study, we propose a methodological framework to evaluate this uncertainty, replacing the topological descriptors, even at the level of a single node, with appropriate probability distributions, eluding the reconstruction phase. Our theoretical framework agrees with the numerical experiments performed on a large set of synthetic and real-world networks. Our results provide a grounded framework for the analysis and the interpretation of widely used topological descriptors, such as degree centrality, clustering, and clusters, in scenarios in which the existence of network connectivity is statistically inferred or when the probabilities of existence pij of the edges are known. To this purpose, we also provide a simple and mathematically grounded process to transform the discriminating statistics into the probabilities pij.

Increasing evidence suggests that cities are complex systems, with structural and dynamical features responsible for a broad spectrum of emerging phenomena. Here we use a unique data set of human flows and couple it with information on the underlying street network to study, simultaneously, the structural and functional organisation of 10 world megacities. We quantify the efficiency of flow exchange between areas of a city in terms of integration and segregation using well defined measures. Results reveal unexpected complex patterns that shed new light on urban organisation. Large cities tend to be more segregated and less integrated, while their overall topological organisation resembles that of small world networks. At the same time, the heterogeneity of flows distribution might act as a catalyst for further integrating a city. Our analysis unravels how human behaviour influences, and is influenced by, the urban environment, suggesting quantitative indicators to control integration and segregation of human flows that can be used, among others, for restriction policies to adopt during emergencies and, as an interesting byproduct, allows us to characterise functional (dis)similarities of different metropolitan areas, countries, and cultures.

How components of the distributed brain networks that support cognition participate in typical functioning remains a largely unanswered question. An important subgroup of regions in the larger network are connector hubs, which are areas that are highly connected to several other functionally-specialized sets of regions, and are likely important for sensorimotor integration. The present study attempts to characterize connector hubs involved in typical expressive language functioning using a data-driven, multimodal, full multilayer MEG connectivity-based pipeline. Twelve adolescents, 16-18 years of age (5 male) participated in this study. Participants underwent MEG scanning during a verb generation task. MEG and structural connectivity were calculated at the whole-brain level. Amplitude-amplitude coupling (AAC) was used to compute functional connections both within and between discrete frequency bins. AAC values were then multiplied by a binary structural connectivity matrix, then entered into full multilayer network analysis. Initially, hubs were defined based on multilayer versatility and subsequently re-ranked by a novel measure called delta centrality on interconnectedness (DCI). DCI is defined as the percent change in inter-frequency interconnectedness after removal of a hub. We resolved regions that are important for between-frequency communication among other areas during expressive language, with several potential theoretical and clinical applications that can be generalized to other cognitive domains. Our multilayer, data-driven framework captures nonlinear connections that span across scales that are often missed in conventional analyses. The present study suggests that crucial hubs may be conduits for inter-frequency communication between action and perception systems that are crucial for typical functioning.

Political and environmental factors—e.g., regional conflicts and global warming—increase large-scale migrations, posing extraordinary societal challenges to policymakers of destination countries. A common concern is that such a massive arrival of people—often from a country with a disrupted healthcare system—can increase the risk of vaccine-preventable disease outbreaks like measles. We analyze human flows of 3.5 million (M) Syrian refugees in Turkey inferred from massive mobile-phone data to verify this concern. We use multilayer modeling of interdependent social and epidemic dynamics to demonstrate that the risk of disease reemergence in Turkey, the main host country, can be dramatically reduced by 75 to 90% when the mixing of Turkish and Syrian populations is high. Our results suggest that maximizing the dispersal of refugees in the recipient population contributes to impede the spread of sustained measles epidemics, rather than favoring it. Targeted vaccination campaigns and policies enhancing social integration of refugees are the most effective strategies to reduce epidemic risks for all citizens.

Introduction: We introduce in this study CovMulNet19, a comprehensive COVID-19 network containing all available known interactions involving SARS-CoV-2 proteins, interacting-human proteins, diseases and symptoms that are related to these human proteins, and compounds that can potentially target them. Materials and Methods: Extensive network analysis methods, based on a bootstrap approach, allow us to prioritize a list of diseases that display a high similarity to COVID-19 and a list of drugs that could potentially be beneficial to treat patients. As a key feature of CovMulNet19, the inclusion of symptoms allows a deeper characterization of the disease pathology, representing a useful proxy for COVID-19-related molecular processes. Results: We recapitulate many of the known symptoms of the disease and we find the most similar diseases to COVID-19 reflect conditions that are risk factors in patients. In particular, the comparison between CovMulNet19 and randomized networks recovers many of the known associated comorbidities that are important risk factors for COVID-19 patients, through identified similarities with intestinal, hepatic, and neurological diseases as well as with respiratory conditions, in line with reported comorbidities. Conclusion: CovMulNet19 can be suitably used for network medicine analysis, as a valuable tool for exploring drug repurposing while accounting for the intervening multidimensional factors, from molecular interactions to symptoms.

During COVID-19, governments and the public are fighting not only a pandemic but also a co-evolving infodemic—the rapid and far-reaching spread of information of questionable quality. We analysed more than 100 million Twitter messages posted worldwide during the early stages of epidemic spread across countries (from 22 January to 10 March 2020) and classified the reliability of the news being circulated. We developed an Infodemic Risk Index to capture the magnitude of exposure to unreliable news across countries. We found that measurable waves of potentially unreliable information preceded the rise of COVID-19 infections, exposing entire countries to falsehoods that pose a serious threat to public health. As infections started to rise, reliable information quickly became more dominant, and Twitter content shifted towards more credible informational sources. Infodemic early-warning signals provide important cues for misinformation mitigation by means of adequate communication strategies.

Multilayer systems are coupled networks characterized by different contexts (layers) of interaction and have gained much attention recently due to their suitability to describe a broad spectrum of empirical complex systems. They are very fragile to percolation and first-neighbor failure propagation, but little is known about how they respond to non-local disruptions, as it occurs in failures induced by flow redistribution, for example. Acknowledging that many socio-technical and biological systems sustain a flow of some physical quantity, such as energy or information, across the their components, it becomes crucial to understand when the flow redistribution can cause global cascades of failures in order to design robust systems, to increase their resilience or to learn how to efficiently dismantle them. In this paper we study the impact that different multiplex topological features have on the robustness of the system when subjected to non-local cascade propagation. We first numerically demonstrate that this dynamics has a critical value at which a small initial perturbation effectively dismantles the entire network, and that the transition appears abruptly. Then we identify that the excess of flow caused by a failure is, in general, more homogeneously distributed the networks in which the average distance between nodes is small. Using this information we find that aggregated versions of multiplex networks tend to overestimate robustness, even though to make the system more robust can be achieved by increasing the number of layers. Our predictions are confirmed by simulated cascading failures in a real multilayer system.

The constituents of a complex system exchange information to function properly. Their signaling dynamics often leads to the appearance of emergent phenomena, such as phase transitions and collective behaviors. While information exchange has been widely modeled by means of distinct spreading processes—such as continuous-time diffusion, random walks, synchronization and consensus—on top of complex networks, a unified and physically grounded framework to study information dynamics and gain insights about the macroscopic effects of microscopic interactions is still eluding us. In this paper, we present this framework in terms of a statistical field theory of information dynamics, unifying a range of dynamical processes governing the evolution of information on top of static or time-varying structures. We show that information operators form a meaningful statistical ensemble and their superposition defines a density matrix that can be used for the analysis of complex dynamics. As a direct application, we show that the von Neumann entropy of the ensemble can be a measure of the functional diversity of complex systems, defined in terms of the functional differentiation of higher-order interactions among their components. Our results suggest that modularity and hierarchy, two key features of empirical complex systems—from the human brain to social and urban networks—play a key role to guarantee functional diversity and, consequently, are favored.

Online social networks are the perfect test bed to better understand large-scale human behavior in interacting contexts. Although they are broadly used and studied, little is known about how their terms of service and posting rules affect the way users interact and information spreads. Acknowledging the relation between network connectivity and functionality, we compare the robustness of two different online social platforms, Twitter and Gab, with respect to banning, or dismantling, strategies based on the recursive censor of users characterized by social prominence (degree) or intensity of inflammatory content (sentiment). We find that the moderated (Twitter) vs. unmoderated (Gab) character of the network is not a discriminating factor for intervention effectiveness. We find, however, that more complex strategies based upon the combination of topological and content features may be effective for network dismantling. Our results provide useful indications to design better strategies for countervailing the production and dissemination of anti-social content in online social platforms.

Peer review is a cornerstone of modern scientific endeavor. However, there is growing consensus that several limitations of the current peer review system, from lack of incentives to reviewers to lack of transparency, risks to undermine its benefits. Here, we introduce the PRINCIPIA (http://www.principia.network/) framework for peer-review of scientific outputs (e.g., papers, grant proposals or patents). The framework allows key players of the scientific ecosystem -- including existing publishing groups -- to create and manage peer-reviewed journals, by building a free market for reviews and publications. PRINCIPIA's referees are transparently rewarded according to their efforts and the quality of their reviews. PRINCIPIA also naturally allows to recognize the prestige of users and journals, with an intrinsic reputation system that does not depend on third-parties. PRINCIPIA re-balances the power between researchers and publishers, stimulates valuable assessments from referees, favors a fair competition between journals, and reduces the costs to access research output and to publish.

In this RISJ Factsheet, we assess the volume and patterns of toxic conversations on social media during the Covid-19 pandemic. We specifically analyse worldwide conversations on Twitter targeting the World Health Organization (WHO), a central actor during the pandemic. Our analysis contributes to the current research on the health of online debates amid the increasing role of social media as a critical entrance to information and mediator of public opinion building.

Equations governing the nonlinear dynamics of complex systems are usually unknown, and indirect methods are used to reconstruct their manifolds. In turn, they depend on embedding parameters requiring other methods and long temporal sequences to be accurate. In this paper, we show that an optimal reconstruction can be achieved by lossless compression of system’s time course, providing a self-consistent analysis of its dynamics and a measure of its complexity, even for short sequences. Our measure of complexity detects system’s state changes such as weak synchronization phenomena, characterizing many systems, in one step, integrating results from Lyapunov and fractal analysis

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.

In the era of social media, every day billions of individuals produce content in socio-technical systems resulting in a deluge of information. However, human attention is a limited resource and it is increasingly challenging to consume the most suitable content for one's interests. In fact, the complex interplay between individual and social activities in social systems overwhelmed by information results in bursty activity of collective attention which are still poorly understood. Here, we tackle this challenge by analyzing the online activity of millions of users in a popular microblogging platform during exceptional events, from NBA Finals to the elections of Pope Francis and the discovery of gravitational waves. We observe extreme fluctuations in collective attention that we are able to characterize and explain by considering the co-occurrence of two fundamental factors: the heterogeneity of social interactions and the preferential attention towards influential users. Our findings demonstrate how combining simple mechanisms provides a route towards complex social phenomena.

Units of complex systems -- such as neurons in the brain or individuals in societies -- must communicate efficiently to function properly: e.g., allowing electrochemical signals to travel quickly among functionally connected neuronal areas in the human brain, or allowing for fast navigation of humans and goods in complex transportation landscapes. The coexistence of different types of relationships among the units, entailing a multilayer represention in which types are considered as networks encoded by layers, plays an important role in the quality of information exchange among them. While altering the structure of such systems -- e.g., by physically adding (or removing) units, connections or layers -- might be costly, coupling the dynamics of subset(s) of layers in a way that reduces the number of redundant diffusion pathways across the multilayer system, can potentially accelerate the overall information flow. To this aim, we introduce a framework for functional reducibility which allow us to enhance transport phenomena in multilayer systems by coupling layers together with respect to dynamics rather than structure. Mathematically, the optimal configuration is obtained by maximizing the deviation of system's entropy from the limit of free and non-interacting layers. Our results provide a transparent procedure to reduce diffusion time and optimize non-compact search processes in empirical multilayer systems, without the cost of altering the underlying structure.

In collective decision-making, a group of independent experts propose individual choices to reach a common decision. This is the case of competitive events such as Olympics, international Prizes or grant evaluation, where groups of experts evaluate individual performances to assign resources, e.g. scores, recognitions, or funding. However, there are systems where evaluating individual’s performance is difficult: in those cases, other factors play a relevant role, leading to unexpected emergent phenomena from micro-scale interactions. The Nobel assignment procedure, rooted on recommendations, is one of these systems. Here we unveil its network, reconstructed from official data and metadata about nominators, nominees and awardees between 1901 and 1965, consisting of almost 12,000 individuals and 17,000 nominations. We quantify the role of homophily, academic reputation of nominators and their prestige neighborhood, showing that nominees endorsed by central actors – who are part of the system’s core because of their prestigious reputation – are more likely to become laureate within a finite time scale than nominees endorsed by nominators in the periphery of the network. We propose a mechanistic model which reproduces all the salient observations and allows to design possible countermeasures to mitigate observed effects..

