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Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at different time points. However, quantifying the similarity between temporal graphs as a whole is an open problem. Here, we use embeddings based on time-respecting random walks to introduce a new notion of distance between temporal graphs. This distance is well-defined for pairs of temporal graphs with different numbers of nodes and different time spans. We study the case of a matched pair of graphs, when a known relation exists between their nodes, and the case of unmatched graphs, when such a relation is unavailable and the graphs may be of different sizes. We use empirical and synthetic temporal network data to show that the distance we introduce discriminates graphs with different topological and temporal properties. We provide an efficient implementation of the distance computation suitable for large-scale temporal graphs.

Contact matrices are a commonly adopted data representation, used to develop compartmental models for epidemic spreading, accounting for the contact heterogeneities across age groups. Their estimation, however, is generally time and effort consuming and model-driven strategies to quantify the contacts are often needed. In this article we focus on household contact matrices, describing the contacts among the members of a family and develop a parametric model to describe them. This model combines demographic and easily quantifiable survey-based data and is tested on high resolution proximity data collected in two sites in South Africa. Given its simplicity and interpretability, we expect our method to be easily applied to other contexts as well and we identify relevant questions that need to be addressed during the data collection procedure.

Digital contact tracing is a public health intervention. It should be integrated with local health policy, provide rapid and accurate notifications to exposed individuals, and encourage high app uptake and adherence to quarantine. Real-time monitoring and evaluation of effectiveness of app-based contact tracing is key for improvement and public trust., Comment: 9 pages

Measuring close proximity interactions between individuals can provide key information on social contacts in human communities. With the present study, we report the quantitative assessment of contact patterns in a village in rural Malawi, based on proximity sensors technology that allows for high-resolution measurements of social contacts. The system provided information on community structure of the village, on social relationships and social assortment between individuals, and on daily contacts activity within the village. Our findings revealed that the social network presented communities that were highly correlated with household membership, thus confirming the importance of family ties within the village. Contacts within households occur mainly between adults and children, and adults and adolescents. This result suggests that the principal role of adults within the family is the care for the youngest. Most of the inter-household interactions occurred among caregivers and among adolescents. We studied the tendency of participants to interact with individuals with whom they shared similar attributes (i.e., assortativity). Age and gender assortativity were observed in inter-household network, showing that individuals not belonging to the same family group prefer to interact with people with whom they share similar age and gender. Age disassortativity is observed in intra-household networks. Family members congregate in the early morning, during lunch time and dinner time. In contrast, individuals not belonging to the same household displayed a growing contact activity from the morning, reaching a maximum in the afternoon. The data collection infrastructure used in this study seems to be very effective to capture the dynamics of contacts by collecting high resolution temporal data and to give access to the level of information needed to understand the social context of the village.

Home detection, assigning a phone device to its home antenna, is a ubiquitous part of most studies in the literature on mobile phone data. Despite its widespread use, home detection relies on a few assumptions that are difficult to check without ground truth, i.e., where the individual that owns the device resides. In this paper, we provide an unprecedented evaluation of the accuracy of home detection algorithms on a group of sixty-five participants for whom we know their exact home address and the antennas that might serve them. Besides, we analyze not only Call Detail Records (CDRs) but also two other mobile phone streams: eXtended Detail Records (XDRs, the ``data'' channel) and Control Plane Records (CPRs, the network stream). These data streams vary not only in their temporal granularity but also they differ in the data generation mechanism', e.g., CDRs are purely human-triggered while CPR is purely machine-triggered events. Finally, we quantify the amount of data that is needed for each stream to carry out successful home detection for each stream. We find that the choice of stream and the algorithm heavily influences home detection, with an hour-of-day algorithm for the XDRs performing the best, and with CPRs performing best for the amount of data needed to perform home detection. Our work is useful for researchers and practitioners in order to minimize data requests and to maximize the accuracy of home antenna location.

Youth unemployment rates are still in alerting levels for many countries, among which Italy. Direct consequences include poverty, social exclusion, and criminal behaviours, while negative impact on the future employability and wage cannot be obscured. In this study, we employ survey data together with social media data, and in particular likes on Facebook Pages, to analyse personality, moral values, but also cultural elements of the young unemployed population in Italy. Our findings show that there are small but significant differences in personality and moral values, with the unemployed males to be less agreeable while females more open to new experiences. At the same time, unemployed have a more collectivist point of view, valuing more in-group loyalty, authority, and purity foundations. Interestingly, topic modelling analysis did not reveal major differences in interests and cultural elements of the unemployed. Utilisation patterns emerged though; the employed seem to use Facebook to connect with local activities, while the unemployed use it mostly as for entertainment purposes and as a source of news, making them susceptible to mis/disinformation. We believe these findings can help policymakers get a deeper understanding of this population and initiatives that improve both the hard and the soft skills of this fragile population., Comment: 8 pages. Published in SocInfo 2020 Proceedings. Title update

