The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.

Empirical data on contacts between individuals in social contexts play an important role in providing information for models describing human behavior and how epidemics spread in populations. Here, we analyze data on face-to-face contacts collected in an office building. The statistical properties of contacts are similar to other social situations, but important differences are observed in the contact network structure. In particular, the contact network is strongly shaped by the organization of the offices in departments, which has consequences in the design of accurate agent-based models of epidemic spread. We consider the contact network as a potential substrate for infectious disease spread and show that its sparsity tends to prevent outbreaks of rapidly spreading epidemics. Moreover, we define three typical behaviors according to the fraction f of links each individual shares outside its own department: residents, wanderers and linkers. Linkers ( f ∼ 50%) act as bridges in the network and have large betweenness centralities. Thus, a vaccination strategy targeting linkers efficiently prevents large outbreaks. As such a behavior may be spotted a priori in the offices' organization or from surveys, without the full knowledge of the time-resolved contact network, this result may help the design of efficient, low-cost vaccination or social-distancing strategies.

Background The exposure and consumption of information during epidemic outbreaks may alter people’s risk perception and trigger behavioral changes, which can ultimately affect the evolution of the disease. It is thus of utmost importance to map the dissemination of information by mainstream media outlets and the public response to this information. However, our understanding of this exposure-response dynamic during the COVID-19 pandemic is still limited. Objective The goal of this study is to characterize the media coverage and collective internet response to the COVID-19 pandemic in four countries: Italy, the United Kingdom, the United States, and Canada. Methods We collected a heterogeneous data set including 227,768 web-based news articles and 13,448 YouTube videos published by mainstream media outlets, 107,898 user posts and 3,829,309 comments on the social media platform Reddit, and 278,456,892 views of COVID-19–related Wikipedia pages. To analyze the relationship between media coverage, epidemic progression, and users’ collective web-based response, we considered a linear regression model that predicts the public response for each country given the amount of news exposure. We also applied topic modelling to the data set using nonnegative matrix factorization. Results Our results show that public attention, quantified as user activity on Reddit and active searches on Wikipedia pages, is mainly driven by media coverage; meanwhile, this activity declines rapidly while news exposure and COVID-19 incidence remain high. Furthermore, using an unsupervised, dynamic topic modeling approach, we show that while the levels of attention dedicated to different topics by media outlets and internet users are in good accordance, interesting deviations emerge in their temporal patterns. Conclusions Overall, our findings offer an additional key to interpret public perception and response to the current global health emergency and raise questions about the effects of attention saturation on people’s collective awareness and risk perception and thus on their tendencies toward behavioral change.

Dynamical processes on time-varying complex networks are key to understanding and modeling a broad variety of processes in socio-technical systems. Here we focus on empirical temporal networks of human proximity and we aim at understanding the factors that, in simulation, shape the arrival time distribution of simple spreading processes. Abandoning the notion of wall-clock time in favour of node-specific clocks based on activity exposes robust statistical patterns in the arrival times across different social contexts. Using randomization strategies and generative models constrained by data, we show that these patterns can be understood in terms of heterogeneous inter-event time distributions coupled with heterogeneous numbers of events per edge. We also show, both empirically and by using a synthetic dataset, that significant deviations from the above behavior can be caused by the presence of edge classes with strong activity correlations.T he field of complex networks has recently undergone an important evolution. Thanks to the recent availability of time-resolved data sources, many studies performed under the assumption of static network structures can now be extended to take into account the network's dynamics. Data on time-varying networks are becoming accessible across a variety of contexts, ranging from communication networks [1][2][3][4][5][6] to proximity networks 7,8 and infrastructure networks 9,10 . This avalanche of data is prompting a surge of activity in the field of ''temporal networks '' 11 . Data analysis has shown the coexistence of statistically stationary properties and topological changes, as well as the burstiness of interactions characterized by highly skewed distributions of interevent times [1][2][3][4][5][6][7][8][9][10][11][12][13][14] . These temporal features of networks influence the dynamics of network processes, just like the topological structure of static networks does 15 . As a consequence, and similarly to the case of static networks, simple dynamical processes such as random walks 16 , synchronization phenomena 17 , consensus formation 18 or spreading processes [19][20][21][22][23][24][25] can be used as probes to investigate the temporal and structural properties of timevarying networks.Previous works on the dynamics of spreading processes over complex networks have considered both the topological and the temporal structure of networks 11,19,23 , as well as the specific impact that the temporal structure bears on the spreading process. The quantities used to quantify the measured effects are typically network averages, such as the outbreak sizes of an epidemic or its prevalence. These average quantities, however, fail to account for important heterogeneities in the arrival times of the spreading process. Recent work 26 showed that the non-stationarity and burstiness of empirical temporal networks lead to noisy distributions of arrival times, and that shifting the perspective from a global notion of wall-clock time to a node-specific ''time'' based on node activity allows to...

We report on a data-driven investigation aimed at understanding the dynamics of message spreading in a real-world dynamical network of human proximity. We use data collected by means of a proximity-sensing network of wearable sensors that we deployed at three different social gatherings, simultaneously involving several hundred individuals. We simulate a message spreading process over the recorded proximity network, focusing on both the topological and the temporal properties. We show that by using an appropriate technique to deal with the temporal heterogeneity of proximity events, a universal statistical pattern emerges for the delivery times of messages, robust across all the data sets. Our results are useful to set constraints for generic processes of data dissemination, as well as to validate established models of human mobility and proximity that are frequently used to simulate realistic behaviors.