Identification of modules in molecular networks is at the core of many current analysis methods in biomedical research. However, how well different approaches identify disease-relevant modules in different types of networks remains poorly understood. We launched the "Disease Module Identification DREAM Challenge", an open competition to comprehensively assess module identification methods across diverse gene, protein and signaling networks. Predicted network modules were tested for association with complex traits and diseases using a unique collection of 180 genome-wide association studies (GWAS). While a number of approaches were successful in terms of discovering complementary trait-associated modules, consensus predictions derived from the challenge submissions performed best. We find that most of these modules correspond to core disease-relevant pathways, which often comprise therapeutic targets and correctly prioritize candidate disease genes. This community challenge establishes benchmarks, tools and guidelines for molecular network analysis to study human disease biology (https://synapse.org/modulechallenge).

Untangling the complex interplay between phenotype and genotype is crucial to the effective characterization and subtyping of diseases. Here we build and analyze the multiplex network of 779 human diseases, which consists of a genotype-based layer and a phenotype-based layer. We show that diseases with common genetic constituents tend to share symptoms, and uncover how phenotype information helps boost genotype information. Moreover, we offer a flexible classification of diseases that considers their molecular underpinnings alongside their clinical manifestations. We detect cohesive groups of diseases that have high intra-group similarity at both the molecular and the phenotypic level. Inspecting these disease classes, we demonstrate the underlying pathways that connect diseases mechanistically. We observe monogenic disorders grouped together with complex diseases for which they increase the risk factor. We propose potentially new disease associations that arise as a unique feature of the information flow within and across the two layers.

Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be considered as the `centre' of a complex network. In fact, this problem corresponds to finding the median of a complex network. The median is a non-parametric and robust estimator of the location parameter of a probability distribution. In this work, we present the most natural generalisation of the concept of median to the realm of complex networks, discussing its advantages for defining the centre of the system and percentiles around that centre. To this aim, we introduce a new statistical data depth and we apply it to networks embedded in a geometric space induced by different metrics. The application of our framework to empirical networks allows us to identify median nodes which are socially or biologically relevant.

Recent progress in applying complex network theory to problems faced in quantum information and computation has resulted in a beneficial crossover between two fields. Complex network methods have successfully been used to characterize quantum walk and transport models, entangled communication networks, graph-theoretic models of emergent space-time and in detecting mesoscale structure in quantum systems. Information physics is setting the stage for a theory of complex and networked systems with quantum information-inspired methods appearing in complex network science, including information-theoretic distance and correlation measures for network characterization. Novel quantum induced effects have been predicted in random graphs---where edges represent entangled links---and quantum computer algorithms have recently been proposed to offer super-polynomial enhancement for several network and graph theoretic problems. Here we review the results at the cutting edge, pinpointing the similarities and reconciling the differences found in the series of results at the intersection of these two fields.

With its fifth edition, the Mediterranean School of Complex Networks is one of the oldest international summer schools, run without interruptions, which is fully devoted to teach the fundamentals of Network Science and its current trends to early-career researchers.

The blockchain technology promises to transform finance, money and even governments. However, analyses of blockchain applicability and robustness typically focus on isolated systems whose actors contribute mainly by running the consensus algorithm. Here, we highlight the importance of considering trustless platforms within the broader ecosystem that includes social and communication networks. As an example, we analyse the flash-crash observed on 21st June 2017 in the Ethereum platform and show that a major phenomenon of social coordination led to a catastrophic cascade of events across several interconnected systems. We propose the concept of “emergent centralisation” to describe situations where a single system becomes critically important for the functioning of the whole ecosystem, and argue that such situations are likely to become more and more frequent in interconnected socio-technical systems. We anticipate that the systemic approach we propose will have implications for future assessments of trustless systems and call for the attention of policy-makers on the fragility of our interconnected and rapidly changing world.

Overwhelming empirical evidence has shown that online social dynamics mirrors real-world events. Hence, understanding the mechanisms leading to social contagion in online ecosystems is fundamental for predicting, and even manouvering, human behavior. It has been shown that one of such mechanisms is based on fabricating armies of automated agents that are known as social bots. Using the recent Italian elections as an emblematic case study, here we provide evidence for the existence of a special class of highly influential users, that we name "augmented humans". They exploit bots for enhancing both their visibility and influence, generating deep information cascades to the same extent of news media and other broadcasters. Augmented humans uniformly infiltrate across the full range of identified clusters of accounts, the latter reflecting political parties and their electoral ranks.

Social 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.

Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several studies are highlighting how simple networks – obtained by aggregating or neglecting temporal or categorical description of biological data – are not able to account for the richness of information characterizing biological systems. More complex models, namely multilayer networks, are needed to account for interdependencies, often varying across time, of biological interacting units within a cell, a tissue or parts of an organism. Gosak et al. [1] review the most recent advances in the application of multilayer networks for modeling complex biological systems, from molecular interactions within a cell to neuronal connectivity of the human brain.

A variety of complex systems exhibit different types of relationships simultaneously that can be modeled by multiplex networks. A typical problem is to determine the community structure of such systems that, in general, depend on one or more parameters to be tuned. In this study we propose one measure, grounded on information theory, to find the optimal value of the relax rate characterizing Multiplex Infomap, the generalization of the Infomap algorithm to the realm of multilayer networks. We evaluate our methodology on synthetic networks, to show that the most representative community structure can be reliably identified when the most appropriate relax rate is used. Capitalizing on these results, we use this measure to identify the most reliable meso-scale functional organization in the human protein-protein interaction multiplex network and compare the observed clusters against a collection of independently annotated gene sets from the Molecular Signatures Database (MSigDB). Our analysis reveals that modules obtained with the optimal value of the relax rate are biologically significant and, remarkably, with higher functional content than the ones obtained from the aggregate representation of the human proteome. Our framework allows us to characterize the meso-scale structure of those multilayer systems whose layers are not explicitly interconnected each other -- as in the case of edge-colored models -- the ones describing most biological networks, from proteomes to connectomes.

Chapter for the book Multiplex and Multilevel Networks, edited by Stefano Battiston, Guido Caldarelli, Antonios Garas

We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated for a variety of synthetic network models. By coupling distance entropy information with closeness centrality, we introduce a network cartography which allows one to reduce the degeneracy of ranking based on closeness alone. We apply this methodology to the empirical multiplex lexical network encoding the linguistic relationships known to English speaking toddlers. We show that the distance entropy cartography better predicts how children learn words compared to closeness centrality. Our results highlight the importance of distance entropy for gaining insights from distance patterns in complex networks.

Word similarities affect language acquisition and use in a multi-relational way barely accounted for in the literature. We propose a multiplex network representation of this mental lexicon of word similarities as a natural framework for investigating large-scale cognitive patterns. Our representation accounts for semantic, taxonomic, and phonological interactions and it identifies a cluster of words which are used with greater frequency, are identified, memorised, and learned more easily, and have more meanings than expected at random. This cluster emerges around age 7 through an explosive transition not reproduced by null models. We relate this explosive emergence to polysemy – redundancy in word meanings. Results indicate that the word cluster acts as a core for the lexicon, increasing both lexical navigability and robustness to linguistic degradation. Our findings provide quantitative confirmation of existing conjectures about core structure in the mental lexicon and the importance of integrating multi-relational word-word interactions in psycholinguistic frameworks.

Collective phenomena emerge from the interaction of natural or artificial units with a complex organization. The interplay between structural patterns and dynamics might induce functional clusters that, in general, are different from topological ones. In biological systems, like the human brain, the overall functionality is often favored by the interplay between connectivity and synchronization dynamics, with functional clusters that do not coincide with anatomical modules in most cases. In social, sociotechnical, and engineering systems, the quest for consensus favors the emergence of clusters. Despite the unquestionable evidence for mesoscale organization of many complex systems and the heterogeneity of their interconnectivity, a way to predict and identify the emergence of functional modules in collective phenomena continues to elude us. Here, we propose an approach based on random walk dynamics to define the diffusion distance between any pair of units in a networked system. Such a metric allows us to exploit the underlying diffusion geometry to provide a unifying framework for the intimate relationship between metastable synchronization, consensus, and random search dynamics in complex networks, pinpointing the functional mesoscale organization of synthetic and biological systems.

Publishing reproducible analyses is a long-standing and widespread challenge for the scientific community, funding bodies and publishers. Although a definitive solution is still elusive, the problem is recognized to affect all disciplines and lead to a critical system inefficiency. Here, we propose a blockchain-based approach to enhance scientific reproducibility, with a focus on life science studies and precision medicine. While the interest of encoding permanently into an immutable ledger all the study key information-including endpoints, data and metadata, protocols, analytical methods and all findings-has been already highlighted, here we apply the blockchain approach to solve the issue of rewarding time and expertise of scientists that commit to verify reproducibility. Our mechanism builds a trustless ecosystem of researchers, funding bodies and publishers cooperating to guarantee digital and permanent access to information and reproducible results. As a natural byproduct, a procedure to quantify scientists and institutions reputation for ranking purposes is obtained.

Understanding how the human brain is structured, and how its architecture is related to the function, is of paramount importance for a variety of applications, including, but not limited to, new ways to prevent, deal with and cure brain diseases, such as Alzheimer’s or Parkinson’s, and psychiatric disorders, such as Schizophrenia. The recent advances in structural and functional neuroimaging, together with the increasing attitude to interdisciplinary approaches involving computer science, mathematics and physics, are fostering interesting results from computational neuroscience, that are quite often based on the analysis of complex network representation of human brain. In the last years, this representation experienced a theoretical and computational revolution that are breaching neuroscience, allowing to cope with the increasing complexity of human brain across multiple scales and in multiple dimensions, and to model structural and functional connectivity from new perspectives, often combined with each other. In this work, we will review the main achievements obtained from interdisciplinary research based on magnetic resonance imaging and establishing, de facto, the birth of multilayer network analysis and modeling of human brain.

While the statistical and resilience properties of the Internet are no more changing significantly across time, the Darknet, a network devoted to keep anonymous its traffic, still experiences rapid changes to improve the security of its users. Here, we study the structure of the Darknet and we find that its topology is rather peculiar, being characterized by non-homogenous distribution of connections -- typical of scale-free networks --, very short path lengths and high clustering -- typical of small-world networks -- and lack of a core of highly connected nodes. We propose a model to reproduce such features, demonstrating that the mechanisms used to improve cyber-security are responsible for the observed topology. Unexpectedly, we reveal that its peculiar structure makes the Darknet much more resilient than the Internet -- used as a benchmark for comparison at a descriptive level -- to random failures, targeted attacks and cascade failures, as a result of adaptive changes in response to the attempts of dismantling the network across time.

Nowadays, scientific challenges usually require approaches that cross traditional boundaries between academic disciplines, driving many researchers towards interdisciplinarity. Despite its obvious importance, there is a lack of studies on how to quantify the influence of interdisciplinarity on the research impact, posing uncertainty in a proper evaluation for hiring and funding purposes. Here we propose a method based on the analysis of bipartite interconnected multilayer networks of citations and disciplines, to assess scholars, institutions and countries interdisciplinary importance. Using data about physics publications and US patents, we show that our method allows to reveal, using a quantitative approach, that being more interdisciplinary causes -- in the Granger sense -- benefits in scientific productivity and impact. The proposed method could be used by funding agencies, universities and scientific policy decision makers for hiring and funding purposes, and to complement existing methods to rank universities and countries.

Despite the success of traditional network analysis, standard networks provide a limited representation of complex systems, which often include different types of relationships (or ‘multiplexity’) between their components. 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 modelling networked systems explicitly allows the incorporation of multiplexity and other features of realistic systems. It allows one to couple different structural relationships by encoding them in a convenient mathematical object. It also allows one to couple different dynamical processes on top of such interconnected structures. The resulting framework plays a crucial role in helping to 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.

Any physical system can be viewed from the perspective that information is implicitly represented in its state. However, the quantification of this information when it comes to complex networks has remained largely elusive. In this work, we use techniques inspired by quantum statistical mechanics to define an entropy measure for complex networks and to develop a set of information-theoretic tools, based on network spectral properties, such as Renyi q-entropy, generalized Kullback-Leibler and Jensen-Shannon divergences, the latter allowing us to define a natural distance measure between complex networks. First we show that by minimizing the Kullback-Leibler divergence between an observed network and a parametric network model, inference of model parameter(s) by means of maximum-likelihood estimation can be achieved and model selection can be performed appropriate information criteria. Second, we show that the information-theoretic metric quantifies the distance between pairs of networks and we can use it, for instance, to cluster the layers of a multilayer system. By applying this framework to networks corresponding to sites of the human microbiome, we perform hierarchical cluster analysis and recover with high accuracy existing community-based associations. Our results imply that spectral based statistical inference in complex networks results in demonstrably superior performance as well as a conceptual backbone, filling a gap towards a network information theory.

Network analysis provides a powerful tool to analyze complex influences of social and ecological structures on community and household dynamics. Most network studies of social–ecological systems use simple, undirected, unweighted networks. We analyze multiplex, directed, and weighted networks of subsistence food flows collected in three small indigenous communities in Arctic Alaska potentially facing substantial economic and ecological changes. Our analysis of plausible future scenarios suggests that changes to social relations and key households have greater effects on community robustness than changes to specific wild food resources

We find that winning European research money (Nature 530, 33; 2016) is, among other things, contingent on how well national governments manage to retain their own scientists and to attract others from abroad. We analysed statistical indicators of scientists' mobility in the European Union for 2007-14 (erc.europa.eu and go.nature.com/bpeylu) to determine the 'attractiveness' of different countries to scientists from abroad, as well as their 'stickiness' in preventing native researchers from moving away (known as brain drain). We quantified attractiveness and stickiness as the relative difference between incoming or remaining researchers, respectively, and outgoing ones. For both measures, we found that the higher the value, the better are that country's chances of securing European research funding. The United Kingdom and Sweden are high scorers in both; Italy is among the lowest (further details from M. de D. and A. A.; see go.nature.com/wyvtls). We conclude that there is a 'rich get richer' effect for countries that have high attractiveness and stickiness scores. Those nations also boast a high gross domestic product per capita, and tend to invest more in research and development. This means that they can lure and retain the best researchers by providing competitive salaries and a guaranteed future in research.

Understanding how people move within a geographic area, e.g. a city, a country or the whole world, is fundamental in several applications, from predicting the spatio-temporal evolution of an epidemics to inferring migration patterns. Mobile phone records provide an excellent proxy of human mobility, showing that movements exhibit a high level of memory. However, the precise role of memory in widely adopted proxies of mobility, as mobile phone records, is unknown. Here we use 560 millions of call detail records from Senegal to show that standard Markovian approaches, including higher-order ones, fail in capturing real mobility patterns and introduce spurious movements never observed in reality. We introduce an adaptive memory-driven approach to overcome such issues. At variance with Markovian models, it is able to realistically model conditional waiting times, i.e. the probability to stay in a specific area depending on individual's historical movements. Our results demonstrate that in standard mobility models the individuals tend to diffuse faster than what observed in reality, whereas the predictions of the adaptive memory approach significantly agree with observations. We show that, as a consequence, the incidence and the geographic spread of a disease could be inadequately estimated when standard approaches are used, with crucial implications on resources deployment and policy making during an epidemic outbreak.

Typical brain networks consist of many peripheral regions and a few highly central ones, i.e. hubs, playing key functional roles in cerebral inter-regional interactions. Studies have shown that networks, obtained from the analysis of specific frequency components of brain activity, present peculiar architectures with unique profiles of region centrality. However, the identification of hubs in networks built from different frequency bands simultaneously is still a challenging problem, remaining largely unexplored. Here we identify each frequency component with one layer of a multiplex network and face this challenge by exploiting the recent advances in the analysis of multiplex topologies. First, we show that each frequency band carries unique topological information, fundamental to accurately model brain functional networks. We then demonstrate that hubs in the multiplex network, in general different from those ones obtained after discarding or aggregating the measured signals as usual, provide a more accurate map of brain's most important functional regions, allowing to distinguish between healthy and schizophrenic populations better than conventional network approaches.

Academic research is driven by several factors causing different disciplines to act as "sources" or "sinks" of knowledge. However, how the flow of authors' research interests -- a proxy of human knowledge -- evolved across time is still poorly understood. Here, we build a comprehensive map of such flows across one century, revealing fundamental periods in the raise of interest in areas of human knowledge. We identify and quantify the most attractive topics over time, when a relatively significant number of researchers moved from their original area to another one, causing what we call a "diaspora of the knowledge" towards sinks of scientific interest, and we relate these points to crucial historical and political events. Noticeably, only a few areas -- like Medicine, Physics or Chemistry -- mainly act as sources of the diaspora, whereas areas like Material Science, Chemical Engineering, Neuroscience, Immunology and Microbiology or Environmental Science behave like sinks.

Real-world complex systems exhibit multiple levels of relationships. In many cases they require to be modeled as interconnected multilayer networks, characterizing interactions of several types simultaneously. It is of crucial importance in many fields, from economics to biology and from urban planning to social sciences, to identify the most (or the less) influential nodes in a network using centrality measures. However, defining the centrality of actors in interconnected complex networks is not trivial. In this paper, we rely on the tensorial formalism recently proposed to characterize and investigate this kind of complex topologies, and extend two well known random walk centrality measures, the random walk betweenness and closeness centrality, to interconnected multilayer networks. For each of the measures we provide analytical expressions that completely agree with numerically results.

The coexistence of multiple types of interactions within social, technological and biological networks has moved the focus of the physics of complex systems towards a multiplex description of the interactions between their constituents. This novel approach has unveiled that the multiplex nature of complex systems has strong influence in the emergence of collective states and their critical properties. Here we address an important issue that is intrinsic to the coexistence of multiple means of interactions within a network: their competition. To this aim, we study a two-layer multiplex in which the activity of users can be localized in each of the layer or shared between them, favoring that neighboring nodes within a layer focus their activity on the same layer. This framework mimics the coexistence and competition of multiple communication channels, in a way that the prevalence of a particular communication platform emerges as a result of the localization of users activity in one single interaction layer. Our results indicate that there is a transition from localization (use of a preferred layer) to delocalization (combined usage of both layers) and that the prevalence of a particular layer (in the localized state) depends on their structural properties.

Many complex systems can be represented as networks composed by distinct layers, interacting and depending on each others. For example, in biology, a good description of the full protein-protein interactome requires, for some organisms, up to seven distinct network layers, with thousands of protein-protein interactions each. A fundamental open question is then how much information is really necessary to accurately represent the structure of a multilayer complex system, and if and when some of the layers can indeed be aggregated. Here we introduce a method, based on information theory, to reduce the number of layers in multilayer networks, while minimizing information loss. We validate our approach on a set of synthetic benchmarks, and prove its applicability to an extended data set of protein-genetic interactions, showing cases where a strong reduction is possible and cases where it is not. Using this method we can describe complex systems with an optimal trade--off between accuracy and complexity.

Real-world complex systems exhibit multiple levels of relationships. In many cases, they require to be modeled by interconnected multilayer networks, characterizing interactions on several levels simultaneously. It is of crucial importance in many fields, from economics to biology, from urban planning to social sciences, to identify the most (or the less) influent nodes in a network. However, defining the centrality of actors in an interconnected structure is not trivial. In this paper, we capitalize on the tensorial formalism, recently proposed to characterize and investigate this kind of complex topologies, to show how several centrality measures -- well-known in the case of standard ("monoplex") networks -- can be extended naturally to the realm of interconnected multiplexes. We consider diagnostics widely used in different fields, e.g., computer science, biology, communication and social sciences, to cite only some of them. We show, both theoretically and numerically, that using the weighted monoplex obtained by aggregating the multilayer network leads, in general, to relevant differences in ranking the nodes by their importance.

Unveiling the community structure of networks is a powerful methodology to comprehend interconnected systems across the social and natural sciences. To identify different types of functional modules in interaction data aggregated in a single network layer, researchers have developed many powerful methods. For example, flow-based methods have proven useful for identifying modular dynamics in weighted and directed networks that capture constraints on flow in the systems they represent. However, many networked systems consist of agents or components that exhibit multiple layers of interactions. Inevitably, representing this intricate network of networks as a single aggregated network leads to information loss and may obscure the actual organization. Here we propose a method based on compression of network flows that can identify modular flows in non-aggregated multilayer networks. Our numerical experiments on synthetic networks show that the method can accurately identify modules that cannot be identified in aggregated networks or by analyzing the layers separately. We capitalize on our findings and reveal the community structure of two multilayer collaboration networks: scientists affiliated to the Pierre Auger Observatory and scientists publishing works on networks on the arXiv. Compared to conventional aggregated methods, the multilayer method reveals smaller modules with more overlap that better capture the actual organization.

Nowadays, millions of people interact on a daily basis on online social media like Facebook and Twitter, where they share and discuss information about a wide variety of topics. In this paper, we focus on a specific online social network, Twitter, and we analyze multiple datasets each one consisting of individuals' online activity before, during and after an exceptional event in terms of volume of the communications registered. We consider important events that occurred in different arenas that range from policy to culture or science. For each dataset, the users' online activities are modeled by a multilayer network in which each layer conveys a different kind of interaction, specifically: retweeting, mentioning and replying. This representation allows us to unveil that these distinct types of interaction produce networks with different statistical properties, in particular concerning the degree distribution and the clustering structure. These results suggests that models of online activity cannot discard the information carried by this multilayer representation of the system, and should account for the different processes generated by the different kinds of interactions. Secondly, our analysis unveils the presence of statistical regularities among the different events, suggesting that the non-trivial topological patterns that we observe may represent universal features of the social dynamics on online social networks during exceptional events.

Human mobility and social structure are at the basis of disease spreading. Disease containment strategies are usually devised from coarse-grained assumptions about human mobility. Cellular networks data, however, provides finer-grained information, not only about how people move, but also about how they communicate.
In this paper, using cellular network data, we analyze the behavior of a large number of individuals in Ivory Coast. We model mobility and communication between individual by means of an interconnected multiplex structure where each node represents the population in a geographic area (i.e. a \textit{sous-pr\'efecture}, a third-level administrative region). We present a model that describes how diseases circulate around the country as people move between regions. We extend the model with a concurrent process of relevant information spreading. This process corresponds to people disseminating disease prevention information, e.g. hygiene practises, vaccination campaign notices and other, within their social network. Thus, this process interferes with the epidemic. We then evaluate how restricting the mobility or using an adverse information spreading process affects the epidemic. We find that restricting mobility does not delay the occurrence of an endemic state and that an information campaign might be an effective countermeasure.

Recent advances in the study of networked systems have highlighted that our interconnected world is composed of networks that are coupled to each other through different layers€™ that each represent one of many possible subsystems or types of interactions. Nevertheless, it is traditional to aggregate multilayer networks into a single weighted network in order to take advantage of existing tools. This is admittedly convenient, but it is also extremely problematic, as important information can be lost as a result. It is therefore important to develop multilayer generalizations of network concepts. In this paper, we analyze triadic relations and generalize the idea of transitivity to multiplex networks. By focusing on triadic relations, which yield the simplest type of transitivity, we generalize the concept and computation of clustering coefficients to multiplex networks. We show how the layered structure of such networks introduces a new degree of freedom that has a fundamental effect on transitivity. We compute multiplex clustering coefficients for several real multiplex networks and illustrate why one must take great care when generalizing standard network concepts to multiplex networks. We also derive analytical expressions for our clustering coefficients for ensemble averages of networks in a family of random multiplex networks. Our analysis illustrates that social networks have a strong tendency to promote redundancy by closing triads at every layer and that they thereby have a different type of multiplex transitivity from transportation networks, which do not exhibit such a tendency. These insights are invisible if one only studies aggregated networks.

Human mobility in a city represents a fascinating complex system that combines social interactions, daily constraints and random explorations. New collections of data that capture human mobility not only help us to understand their underlying patterns but also to design intelligent systems. Bringing us the opportunity to reduce traffic and to develop other applications that make cities more adaptable to human needs. In this paper, we propose an adaptive routing strategy which accounts for individual constraints to recommend personalized routes and, at the same time, for constraints imposed by the collectivity as a whole. Using big data sets recently released during the Telecom Italia Big Data Challenge, we show that our algorithm allows us to reduce the overall traffic in a smart city thanks to synergetic effects, with the participation of individuals in the system, playing a crucial role.

The vertiginous increase of e-platforms for social communication has boosted the ways people use to interact each other. Micro-blogging and decentralized posts are used indistinctly for social interaction, usually by the same individuals acting simultaneously in the different platforms. Multiplex networks are the natural abstraction representation of such "layered" relationships and others, like co-authorship. Here, we re-define the betweenness centrality measure to account for the inherent structure of multiplex networks and propose an algorithm to compute it in an efficient way. To show the necessity and the advantage of the proposed definition, we analyze the obtained centralities for two real multiplex networks, a social multiplex of two layers obtained from Twitter and Instagram and a co-authorship network of four layers obtained from arXiv. Results show that the proposed definition provides more accurate results than the current approach of evaluating the classical betweenness centrality on the aggregated network, in particular for the middle ranked nodes. We also analyze the computational cost of the presented algorithm.

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 checks-out 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.

Multiplex networks are receiving increasing interests because they allow to model relationships between networked agents on several layers simultaneously. In this letter, we extend well-known random walks to multiplexes and we introduce a new type of walk that can exist only in multiplexes. We derive exact expressions for vertex occupation time and the coverage. Finally, we show how the efficiency in exploring the multiplex critically depends on the underlying topology of layers, the weight of their inter-connections and the strategy adopted to walk.

Multilayer relationships among entities and information about entities must be accompanied by the means to analyse, visualize and obtain insights from such data. We present open-source software (muxViz) that contains a collection of algorithms for the analysis of multilayer networks, which are an important way to represent a large variety of complex systems throughout science and engineering. We demonstrate the ability of muxViz to analyse and interactively visualize multilayer data using empirical genetic, neuronal and transportation networks. Our software is available at https://github.com/manlius/muxViz.

The analysis of the activity of neuronal cultures is considered to be a good proxy of the functional connectivity of in vivo neuronal tissues. Thus, the functional complex network inferred from activity patterns is a promising way to unravel the interplay between structure and functionality of neuronal systems. Here, we monitor the spontaneous self-sustained dynamics in neuronal cultures formed by interconnected aggregates of neurons (clusters). Dynamics is characterized by the fast activation of groups of clusters in sequences termed bursts. The analysis of the time delays between clusters' activations within the bursts allows the reconstruction of the directed functional connectivity of the network. We propose a method to statistically infer this connectivity and analyze the resulting properties of the associated complex networks. Surprisingly enough, in contrast to what has been reported for many biological networks, the clustered neuronal cultures present assortative mixing connectivity values, meaning that there is a preference for clusters to link to other clusters that share similar functional connectivity, as well as a rich-club core, which shapes a ‘connectivity backbone’ in the network. These results point out that the grouping of neurons and the assortative connectivity between clusters are intrinsic survival mechanisms of the culture.

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.

The announcement of the discovery of a Higgs boson-like particle at CERN will be remembered as one of the milestones of the scientific endeavor of the 21st century. In this paper we present a study of information spreading processes on Twitter before, during and after the announcement of the discovery of a new particle with the features of the elusive Higgs boson on 4th July 2012. We report evidence for non-trivial spatio-temporal patterns in user activities at individual and global level, such as tweeting, re-tweeting and replying to existing tweets. We provide a possible explanation for the observed time-varying dynamics of user activities during the spreading of this scientific "rumor". We model the information spreading in the corresponding network of individuals who posted a tweet related to the Higgs boson discovery. Finally, we show that we are able to reproduce the global behavior of about 500,000 individuals with remarkable accuracy.

One of the more challenging tasks in the understanding of dynamical properties of models on top of complex networks is to capture the precise role of multiplex topologies. In a recent paper, Gomez et al. [Phys. Rev. Lett. 101, 028701 (2013)] proposed a framework for the study of diffusion processes in such networks. Here, we extend the previous framework to deal with general configurations in several layers of networks, and analyze the behavior of the spectrum of the Laplacian of the full multiplex. We derive an interesting decoupling of the problem that allow us to unravel the role played by the interconnections of the multiplex in the dynamical processes on top of them. Capitalizing on this decoupling we perform an asymptotic analysis that allow us to derive analytical expressions for the full spectrum of eigenvalues. This spectrum is used to gain insight into physical phenomena on top of multiplex, specifically, diffusion processes and synchronizability.

Human mobility is one of the key factors at the basis of the spreading of diseases in a population. Containment strategies are usually devised on movement scenarios based on coarse-grained assumptions. Mobility phone data provide a unique opportunity for building models and defining strategies based on very precise information about the movement of people in a region or in a country. Another very important aspect is the underlying social structure of a population, which might play a fundamental role in devising information campaigns to promote vaccination and preventive measures, especially in countries with a strong family (or tribal) structure. In this paper we analyze a large-scale dataset describing the mobility and the call patterns of a large number of individuals in Ivory Coast. We present a model that describes how diseases spread across the country by exploiting mobility patterns of people extracted from the available data. Then, we simulate several epidemics scenarios and we evaluate mechanisms to contain the epidemic spreading of diseases, based on the information about people mobility and social ties, also gathered from the phone call data. More specifically, we find that restricting mobility does not delay the occurrence of an endemic state and that an information campaign based on one-to-one phone conversations among members of social groups might be an effective countermeasure.

We present a novel way to characterize the structure of complex networks by studying the statistical properties of the trajectories of random walks over them. We consider time series corresponding to different properties of the nodes visited by the walkers. We show that the analysis of the fluctuations of these time series allows to define a set of characteristic exponents which capture the local and global organization of a network. This approach provides a way of solving two classical problems in network science, namely the systematic classification of networks, and the identification of the salient properties of growing networks. The results contribute to the construction of a unifying framework for the investigation of the structure and dynamics of complex systems.

Previous studies have shown that human movement is predictable to a certain extent at different geographic scales. Existing prediction techniques exploit only the past history of the person taken into consideration as input of the predictors. In this paper, we show that by means of multivariate nonlinear time series prediction techniques it is possible to increase the accuracy of movement forecasting by considering movements of friends or people with correlated mobility patterns (i.e., characterised by high mutual information) as input of the predictor. Finally, we evaluate the proposed techniques on the Nokia Mobile Data Challenge and Cabspotting datasets.

The study of the interdependence of human movement and social ties of individuals is one of the most interesting re- search areas in computational social science. Previous stud- ies have shown that human movement is predictable to a certain extent at different geographic scales. One of the open problems is how to improve the prediction exploiting additional available information. In particular, one of the key questions is how to characterise and exploit the corre- lation between movements of friends and acquaintances to increase the accuracy of the forecasting algorithms.

Prediction of sea-level is an important task for navigation, coastal engineering and geodetic applications, as well as recreational activities. This study presents a comparison of Chaos theory and Auto-Regressive Integrated Moving Average (ARIMA) techniques for sea level modelling for daily, weekly, 10-day and monthly time scale at the Cocos (Keeling) islands from 1992 to 2001. The state space reconstruction of the unknown underlying process is directly employed from time series data, through Takens delay embedding method: opti- mal embedding dimension and delay time are obtained from false nearest neighbours and average mutual information techniques, respectively. Optimal values are then used for the estimation of the correlation dimension and the largest Lyapunov exponent, for inspecting possible signatures of chaotic dynamics. We find a positive Lyapunov exponent an evident feature of chaos. Indeed, the nonlinear prediction of sea level, in the period ranging from January 2001 to December 2001, is in an excellent agreement with the data for the same period, evidencing the nonlinear nature of the process. ARIMA method is also used for sea level modelling, for the same time scales; the performances of the two models are compared using such statistical indices as the root mean square error (RMSE) and correlation coefficient (CC). The comparative analyses show that the chaos theory model has a slight edge over ARIMA while both models are in principal acceptable.

We investigate flow dynamics in rivers characterized by basin areas and daily mean discharge spanning different orders of magnitude. We show that the delayed increments evaluated at time scales ranging from days to months can be opportunely rescaled to the same non-Gaussian probability density function. Such a scaling breaks up above a certain critical horizon, where a behavior typical of thermodynamic systems at the critical point emerges. We finally show that both the scaling behavior and the break up of the scaling are universal features of river flow dynamics.

We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators on the market, yet it depends only on one parameter, is easier to implement and faster. Applications to real data sets reject the null hypothesis of an underlying stationary linear stochastic process with a higher confidence interval than the best known nonlinear discriminators up to date.

Adequate knowledge of the nature of river flow process is crucial for proper planning and management of our water resources and environment. This study attempts to detect the salient characteristics of flow dynamics of the Karoon River in Iran. Daily discharge series observed over a period of six years (1999-2004) is analyzed to examine the chaotic and scaling characteristics of the flow dynamics. The presence of chaos is investigated through the correlation dimension and Lyapunov exponent methods, while the Hurst exponent and Renyi dimension analyses are performed to explore the scaling characteristics. The low correlation dimension (2.60 +- 0.07) and the positive largest Lyapunov exponent (0.014 +- 0.001) suggest the presence of low-dimensional chaos; they also imply that the flow dynamics are dominantly governed by three variables and can be reliably predicted up to 48 days (i.e. prediction horizon). Results from the Hurst exponent and Renyi dimension analyses reveal the multifractal character of the flow dynamics, with persistent and anti-persistent behaviors observed at different time scales.

A linear and a nonlinear time series analysis on the experimental rate of SD events normalized to the sensitive detector area, as described in [1], has been done. The same analysis have been performed on simulated time series with annual periodic behavior. An evident annual period has been found in the P. Auger data due to a deterministic ciclostationary physical effect which a recent paper from the P. Auger Collaboration attributes to atmospheric effects, such as pressure, temperature and density, on extensive air showers [2] [3]. Our results are in good agreement with this interpretation. Another deterministic stationary aperiodic (or quasi-periodic) or nonstationary (deterministic or stochastic) behavior has been found in the P. Auger data, probably due to some physical unknown effect which needs further investigations in the next years, when a larger amount of data will be available.

We present the results about a deep and detailed nonlinear time series anal- ysis of the UHECR arrival times series observed at the P. Auger Observatory, Malargue, Argentina. The analysis has been developed over a known chaotic time series (derived from a Lorenz standard model) in order to test that our algorithms and our software work fine. We analysed in addition 2 arrival times series obtained from a chaotic system and a stochastic one, in order to get our conclusion by a direct comparison among the UHECR system’s dynamical properties and the 2 known ones. We tried to reconstruct the phase space of each dynamical system from a non-linear analysis of its own time arrival series by using a special multidimensional space, called embedding, with the same dynamical invariants of the original phase space like the fractal dimension, the Renyi dimension, the Lyapunov exponents and the time reversal asymmetry. We performed a statistical analysis based on the surrogate data method and nonparametric statistics with about 2400 numerical analysis to test the null hypothesis of white noise, linear gaussian model, nonlinear gaussian model. From the analysis of the Lyapunov spectrums and the time reversal asymmetry we deduced that there are time correlation in UHECR with energy above 1019eV and that, at this preliminary step, it is possible that the dynamical system, which they depend to, can be considered deterministic and low-dimensional chaotic with a time-projected attractor of fractal dimension D2 = 1.14. Important implications on the nature of their cosmological origin and propagation need further investigations.

Arrival time distributions of the UHECRs should contain relevant information about specific feature of the source. To distinguish these ’source features’ is not an easy task. We suggest to use nonlinear time series analysis. The approach has two main goals: on one side we will try to investigate the astrophysical nature of the process (origin, propagation feature), while on the other side we would like to investigate the deterministic, low-dimensional chaotic or stochastic natute of the dynamical system they belong to. We present preliminary results about the nonlinearity and the nonstationarity of UHECR with E > 10EeV detected from surface detector at PAO with zenith angle θ < 60◦, for both T5 and no T5 cuts. Preliminary results for UHECR with E > 40EeV are also included.

The surface detector array of the Pierre Auger Observatory provides information about the longitudinal development of the muonic component of extensive air showers. Using the timing information from the flash analog-to-digital converter traces of surface detectors far from the shower core, it is possible to reconstruct a muon production depth distribution. We characterize the goodness of this reconstruction for zenith angles around 60 deg. and different energies of the primary particle. From these distributions we define X(mu)max as the depth along the shower axis where the production of muons reaches maximum. We explore the potentiality of X(mu)max as a useful observable to infer the mass composition of ultrahigh-energy cosmic rays. Likewise, we assess its ability to constrain hadronic interaction models.

The Pierre Auger Observatory, located on a vast, high plain in western Argentina, is the world's largest cosmic ray observatory. The objectives of the Observatory are to probe the origin and characteristics of cosmic rays above 1017 eV and to study the interactions of these, the most energetic particles observed in nature. The Auger design features an array of 1660 water-Cherenkov particle detector stations spread over 3000 km2 overlooked by 24 air fluorescence telescopes. In addition, three high elevation fluorescence telescopes overlook a 23.5 km2, 61-detector infilled array with 750 m spacing. The Observatory has been in successful operation since completion in 2008 and has recorded data from an exposure exceeding 40,000 km2 sr yr. This paper describes the design and performance of the detectors, related subsystems and infrastructure that make up the Auger Observatory

We analyze the distribution of arrival directions of ultra-high energy cosmic rays recorded at the Pierre Auger Observatory in 10 years of operation. The data set, about three times larger than that used in earlier studies, includes arrival directions with zenith angles up to 80∘, thus covering from −90∘ to +45∘ in declination. After updating the fraction of events correlating with the active galactic nuclei (AGNs) in the V\'eron-Cetty and V\'eron catalog, we subject the arrival directions of the data with energies in excess of 40 EeV to different tests for anisotropy. We search for localized excess fluxes and for self-clustering of event directions at angular scales up to 30∘ and for different threshold energies between 40~EeV and 80~EeV. We then look for correlations of cosmic rays with celestial structures both in the Galaxy (the Galactic Center and Galactic Plane) and in the local Universe (the Super-Galactic Plane). We also examine their correlation with different populations of nearby extragalactic objects: galaxies in the 2MRS catalog, AGNs detected by Swift-BAT, radio galaxies with jets and the Centaurus~A galaxy. None of the tests shows a statistically significant evidence of anisotropy. The strongest departures from isotropy (post-trial probability ∼1.4\%) are obtained for cosmic rays with E>58~EeV in rather large windows around Swift AGNs closer than 130~Mpc and brighter than 1044~erg/s (18∘ radius) and around the direction of Centaurus~A (15∘ radius).

We report a study of the distributions of the depth of maximum, Xmax, of extensive air-shower profiles with energies above 10^17.8 eV as observed with the fluorescence telescopes of the Pierre Auger Observatory. The analysis method for selecting a data sample with minimal sampling bias is described in detail as well as the experimental cross-checks and systematic uncertainties. Furthermore, we discuss the detector acceptance and the resolution of the Xmax measurement and provide parameterizations thereof as a function of energy. The energy dependence of the mean and standard deviation of the Xmax-distributions are compared to air-shower simulations for different nuclear primaries and interpreted in terms of the mean and variance of the logarithmic mass distribution at the top of the atmosphere.

Using the data taken at the Pierre Auger Observatory between December 2004 and December 2012, we have examined the implications of the distributions of depths of atmospheric shower maximum (Xmax), using a hybrid technique, for composition and hadronic interaction models. We do this by fitting the distributions with predictions from a variety of hadronic interaction models for variations in the composition of the primary cosmic rays and examining the quality of the fit. Regardless of what interaction model is assumed, we find that our data are not well described by a mix of protons and iron nuclei over most of the energy range. Acceptable fits can be obtained when intermediate masses are included, and when this is done consistent results for the proton and iron-nuclei contributions can be found using the available models. We observe a strong energy dependence of the resulting proton fractions, and find no support from any of the models for a significant contribution from iron nuclei. However, we also observe a significant disagreement between the models with respect to the relative contributions of the intermediate components.

We present the results of an analysis of the large angular scale distribution of the arrival directions of cosmic rays with energy above 4 EeV detected at the Pierre Auger Observatory including for the first time events with zenith angle between 60° and 80°. We perform two Rayleigh analyses, one in the right ascension and one in the azimuth angle distributions, that are sensitive to modulations in right ascension and declination, respectively. The largest departure from isotropy appears in the E>8 EeV energy bin, with an amplitude for the first harmonic in right ascension rα1=(4.4±1.0)x1e-2, that has a chance probability P(≥rα1)=6.4x1e-5, reinforcing the hint previously reported with vertical events alone.

Spherical harmonic moments are well-suited for capturing anisotropy at any scale in the flux of cosmic rays. An unambiguous measurement of the full set of spherical harmonic coefficients requires full-sky coverage. This can be achieved by combining data from observatories located in both the northern and southern hemispheres. To this end, a joint analysis using data recorded at the Telescope Array and the Pierre Auger Observatory above 1019 eV is presented in this work. The resulting multipolar expansion of the flux of cosmic rays allows us to perform a series of anisotropy searches, and in particular to report on the angular power spectrum of cosmic rays above 1019 eV. No significant deviation from isotropic expectations is found throughout the analyses performed. Upper limits on the amplitudes of the dipole and quadrupole moments are derived as a function of the direction in the sky, varying between 7% and 13% for the dipole and between 7% and 10% for a symmetric quadrupole.

Measurements of air showers made using the hybrid technique developed with the fluorescence and surface detectors of the Pierre Auger Observatory allow a sensitive search for point sources of EeV photons anywhere in the exposed sky. A multivariate analysis reduces the background of hadronic cosmic rays. The search is sensitive to a declination band from -85{\deg} to +20{\deg}, in an energy range from 10E17.3 eV to 10E18.5 eV. No photon point source has been detected. An upper limit on the photon flux has been derived for every direction. The mean value of the energy flux limit that results from this, assuming a photon spectral index of -2, is 0.06 eV cm-2 s-1, and no celestial direction exceeds 0.25 eV cm-2 s-1. These upper limits constrain scenarios in which EeV cosmic ray protons are emitted by non-transient sources in the Galaxy.

We present the first hybrid measurement of the average muon number in air showers at ultra-high energies, initiated by cosmic rays with zenith angles between 62{\deg} and 80{\deg}. The measurement is based on 174 hybrid events recorded simultaneously with the Surface Detector array and the Fluorescence Detector of the Pierre Auger Observatory. The muon number for each shower is derived by scaling a simulated reference profile of the lateral muon density distribution at the ground until it fits the data. A 1019 eV shower with a zenith angle of 67{\deg}, which arrives at the Surface Detector array at an altitude of 1450 m above sea level, contains on average (2.68\pm0.04\pm0.48(sys.))x10E7 muons with energies larger than 0.3 GeV. The logarithmic gain dlnNμ/dlnE of muons with increasing energy between 4x1018 eV and 5x1019 eV is measured to be (1.029\pm0.024\pm0.030(sys.)).

The emission of radio waves from air showers has been attributed to the so-called geomagnetic emission process. At frequencies around 50 MHz this process leads to coherent radiation which can be observed with rather simple setups. The direction of the electric field induced by this emission process depends only on the local magnetic field vector and on the incoming direction of the air shower. We report on measurements of the electric field vector where, in addition to this geomagnetic component, another component has been observed which cannot be described by the geomagnetic emission process. The data provide strong evidence that the other electric field component is polarized radially with respect to the shower axis, in agreement with predictions made by Askaryan who described radio emission from particle showers due to a negative charge-excess in the front of the shower. Our results are compared to calculations which include the radiation mechanism induced by this charge-excess process.

We describe a new method of identifying night-time clouds over the Pierre Auger Observatory using infrared data from the Imager instruments on the GOES-12 and GOES-13 satellites. We compare cloud identifications resulting from our method to those obtained by the Central Laser Facility of the Auger Observatory. Using our new method we can now develop cloud probability maps for the 3000 km2 of the Pierre Auger Observatory twice per hour with a spatial resolution of 2.4 km by 5.5 km. Our method could also be applied to monitor cloud cover for other ground-based observatories and for space-based observatories.

Ultra-high energy (UHE) photons play an important role as an independent probe of the photo-pion production mechanism by UHE cosmic rays. Their observation, or non-observation, may constrain astrophysical scenarios for the origin of UHECRs and help to understand the nature of the flux suppression observed by several experiments at energies above 1019.5 eV. Whereas the interaction length of UHE photons above 1017 eV ranges from a few hundred kpc up to tenths of Mpc, photons can interact with the extragalactic background radiation initiating the development of electromagnetic cascades which affect the fluxes of photons observed at Earth. The interpretation of the current experimental results rely on the simulations of the UHE photon propagation. In this paper, we present the novel Monte Carlo code EleCa to simulate the Electromagnetic Cascading initiated by high-energy photons and electrons.
We provide an estimation of the surviving probability for photons inducing electromagnetic cascades as a function of their distance from the observer and we calculate the distances within which we expect to observe UHE photons with energy between 1017 and 1019 eV. Furthermore, the flux of GZK photons at Earth is investigated in several astrophysical scenarios where we vary both injection spectrum and composition at the source and the intensity of the intervening extragalactic magnetic field. Although the photon propagation depends on several astrophysical factors, our numerical predictions combined with future experimental observations (or non-observations) of UHE photons -- in the energy range between 1017.5 eV and 1020 eV -- can help to constrain these scenarios.

To interpret the mean depth of cosmic ray air shower maximum and its dispersion, we parametrize those two observables as functions of the first two moments of the ln A distribution. We examine the goodness of this simple method through simulations of test mass distributions. The application of the parameterization to Pierre Auger Observatory data allows one to study the energy dependence of the mean ln A and of its variance under the assumption of selected hadronic interaction models. We discuss possible implications of these dependences in term of interaction models and astrophysical cosmic ray sources.

Contributions of the Pierre Auger Collaboration to the 33rd International Cosmic Ray Conference, Rio de Janeiro, Brazil, July 2013

Although the recent experimental efforts to improve the observation of Ultra-High Energy Cosmic Rays (UHECRs) above $10^{18}$ eV, the origin and the composition of such particles is still unknown. In this work, we present the novel Monte Carlo code (HERMES) simulating the propagation of UHE nuclei, in the energy range between $10^{16}$ and $10^{22}$ eV, accounting for propagation in the intervening extragalactic and Galactic magnetic fields and nuclear interactions with relic photons of the extragalactic background radiation. In order to show the potential applications of HERMES for astroparticle studies, we estimate the expected flux of UHE nuclei in different astrophysical scenarios, the GZK horizons and we show the expected arrival direction distributions in the presence of turbulent extragalactic magnetic fields. A stable version of HERMES will be released in the next future for public use together with libraries of already propagated nuclei to allow the community to perform mass composition and energy spectrum analysis with our simulator.

Ultra high energy photons play an important role as an independent probe of the photo-pion production mechanism by UHE cosmic rays. Their observation, or non-observation, may constrain astrophysical scenarios for the origin of UHECRs and help to understand the nature of the flux suppression observed by several experiments at energies above 10$^{19.5}$ eV. Whereas the interaction length of UHE photons above 10$^{17}$ eV is only of a few hundred kpc up to tenths of Mpc, photons can interact with the extragalactic background radiation leading to the development of electromagnetic cascades which affect the fluxes of photons observed at Earth. The interpretation of the current experimental results rely on the simulations of the UHE photon propagation. In this contribution, we present the novel Monte Carlo code "EleCa" to simulate the \emph{Ele}ctromagnetic \emph{Ca}scading initiated by high-energy photons and electrons. The distance within which we expect to observe UHE photons is discussed and the flux of GZK photons at Earth is investigated in several astrophysical scenarios.

Ultra high energy photons, above 1e17-1e18 eV, can interact with the extragalactic background radiation leading to the development of electromagnetic cascades. A Monte Carlo code to simulate the electromagnetic cascades initiated by high-energy photons and electrons is presented. Results from simulations and their impact on the predicted flux at Earth are discussed in different astrophysical scenarios.

The study of ultra-high energy cosmic rays (UHECR) at Earth cannot prescind from the study of their propagation in the Universe. In this paper, we present HERMES, the \emph{ad hoc} Monte Carlo code we have developed for the realistic simulation of UHECR propagation. We discuss the modeling adopted to simulate the cosmology, the magnetic fields, the interactions with relic photons and the production of secondary particles. In order to show the potential applications of HERMES for astroparticle studies, we provide an estimation of the surviving probability of UHE protons, the GZK horizons of nuclei and the all-particle spectrum observed at Earth in different astrophysical scenarios. Finally, we show the expected arrival direction distribution of UHECR produced from nearby candidate sources. A stable version of HERMES will be released in the next future for public use together with libraries of already propagated nuclei to allow the community to perform mass composition and energy spectrum analysis with our simulator.

Ultra-high energy cosmic rays (UHECRs) interacting with the atmosphere generate extensive air showers (EAS) of secondary particles. The depth corresponding to the maximum development of the shower, $\Xmax$, is a well-known observable for determining the nature of the primary cosmic ray which initiated the cascade process. In this paper, we present an empirical model to describe the distribution of $\Xmax$ for EAS initiated by nuclei and photons in the energy range from $10^{17}$ eV up to $10^{21}$ eV. Our model adopts the generalized Gumbel distribution motivated by the relationship between the generalized Gumbel statistics and the distribution of the sum of non-identically distributed variables in dissipative stochastic systems. We provide an analytical expression for describing the $\Xmax$ distribution for photons and for nuclei. The impact of the hadronic interaction model is investigated in detail, even in the case of the most up-to-date models accounting for LHC observations. We also briefly discuss the differences with a more classical approach and possible applications to the experimental data.

We derive lower bounds on the density of sources of ultra-high energy cosmic rays from the lack of significant clustering in the arrival directions of the highest energy events detected at the Pierre Auger Observatory. The density of uniformly distributed sources of equal intrinsic intensity was found to be larger than $\sim (0.06 - 5) \times 10^{-4}$ Mpc$^{-3}$ at 95% CL, depending on the magnitude of the magnetic deflections. Similar bounds, in the range $(0.2 - 7) \times 10^{-4}$ Mpc$^{-3}$, were obtained for sources following the local matter distribution.

The observation of ultrahigh energy (UHE) neutrinos has become a priority in experimental astroparticle physics. UHE neutrinos can be detected with a variety of techniques. In particular, neutrinos can interact in the atmosphere (downward-going neutrinos) or in the Earth crust (Earth-skimming neutrinos), producing air showers that can be observed with arrays of detectors at the ground. With the Surface Detector Array of the Pierre Auger Observatory we can detect these types of cascades. The distinguishing signature for neutrino events is the presence of very inclined showers produced close to the ground (i.e. after having traversed a large amount of atmosphere). In this work we review the procedure and criteria established to search for UHE neutrinos in the data collected with the ground array of the Pierre Auger Observatory. This includes Earth-skimming as well as downward-going neutrinos. No neutrino candidates have been found, which allows us to place competitive limits to the diffuse flux of UHE neutrinos in the EeV range and above.

The Pierre Auger Observatory in Malarg\"ue, Argentina, is designed to study the properties of ultra-high energy cosmic rays with energies above 1018 eV. It is a hybrid facility that employs a Fluorescence Detector to perform nearly calorimetric measurements of Extensive Air Shower energies. To obtain reliable calorimetric information from the FD, the atmospheric conditions at the observatory need to be continuously monitored during data acquisition. In particular, light attenuation due to aerosols is an important atmospheric correction. The aerosol concentration is highly variable, so that the aerosol attenuation needs to be evaluated hourly. We use light from the Central Laser Facility, located near the center of the observatory site, having an optical signature comparable to that of the highest energy showers detected by the FD. This paper presents two procedures developed to retrieve the aerosol attenuation of fluorescence light from CLF laser shots. Cross checks between the two methods demonstrate that results from both analyses are compatible, and that the uncertainties are well understood. The measurements of the aerosol attenuation provided by the two procedures are currently used at the Pierre Auger Observatory to reconstruct air shower data.

We investigate how the density of baryonic and cold dark matter, the density of dark energy and the value of the Hubble parameter at the present time influence the propagation of ultrahigh energy protons in the nearby Universe. We take into account energy losses in the cosmic microwave radiation, the only one relevant for protons above $10^{18}$ eV, and we explore the dependence of Greisen-Zatsepin-Kuz'min (GZK) horizon on the cosmology. We investigate several cosmological scenarios, from matter dominated to energy dominated ones, and we consider the impact of uncertainties in the Hubble parameter in a $\Lambda-$Cold Dark Matter (CDM) Universe, estimated from recent observations, on the GZK horizon. The impact of the (unknown) extragalactic magnetic field on our study is discussed, as well as possible probes of the Hubble parameter attainable by current and future experiments.

Recently, a novel method has been introduced to estimate the statistical significance of clustering in the direction distribution of objects. The method involves a multiscale procedure, based on the Kullback–Leibler divergence and the Gumbel statistics of extreme values, providing high discrimination power, even in presence of strong background isotropic contamination. It is shown that the method is: (i) semi-analytical, drastically reducing computation time; (ii) very sensitive to small, medium and large scale clustering; (iii) not biased against the null hypothesis. Applications to the physics of ultra-high energy cosmic rays, as a cosmological probe, are presented and discussed.

We present a novel catalog-independent method, based on a scale dependent approach, to detect anisotropy signatures in the arrival direction distribution of the ultra highest energy cosmic rays (UHECR). The method provides a good discrimination power for both large and small data sets, even in presence of strong contaminating isotropic background. We present some applications to simulated data sets of events corresponding to plausible scenarios for charged particles detected by world-wide surface detector-based observatories, in the last decades.

We present a novel method to generate a synthetic distribution of objects (mock) on a spherical surface (i.e. a sky), by using a real distribution. The resulting surrogate map mimics the clustering features of the real data, including the effects of non-uniform exposure, if any. The method is model-independent, also preserving the angular correlation function, as well as the angular power spectrum, of the original data. It can be reliably adopted to mimic the angular clustering of objects distributed on a spherical surface and it can be easily extended to include further information, as the spatial clustering of objects distributed inside a sphere. Applications to real data are presented and discussed. In particular, we consider the distribution of galaxies recently presented in the 2MASS Redshift Survey (2MRS) catalog.

A thorough search for large scale anisotropies in the distribution of arrival directions of cosmic rays detected above 10^18 eV at the Pierre Auger Observatory is reported. For the first time, these large scale anisotropy searches are performed as a function of both the right ascension and the declination and expressed in terms of dipole and quadrupole moments. Within the systematic uncertainties, no significant deviation from isotropy is revealed. Upper limits on dipole and quadrupole amplitudes are derived under the hypothesis that any cosmic ray anisotropy is dominated by such moments in this energy range. These upper limits provide constraints on the production of cosmic rays above 10^18 eV, since they allow us to challenge an origin from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions.

A thorough search for large scale anisotropies in the distribution of arrival directions of cosmic rays detected above 10^18 eV at the Pierre Auger Observatory is presented. This search is performed as a function of both declination and right ascension in several energy ranges above 10^18 eV, and reported in terms of dipolar and quadrupolar coefficients. Within the systematic uncertainties, no significant deviation from isotropy is revealed. Assuming that any cosmic ray anisotropy is dominated by dipole and quadrupole moments in this energy range, upper limits on their amplitudes are derived. These upper limits allow us to challenge an origin of cosmic rays above 10^18 eV from stationary galactic sources densely distributed in the galactic disk and emitting predominantly light particles in all directions.

A thorough search of the sky exposed at the Pierre Auger Cosmic Ray Observatory reveals no statistically significant excess of events in any small solid angle that would be indicative of a flux of neutral particles from a discrete source. The search covers from -90 to +15 degrees in declination using four different energy ranges above 1 EeV (10^18 eV). The method used in this search is more sensitive to neutrons than to photons. The upper limit on a neutron flux is derived for a dense grid of directions for each of the four energy ranges. These results constrain scenarios for the production of ultra-high energy cosmic rays in the Galaxy.

We describe the experimental setup and the results of RAuger, a small radio-antenna array, consisting of three fully autonomous and self-triggered radio-detection stations, installed close to the center of the Surface Detector (SD) of the Pierre Auger Observatory in Argentina. The setup has been designed for the detection of the electric field strength of air showers initiated by ultra-high energy cosmic rays, without using an auxiliary trigger from another detection system. Installed in December 2006, RAuger was terminated in May 2010 after 65 registered coincidences with the SD. The sky map in local angular coordinates (i.e., zenith and azimuth angles) of these events reveals a strong azimuthal asymmetry which is in agreement with a mechanism dominated by a geomagnetic emission process. The correlation between the electric field and the energy of the primary cosmic ray is presented for the first time, in an energy range covering two orders of magnitude between 0.1 EeV and 10 EeV. It is demonstrated that this setup is relatively more sensitive to inclined showers, with respect to the SD. In addition to these results, which underline the potential of the radio-detection technique, important information about the general behavior of self-triggering radio-detection systems has been obtained. In particular, we will discuss radio self-triggering under varying local electric-field conditions.

The Pierre Auger Observatory is exploring the potential of the radio detection technique to study extensive air showers induced by ultra-high energy cosmic rays. The Auger Engineering Radio Array (AERA) addresses both technological and scientific aspects of the radio technique. A first phase of AERA has been operating since September 2010 with detector stations observing radio signals at frequencies between 30 and 80 MHz. In this paper we present comparative studies to identify and optimize the antenna design for the final configuration of AERA consisting of 160 individual radio detector stations. The transient nature of the air shower signal requires a detailed description of the antenna sensor. As the ultra-wideband reception of pulses is not widely discussed in antenna literature, we review the relevant antenna characteristics and enhance theoretical considerations towards the impulse response of antennas including polarization effects and multiple signal reflections. On the basis of the vector effective length we study the transient response characteristics of three candidate antennas in the time domain. Observing the variation of the continuous galactic background intensity we rank the antennas with respect to the noise level added to the galactic signal.

We report a measurement of the proton-air cross-section for particle production at the center-of-mass energy per nucleon of 57 TeV. This is derived from the distribution of the depths of shower maxima observed with the Pierre Auger Observatory: systematic uncertainties are studied in detail. Analysing the tail of the distribution of the shower maxima, a proton-air cross-section of 505\pm22(stat)^{+28}_{-36}(sys) mb is found.

The energy spectrum of ultra-high energy cosmic rays above 10$^{18}$ eV is measured using the hybrid events collected by the Pierre Auger Observatory between November 2005 and September 2010. The large exposure of the Observatory allows the measurement of the main features of the energy spectrum with high statistics. Full Monte Carlo simulations of the extensive air showers (based on the CORSIKA code) and of the hybrid detector response are adopted here as an independent cross check of the standard analysis (Phys. Lett. B 685, 239 (2010)). The dependence on mass composition and other systematic uncertainties are discussed in detail and, in the full Monte Carlo approach, a region of confidence for flux measurements is defined when all the uncertainties are taken into account. An update is also reported of the energy spectrum obtained by combining the hybrid spectrum and that measured using the surface detector array.

The surface detector array of the Pierre Auger Observatory can detect neutrinos with energy E ν between 1017 eV and 1020 eV from point-like sources across the sky south of +55° and north of –65° declinations. A search has been performed for highly inclined extensive air showers produced by the interaction of neutrinos of all flavors in the atmosphere (downward-going neutrinos), and by the decay of tau leptons originating from tau neutrino interactions in Earth's crust (Earth-skimming neutrinos). No candidate neutrinos have been found in data up to 2010 May 31. This corresponds to an equivalent exposure of ~3.5 years of a full surface detector array for the Earth-skimming channel and ~2 years for the downward-going channel. An improved upper limit on the diffuse flux of tau neutrinos has been derived. Upper limits on the neutrino flux from point-like sources have been derived as a function of the source declination. Assuming a differential neutrino flux k PS E –2 ν from a point-like source, 90% confidence level upper limits for k PS at the level of 5 x 10–7 and 2.5 x 10–6 GeV cm–2 s–1 have been obtained over a broad range of declinations from the searches for Earth-skimming and downward-going neutrinos, respectively.

The Pierre Auger Observatory is a facility built to detect air showers produced by cosmic rays above 10^17 eV. During clear nights with a low illuminated moon fraction, the UV fluorescence light produced by air showers is recorded by optical telescopes at the Observatory. To correct the observations for variations in atmospheric conditions, atmospheric monitoring is performed at regular intervals ranging from several minutes (for cloud identification) to several hours (for aerosol conditions) to several days (for vertical profiles of temperature, pressure, and humidity). In 2009, the monitoring program was upgraded to allow for additional targeted measurements of atmospheric conditions shortly after the detection of air showers of special interest, e.g., showers produced by very high-energy cosmic rays or showers with atypical longitudinal profiles. The former events are of particular importance for the determination of the energy scale of the Observatory, and the latter are characteristic of unusual air shower physics or exotic primary particle types. The purpose of targeted (or "rapid") monitoring is to improve the resolution of the atmospheric measurements for such events. In this paper, we report on the implementation of the rapid monitoring program and its current status. The rapid monitoring data have been analyzed and applied to the reconstruction of air showers of high interest, and indicate that the air fluorescence measurements affected by clouds and aerosols are effectively corrected using measurements from the regular atmospheric monitoring program. We find that the rapid monitoring program has potential for supporting dedicated physics analyses beyond the standard event reconstruction.

Atmospheric conditions at the site of a cosmic ray observatory must be known for reconstructing observed extensive air showers. The Global Data Assimilation System (GDAS) is a global atmospheric model predicated on meteorological measurements and numerical weather predictions. GDAS provides altitude-dependent profiles of the main state variables of the atmosphere like temperature, pressure, and humidity. The original data and their application to the air shower reconstruction of the Pierre Auger Observatory are described. By comparisons with radiosonde and weather station measurements obtained on-site in Malargue and averaged monthly models, the utility of the GDAS data is shown.

Observations of cosmic ray arrival directions made with the Pierre Auger Observatory have previously provided evidence of anisotropy at the 99% CL using the correlation of ultra high energy cosmic rays (UHECRs) with objects drawn from the Véron-Cetty Véron catalog. In this paper we report on the use of three catalog independent methods to search for anisotropy. The 2pt–L, 2pt+ and 3pt methods, each giving a different measure of self-clustering in arrival directions, were tested on mock cosmic ray data sets to study the impacts of sample size and magnetic smearing on their results, accounting for both angular and energy resolutions. If the sources of UHECRs follow the same large scale structure as ordinary galaxies in the local Universe and if UHECRs are deflected no more than a few degrees, a study of mock maps suggests that these three methods can efficiently respond to the resulting anisotropy with a P-value = 1.0% or smaller with data sets as few as 100 events. Using data taken from January 1, 2004 to July 31, 2010 we examined the 20,30,...,110 highest energy events with a corresponding minimum energy threshold of about 49.3 EeV. The minimum P-values found were 13.5% using the 2pt-L method, 1.0% using the 2pt+ method and 1.1% using the 3pt method for the highest 100 energy events. In view of the multiple (correlated) scans performed on the data set, these catalog-independent methods do not yield strong evidence of anisotropy in the highest energy cosmic rays.

We present a comprehensive study of the influence of the geomagnetic field on the energy estimation of extensive air showers with a zenith angle smaller than 60°, detected at the Pierre Auger Observatory. The geomagnetic field induces an azimuthal modulation of the estimated energy of cosmic rays up to the ~2% level at large zenith angles. We present a method to account for this modulation of the reconstructed energy. We analyse the effect of the modulation on large scale anisotropy searches in the arrival direction distributions of cosmic rays. At a given energy, the geomagnetic effect is shown to induce a pseudo-dipolar pattern at the percent level in the declination distribution that needs to be accounted for.

We present the results of an analysis of data recorded at the Pierre Auger Observatory in which we search for groups of directionally-aligned events (or `multiplets') which exhibit a correlation between arrival direction and the inverse of the energy. These signatures are expected from sets of events coming from the same source after having been deflected by intervening coherent magnetic fields. The observation of several events from the same source would open the possibility to accurately reconstruct the position of the source and also measure the integral of the component of the magnetic field orthogonal to the trajectory of the cosmic rays. We describe the largest multiplets found and compute the probability that they appeared by chance from an isotropic distribution. We find no statistically significant evidence for the presence of multiplets arising from magnetic deflections in the present data.

The Surface Detector of the Pierre Auger Observatory is sensitive to neutrinos of all flavors above 0.1 EeV. These interact through charged and neutral currents in the atmosphere giving rise to extensive air showers. When interacting deeply in the atmosphere at nearly horizontal incidence, neutrinos can be distinguished from regular hadronic cosmic rays by the broad time structure of their shower signals in the water-Cherenkov detectors. In this paper we present for the first time an analysis based on down-going neutrinos. We describe the search procedure, the possible sources of background, the method to compute the exposure and the associated systematic uncertainties. No candidate neutrinos have been found in data collected from 1 January 2004 to 31 May 2010. Assuming an E-2 differential energy spectrum the limit on the single-flavor neutrino is E2dN/dE<1.74x10-7GeVcm-2s-1sr-1 at 90% C.L. in the energy range 1x1017eV

In this paper we introduce the concept of Lateral Trigger Probability (LTP) function, i.e., the probability for an extensive air shower (EAS) to trigger an individual detector of a ground based array as a function of distance to the shower axis, taking into account energy, mass and direction of the primary cosmic ray. We apply this concept to the surface array of the Pierre Auger Observatory consisting of a 1.5 km spaced grid of about 1600 water Cherenkov stations. Using Monte Carlo simulations of ultra-high energy showers the LTP functions are derived for energies in the range between 10^17 and 10^19 eV and zenith angles up to 65 degs. A parametrization combining a step function with an exponential is found to reproduce them very well in the considered range of energies and zenith angles. The LTP functions can also be obtained from data using events simultaneously observed by the fluorescence and the surface detector of the Pierre Auger Observatory (hybrid events). We validate the Monte-Carlo results showing how LTP functions from data are in good agreement with simulations.

The Pierre Auger Collaboration has reported evidence for anisotropy in the distribution of arrival directions of the cosmic rays with energies E>E_{th}=5.5\times 10^{19} eV. These show a correlation with the distribution of nearby extragalactic objects, including an apparent excess around the direction of Centaurus A. If the particles responsible for these excesses at E>E_{th} are heavy nuclei with charge Z, the proton component of the sources should lead to excesses in the same regions at energies E/Z. We here report the lack of anisotropies in these directions at energies above E_{th}/Z (for illustrative values of Z=6,13,26). If the anisotropies above E_{th} are due to nuclei with charge Z, and under reasonable assumptions about the acceleration process, these observations imply stringent constraints on the allowed proton fraction at the lower energies.

We present the results of searches for dipolar-type anisotropies in different energy ranges above 2.5 x 10^17 eV with the surface detector array of the Pierre Auger Observatory, reporting on both the phase and the amplitude measurements of the first harmonic modulation in the right-ascension distribution. Upper limits on the amplitudes are obtained, which provide the most stringent bounds at present, being below 2% at 99% C.L. for EeV energies. We also compare our results to those of previous experiments as well as with some theoretical expectations.

The advent of the Auger Engineering Radio Array (AERA) necessitates the development of a powerful framework for the analysis of radio measurements of cosmic ray air showers. As AERA performs "radio-hybrid" measurements of air shower radio emission in coincidence with the surface particle detectors and fluorescence telescopes of the Pierre Auger Observatory, the radio analysis functionality had to be incorporated in the existing hybrid analysis solutions for fluoresence and surface detector data. This goal has been achieved in a natural way by extending the existing Auger Offline software framework with radio functionality. In this article, we lay out the design, highlights and features of the radio extension implemented in the Auger Offline framework. Its functionality has achieved a high degree of sophistication and offers advanced features such as vectorial reconstruction of the electric field, advanced signal processing algorithms, a transparent and efficient handling of FFTs, a very detailed simulation of detector effects, and the read-in of multiple data formats including data from various radio simulation codes. The source code of this radio functionality can be made available to interested parties on request.

The Pierre Auger Observatory is a detector for ultra-high energy cosmic rays. It consists of a surface array to measure secondary particles at ground level and a fluorescence detector to measure the development of air showers in the atmosphere above the array. The "hybrid" detection mode combines the information from the two subsystems. We describe the determination of the hybrid exposure for events observed by the fluorescence telescopes in coincidence with at least one water-Cherenkov detector of the surface array. A detailed knowledge of the time dependence of the detection operations is crucial for an accurate evaluation of the exposure. We discuss the relevance of monitoring data collected during operations, such as the status of the fluorescence detector, background light and atmospheric conditions, that are used in both simulation and reconstruction.

Since data-taking began in January 2004, the Pierre Auger Observatory has been recording the count rates of low energy secondary cosmic ray particles for the self-calibration of the ground detectors of its surface detector array. After correcting for atmospheric effects, modulations of galactic cosmic rays due to solar activity and transient events are observed. Temporal variations related with the activity of the heliosphere can be determined with high accuracy due to the high total count rates. In this study, the available data are presented together with an analysis focused on the observation of Forbush decreases, where a strong correlation with neutron monitor data is found.

Data collected by the Pierre Auger Observatory through 31 August 2007 showed evidence for anisotropy in the arrival directions of cosmic rays above the Greisen-Zatsepin-Kuz'min energy threshold, \nobreak{6\times 10^{19}eV}. The anisotropy was measured by the fraction of arrival directions that are less than 3.1^\circ from the position of an active galactic nucleus within 75 Mpc (using the V\'eron-Cetty and V\'eron 12^{\rm th} catalog). An updated measurement of this fraction is reported here using the arrival directions of cosmic rays recorded above the same energy threshold through 31 December 2009. The number of arrival directions has increased from 27 to 69, allowing a more precise measurement. The correlating fraction is (38^{+7}_{-6})%, compared with 21% expected for isotropic cosmic rays. This is down from the early estimate of (69^{+11}_{-13})%. The enlarged set of arrival directions is examined also in relation to other populations of nearby extragalactic objects: galaxies in the 2 Microns All Sky Survey and active galactic nuclei detected in hard X-rays by the Swift Burst Alert Telescope. A celestial region around the position of the radiogalaxy Cen A has the largest excess of arrival directions relative to isotropic expectations. The 2-point autocorrelation function is shown for the enlarged set of arrival directions and compared to the isotropic expectation.

The Pierre Auger Observatory is a hybrid detector for ultra-high energy cosmic rays. It combines a surface array to measure secondary particles at ground level together with a fluorescence detector to measure the development of air showers in the atmosphere above the array. The fluorescence detector comprises 24 large telescopes specialized for measuring the nitrogen fluorescence caused by charged particles of cosmic ray air showers. In this paper we describe the components of the fluorescence detector including its optical system, the design of the camera, the electronics, and the systems for relative and absolute calibration. We also discuss the operation and the monitoring of the detector. Finally, we evaluate the detector performance and precision of shower reconstructions.

The Pierre Auger Observatory is an international facility dedicated to the full-sky study of the highest-energy cosmic rays. The southern site of the Auger Observatory was completed in June 2008. Data collected since January 2004 have yielded important information on the energy spectrum, the primary particle composition, the fluxes of photons and neutrinos and on the anisotropic distribution of the arrival directions of the most energetic particles. On this basis, the scientific motivation for the northern Auger Observatory site in Colorado, USA, is discussed. The overall layout, the key components and the expected performance of this 20 000 km2 hybrid observatory comprised of an array of 4400 surface detectors and 39 fluorescence telescopes are described.

The air fluorescence detector of the Pierre Auger Observatory is designed to perform calorimetric measurements of extensive air showers created by cosmic rays of above 10^18 eV. To correct these measurements for the effects introduced by atmospheric fluctuations, the Observatory contains a group of monitoring instruments to record atmospheric conditions across the detector site, an area exceeding 3,000 km^2. The atmospheric data are used extensively in the reconstruction of air showers, and are particularly important for the correct determination of shower energies and the depths of shower maxima. This paper contains a summary of the molecular and aerosol conditions measured at the Pierre Auger Observatory since the start of regular operations in 2004, and includes a discussion of the impact of these measurements on air shower reconstructions. Between 10^18 and 10^20 eV, the systematic uncertainties due to all atmospheric effects increase from 4% to 8% in measurements of shower energy, and 4 g/cm^2 to 8 g/cm^2 in measurements of the shower maximum.

We 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. The spectrum can be described by a broken power law E^-gamma with index gamma=3.3 below the ankle which is measured at log10(E/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 log10(E/eV) = 19.5, detected with high statistical significance.

We describe the measurement of the depth of maximum, Xmax, of the longitudinal development of air showers induced by cosmic rays. Almost four thousand events above 10^18 eV observed by the fluorescence detector of the Pierre Auger Observatory in coincidence with at least one surface detector station are selected for the analysis. The average shower maximum was found to evolve with energy at a rate of (106 +35/-21) g/cm^2/decade below 10^(18.24 +/- 0.05) eV and (24 +/- 3) g/cm^2/decade above this energy. The measured shower-to-shower fluctuations decrease from about 55 to 26 g/cm^2. The interpretation of these results in terms of the cosmic ray mass composition is briefly discussed.

The Pierre Auger Observatory is a hybrid detector for ultra-high energy cosmic rays. It combines a surface array to measure secondary particles at ground level together with a fluorescence detector to measure the development of air showers in the atmosphere above the array. The fluorescence detector comprises 24 large telescopes specialized for measuring the nitrogen fluorescence caused by charged particles of cosmic ray air showers. In this paper we describe the components of the fluorescence detector including its optical system, the design of the camera, the electronics, and the systems for relative and absolute calibration. We also discuss the operation and the monitoring of the detector. Finally, we evaluate the detector performance and precision of shower reconstructions.

Atmospheric parameters, such as pressure (P), temperature (T) and density, affect the development of extensive air showers initiated by energetic cosmic rays. We have studied the impact of atmospheric variations on extensive air showers by means of the surface detector of the Pierre Auger Observatory. The rate of events shows a ~10% seasonal modulation and ~2% diurnal one. We find that the observed behaviour is explained by a model including the effects associated with the variations of pressure and density. The former affects the longitudinal development of air showers while the latter influences the Moliere radius and hence the lateral distribution of the shower particles. The model is validated with full simulations of extensive air showers using atmospheric profiles measured at the site of the Pierre Auger Observatory.

From direct observations of the longitudinal development of ultra-high energy air showers performed with the Pierre Auger Observatory, upper limits of 3.8%, 2.4%, 3.5% and 11.7% (at 95% c.l.) are obtained on the fraction of cosmic-ray photons above 2, 3, 5 and 10 EeV (1 EeV = 10^18 eV) respectively. These are the first experimental limits on ultra-high energy photons at energies below 10 EeV. The results complement previous constraints on top-down models from array data and they reduce systematic uncertainties in the interpretation of shower data in terms of primary flux, nuclear composition and proton-air cross-section.

Data collected at the Pierre Auger Observatory are used to establish an upper limit on the diffuse flux of tau neutrinos in the cosmic radiation. Earth-skimming \nu_{\tau} may interact in the Earth's crust and produce a \tau lepton by means of charged-current interactions. The \tau lepton may emerge from the Earth and decay in the atmosphere to produce a nearly horizontal shower with a typical signature, a persistent electromagnetic component even at very large atmospheric depths. The search procedure to select events induced by \tau decays against the background of normal showers induced by cosmic rays is described. The method used to compute the exposure for a detector continuously growing with time is detailed. Systematic uncertainties in the exposure from the detector, the analysis and the involved physics are discussed. No \tau neutrino candidates have been found. For neutrinos in the energy range 2\times10^{17} eV < E_{\nu} < 2\times10^{19} eV, assuming a diffuse spectrum of the form E_{\nu}^{-2}, data collected between 1 January 2004 and 30 April 2008 yield a 90% confidence-level upper limit of E_\nu^{2} \mathrm{d}N_{\nu_\tau}/\mathrm{d}E_{\nu} < 9 \times 10^{-8} GeV cm^{-2} s^{-1} sr^{-1}.

It contains Bounds on the density of sources of ultra high energy cosmic rays from Pierre Auger Observatory data, M. De Domenico for the Pierre Auger Collaboration

In a previous work [1], an empirical model, based on the Gumbel statistics, has been introduced to describe the development of extensive air showers initiated by ultra-high energy (UHE) nuclei. The model allows us to parameterize accurately the distribution of Xmax over a wide range of energies and nuclear masses. In this note, we adapt and extend the previous model to the case of UHE photon primaries. We show that a model based on the simplest version of the generalized Gumbel distribution is sufficient for a good description of the simulated Xmax distribution in an energy regime where the shower development is not significantly influenced by the pre-showering effect. However, the generalized Gumbel distribution is suitable for describing the Xmax distribution for any energy, even in the range where LPM and pre-showering effects are significant.

Within the present note, we introduce an empirical model, motivated by theoretical arguments, to describe the distribution of maxima for extensive air showers initiated by ultra-high energy nuclei. We show that the generalized Gumbel distribution, derived from extreme value statistics, provides an excellent framework to parameterize Xmax for a wide range of nuclear masses, spanning over four orders of magnitude in energy. Our model is motivated by the relationship between the generalized Gumbel statistics and the distribution of the sum of correlated variables in dissipative stochastic systems. The main advantage of our analytical approach is to dramatically reduce the time for the computation of Xmax distributions generally adopted to fit the data.

Within the present study, we explore the possibility that nearby black holes are sources of UHECRs detected by the Pierre Auger Observatory. For such a purpose, we make use of the most updated and unbiased catalog of black holes within 100 Mpc [1, 2]. In our analysis, we assume that UHECRs are protons. We take into account the effects of the intervening extragalactic magnetic field and we consider the propagation in a ΛCDM universe, including the main energy-loss processes due to the interaction with the cosmic microwave background (CMB) radiation, relevant for the present study. The effect of experimental uncertainty on the angular resolution is taken into account. We investigate the clustering features of the data and of the simulated data sets by using global and local methods previously adopted to put bounds on the source density. This involves the estimation of the clustering coefficient within the multiscale autocorrelation function (MAF).Finally, we constrain the minimum mass threshold by using Auger data with energy above 60 and 80 EeV, and we find that only black holes with mass larger than MBH, with 10^7.3 < MBH/Msun < 10^8.75 can be sources of UHE protons above such energy thresholds, at 95% CL. The dependence of the result on the strength of the magnetic field and on the energy threshold is discussed.

We explore some representative astrophysical scenarios involving different configurations of mag- netic fields, composition of UHECRs and distribution of candidate sources. We adopt a mixed composition model, by considering skies populated with a fraction fp of protons and a fraction 1 − fp of iron nuclei. By varying the parameter fp, we estimate, through the multiscale autocorrelation function (MAF), the intrinsic clustering signal in the arrival directions of events generated according to models and we exploit the P. Auger data to constrain the simulations. Hence, we use the value of Xmax above 60 EeV, extrapolated from the data, to select the compatible astrophysical scenario(s) for different hadronic models. The observed flux of UHECRs is used for probing two plausible injection spectral indices and the correlation with active galactic nuclei (AGN) within 75 Mpc (from the SWIFT-BAT 58-months catalog) to restrict the number of scenarios compatible with the data within such an extended framework.

We extend the results about the constraints on the source density of UHECRs that we have recently reported in a previous note [1]. Within the present study, we consider different distribution of sources (either mimicking the large scale structure of the matter or a uniform distribution in the nearby universe), we also include the effects of the (galactic and extragalactic) magnetic fields and of the mass composition. We consider equal-luminosity sources (injection index s = 2.7) of UHECRs propagating in a ΛCDM universe and subjected to the main energy-loss processes due to the interaction with the extragalactic background radiation (IRB and CMB). The effect of experimental uncertainty on the angular resolution is taken into account. We investigate the clustering features of the simulated data sets by using global method previously described in our note [1], and involving the estimation of the maximum clustering coefficient within the multiscale autocorrelation function (MAF). Finally, we constrain the parameter space by using Auger data with energy above 60 and 80 EeV, obtaining results compatible with our previous studies at 99% CL. The dependence of the result on the model of sources, on the magnetic field, on the composition and on the energy threshold is discussed, as well as the consistency with the density of candidate UHECR sources.

We propose a new method for simulating the arrival directions of UHECR events produced by point sources placed on a spherical surface. The method makes an extensive use of the von Mises- Fisher distributions from directional statistics theory, and it is suitable for analyses involving the smearing of real events. Deviations from the Gaussian distribution of the spherical coordinates and from the Rayleigh distribution of the angular distance between smeared points and source, are also discussed.

We use the Multiscale Autocorrelation Function (MAF) to investigate the clustering features of the arrival directions of events distributed according to different astrophysical models. We report the statistical power of MAF by testing the null hypothesis of an underlying isotropic distribution against the alternative hypothesis of an anisotropic distribution, for two values of the Type I error, α = 0.1% and 1%, and by varying the number of events in the sample distribution from 20 to 60.

We constrain the source density of UHECR within three different approaches, by using Auger data (E > 50, 55 and 60 EeV) and different models for sources: either mimicking the large scale structure of the matter or a uniform distribution in the nearby universe. We have considered equal- luminosity sources (injection index s = 2.7) of high energy protons propagating in a ΛCDM universe and subjected to the main energy-loss processes, such as adiabatic, pair and photopion production due to the interaction with the cosmic microwave background radiation. All methods provide the confidence interval 0.32 − 10 x 10^-4 Mpc−3 at 95% confidence level, in agreement with previous studies. The dependence of the result on the model of sources and on the energy threshold is discussed, as well as the consistency with the density of candidate UHECR sources.

In a recent note [1], we presented the results about the impact of experimental uncertainties on the anisotropy signal detection by mean of the (catalog independent) multiscale autocorrelation function. Even catalog dependent analyses for correlation signal detection, generally work on data sets of events without taking into account experimental uncertainties due to the detector resolution. A possible way to investigate the effect of uncertainties is to perform a smearing procedure on the physical observables of interest, in order to create ensambles of smeared data to be analyzed. The final goal of this approach, is to obtain the distribution of significances from smeared skies and to estimate the impact of the smearing on the decision making process about the null hypothesis. We investigate, separately, the impact of the angular and energy resolution on the cross-correlation signal between Auger events with E ≥ 55 EeV and the SWIFT-BAT 39-month catalog [2] of candidate sources, by mean of the smearing procedure.

Catalog independent analyses for anisotropy signal detection, generally work on data sets of events without taking into account experimental uncertainties due to the detector resolution. A possible way to investigate the effect of uncertainties is to perform a smearing procedure on the physical observables of interest, in order to create ensambles of smeared data to be analyzed. The final goal of this approach, is to obtain the distribution of significances from smeared skies and to estimate the impact of the smearing on the decision making process about the null hypothesis. Firstly, we investigate the chance probability that Auger data is drawn from an isotropic distribu- tion by varying both energy and angular scales of the analysis. Finally, we investigate, separately, the impact of the angular and energy resolution on the previous result by mean of the smearing procedure.

In recent years many procedures have been proposed to detect the correlation between the arrival directions of ultra high energy cosmic rays (UHECR) and powerful astrophysical objects, as active galactic nuclei (AGN), magnetars or gamma-ray bursts (GRB). The experimental evidence of GZK features in the energy spectrum and the expected anisotropy of the possible sources distribution in the local universe (within the GZK radius of 100-200 Mpc), makes the investigation of the anisotropy of UHECR directions an intriguing and hot topic in the field. A new simple and efficient procedure is presented for scale dependent cross-correlation analysis with particular attention to small data sets, particularly interesting for applications to P. Auger Observatory data. Results on P. Auger Observatory data (up to Dec. 2009) are presented, by considering two catalogs of nearby candidate sources: Veron-Cetty-Veron 12th ed. and SWIFT- BAT 39-month.

In recent years many procedures have been proposed to detect an anisotropy signal in the arrival direction distribution of ultra high energy cosmic rays (UHECR). The search for anisotropy in experimental data is covered by a large literature. A new simple and efficient procedure is presented for scale dependent anisotropy analysis with particular attention to small data sets, interesting for applications to P. Auger Observatory data.

In recent years many procedures have been proposed to detect the anisotropy of arrival direction distribution of ultra high energy cosmic rays (UHECR). The search for anisotropy in experimental data is covered by a large literature. A new simple and efficient procedure is presented for scale dependent anisotropy analysis with particular attention to small data sets, particularly interesting for applications to P. Auger Observatory data. Results on P. Auger data sets of 27 public events and of events with energy E > 57 EeV (CDAS v4r6p3 Herald archive, Jan 2010) are presented.

A seasonal modulation has been found in the P. Auger Observatory data due to a deterministic ciclostationary physical effect which a recent paper from the P. Auger Collaboration attributes to atmospheric effects, such as pressure, temperature and density, on extensive air showers. An additional deterministic stationary aperiodic (or quasi-periodic) or nonstationary (determin- istic or stochastic) behavior has been found in the data. Within the present work the Surface Detector (SD) events rate is deconvolved from the temper- ature signal and it is cleaned by a Wiener filtering procedure in order to estimate the all-particle and energy-integrated rate of events described by the Ginzburg-Syrovatskii transport equations, for future nonlinear time series analysis.

A linear and a nonlinear time series analysis on the experimental rate of SD events normalized to the sensitive detector area, as described in [1], has been done. The same analysis have been performed on simulated time series with annual periodic behavior. An evident annual period has been found in the P. Auger data due to a deterministic ciclostationary physical effect which a recent paper from the P. Auger Collaboration attributes to atmospheric effects, such as pressure, temperature and density, on extensive air showers [2] [3]. Our results are in good agreement with this interpretation. Another deterministic stationary aperiodic (or quasi-periodic) or nonstationary (deterministic or stochastic) behavior has been found in the P. Auger data, probably due to some physical unknown effect which needs further investigations in the next years, when a larger amount of data will be available.

A revision of the FD calibration database was released in April, 2009. This new DB contains a calibration for each pixel for each night for the period from March 2006 to March 2009, updating the DB to cover recent shifts and overwriting some sections of the less precise epoch-based calibration. Calibration for earlier shifts back to December 2004 are still based on epochs of camera stability. A 3.5% global correction has been applied to correct for LED effects. This note describes the general procedures for generating the nightly calibration constants and documents the present state of the DB.

An analysis on the number of 6T5 cells and the rate of T5 and 0 < θ < 60 cosmic ray events detected from the surface detector since Jan 2005 to Mar 2009 has been performed. As it was found in [2], from this analysis comes out that the rate of events shows a seasonal modulation that will be investigated in subsequent works.

We present an algoritm to reconstruct the direction detected at the Earth of CRs coming from extragalactic sources. This algorithm uses the forward-tracking method to make the correlation between CR direction detected at the earth and the direction at the galactic halo, by taking into account the impact point of the CR tracks with the galactic halo. By running a large set of simulations, we build many lookup correspondence tables for CR protons in the energy range of 10-130 EeV.

We present the results of relative calibration analysis (from January 2007 to December 2008) of Coihueco Fluorescence Detector (FD). By the analysis of these data we can obtain the constants necessary to rescale absolute calibration constants. At the same time we can monitor the FD response. We find that the Coihueco FD is quite stable overall the considered period. A small seasonal modulation is still visible in the data.

We present the results about a deep and detailed nonlinear time series anal- ysis of the UHECR arrival times series observed at the P. Auger Observatory, Malargue, Argentina. The analysis has been developed over a known chaotic time series (derived from a Lorenz standard model) in order to test that our algorithms and our software work fine. We analysed in addition 2 arrival times series obtained from a chaotic system and a stochastic one, in order to get our conclusion by a direct comparison among the UHECR system’s dynamical properties and the 2 known ones. We tried to reconstruct the phase space of each dynamical system from a non-linear analysis of its own time arrival series by using a special multidimensional space, called embedding, with the same dynamical invariants of the original phase space like the fractal dimension, the Renyi dimension, the Lyapunov exponents and the time reversal asymmetry. We performed a statistical analysis based on the surrogate data method and nonparametric statistics with about 2400 numerical analysis to test the null hypothesis of white noise, linear gaussian model, nonlinear gaussian model. From the analysis of the Lyapunov spectrums and the time reversal asymmetry we deduced that there are time correlation in UHECR with energy above 1019eV and that, at this preliminary step, it is possible that the dynamical system, which they depend to, can be considered deterministic and low-dimensional chaotic with a time-projected attractor of fractal dimension D2 = 1.14. Important implications on the nature of their cosmological origin and propagation need further investigations.

We report the results of a mass composition analysis performed using a likelihood fit to hybrid Xmax data. The method has been validated using MC simulations, with different primary nuclei and hadronic model scenarios. Typical analysis outputs include the reconstruction of the mass abundances, Xmax mean and RMS as a function of the primary energy.

Arrival time distributions of the UHECRs should contain relevant information about specific feature of the source. To distinguish these ’source features’ is not an easy task. We suggest to use nonlinear time series analysis. The approach has two main goals: on one side we will try to investigate the astrophysical nature of the process (origin, propagation feature), while on the other side we would like to investigate the deterministic, low-dimensional chaotic or stochastic natute of the dynamical system they belong to. We present preliminary results about the nonlinearity and the nonstationarity of UHECR with E > 10EeV detected from surface detector at PAO with zenith angle θ < 60◦, for both T5 and no T5 cuts. Preliminary results for UHECR with E > 40EeV are also included.

We present ViMAS, a Fedora Core 7 based virtual machine framework for the P. Auger data analysis software. Through a platform-independent player, the virtual machine installed on virtual disk, represented by a single file, can be used from every supported Operating System as Linux distributions, Microsoft Windows and Mac OS X. ViMAS includes fundamental data analysis software used or developed by the P. Auger collaboration as the ROOT framework, the OffLine framework, the FDEventLib library, the CDAS libraries and those ones required for the extended air shower simulations and animations. The virtual platform solves all the compatibility problems among the various data analysis softwares and frameworks actually used by the P. Auger collaboration.

We present iPlot, a framework that is the result of two different technologies: a) Server-Side: a PHP Environment finds and analyses the FD calibration files in ASCII format, stored in the web server and produces the analysis results in order to be computed by the Client-Side Environment; b) Client-Side: a javascript- enabled client is the Javascript Environment that elaborates the formatted input and shows the plots in the web browser. Technically the client doesn’t need to know any programming language to install and to use iPlot: the javascript-enable web browser will install the iPlot client side environment the first time that the client will use it. iPlot actually is able to find and analyse all FD calibration file in order to plot calibration constants vs pixel or versus time and to detect bad pixel and values out of range.