This document describes and analyzes a system for secure and privacy-preserving proximity tracing at large scale. This system, referred to as DP3T, provides a technological foundation to help slow the spread of SARS-CoV-2 by simplifying and accelerating the process of notifying people who might have been exposed to the virus so that they can take appropriate measures to break its transmission chain. The system aims to minimise privacy and security risks for individuals and communities and guarantee the highest level of data protection. The goal of our proximity tracing system is to determine who has been in close physical proximity to a COVID-19 positive person and thus exposed to the virus, without revealing the contact's identity or where the contact occurred. To achieve this goal, users run a smartphone app that continually broadcasts an ephemeral, pseudo-random ID representing the user's phone and also records the pseudo-random IDs observed from smartphones in close proximity. When a patient is diagnosed with COVID-19, she can upload pseudo-random IDs previously broadcast from her phone to a central server. Prior to the upload, all data remains exclusively on the user's phone. Other users' apps can use data from the server to locally estimate whether the device's owner was exposed to the virus through close-range physical proximity to a COVID-19 positive person who has uploaded their data. In case the app detects a high risk, it will inform the user., Comment: 46 pages, 6 figures, first published 3 April 2020 on https://github.com/DP-3T/documents where companion documents and code can be found

The rapid dynamics of COVID-19 calls for quick and effective tracking of virus transmission chains and early detection of outbreaks, especially in the phase 2 of the pandemic, when lockdown and other restriction measures are progressively withdrawn, in order to avoid or minimize contagion resurgence. For this purpose, contact-tracing apps are being proposed for large scale adoption by many countries. A centralized approach, where data sensed by the app are all sent to a nation-wide server, raises concerns about citizens' privacy and needlessly strong digital surveillance, thus alerting us to the need to minimize personal data collection and avoiding location tracking. We advocate the conceptual advantage of a decentralized approach, where both contact and location data are collected exclusively in individual citizens' "personal data stores", to be shared separately and selectively, voluntarily, only when the citizen has tested positive for COVID-19, and with a privacy preserving level of granularity. This approach better protects the personal sphere of citizens and affords multiple benefits: it allows for detailed information gathering for infected people in a privacy-preserving fashion; and, in turn this enables both contact tracing, and, the early detection of outbreak hotspots on more finely-granulated geographic scale. Our recommendation is two-fold. First to extend existing decentralized architectures with a light touch, in order to manage the collection of location data locally on the device, and allow the user to share spatio-temporal aggregates - if and when they want, for specific aims - with health authorities, for instance. Second, we favour a longer-term pursuit of realizing a Personal Data Store vision, giving users the opportunity to contribute to collective good in the measure they want, enhancing self-awareness, and cultivating collective efforts for rebuilding society., Comment: Revised text. Additional authors

This paper describes how mobile phone data can guide government and public health authorities in determining the best course of action to control the COVID-19 pandemic and in assessing the effectiveness of control measures such as physical distancing. It identifies key gaps and reasons why this kind of data is only scarcely used, although their value in similar epidemics has proven in a number of use cases. It presents ways to overcome these gaps and key recommendations for urgent action, most notably the establishment of mixed expert groups on national and regional level, and the inclusion and support of governments and public authorities early on. It is authored by a group of experienced data scientists, epidemiologists, demographers and representatives of mobile network operators who jointly put their work at the service of the global effort to combat the COVID-19 pandemic.

Temporal networks are widely used to represent a vast diversity of systems, including in particular social interactions, and the spreading processes unfolding on top of them. The identification of structures playing important roles in such processes remains largely an open question, despite recent progresses in the case of static networks. Here, we consider as candidate structures the recently introduced concept of span-cores: the span-cores decompose a temporal network into subgraphs of controlled duration and increasing connectivity, generalizing the core-decomposition of static graphs. To assess the relevance of such structures, we explore the effectiveness of strategies aimed either at containing or maximizing the impact of a spread, based respectively on removing span-cores of high cohesiveness or duration to decrease the epidemic risk, or on seeding the process from such structures. The effectiveness of such strategies is assessed in a variety of empirical data sets and compared to baselines that use only static information on the centrality of nodes and static concepts of coreness, as well as to a baseline based on a temporal centrality measure. Our results show that the most stable and cohesive temporal cores play indeed an important role in epidemic processes on temporal networks, and that their nodes are likely to represent influential spreaders.

When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). In this paper we tackle this task by introducing a notion of temporal core decomposition where each core is associated with two quantities, its coreness, which quantifies how densely it is connected, and its span, which is a temporal interval: we call such cores \emph{span-cores}. For a temporal network defined on a discrete temporal domain $T$, the total number of time intervals included in $T$ is quadratic in $|T|$, so that the total number of span-cores is potentially quadratic in $|T|$ as well. Our first main contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the \emph{maximal span-cores}, i.e., span-cores that are not dominated by any other span-core by both their coreness property and their span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly extract the maximal ones without computing all span-cores. Finally, as a third contribution, we introduce the problem of \emph{temporal community search}, where a set of query vertices is given as input, and the goal is to find a set of densely-connected subgraphs containing the query vertices and covering the whole underlying temporal domain $T$. We derive a connection between this problem and the problem of finding (maximal) span-cores. Based on this connection, we show how temporal community search can be solved in polynomial-time via dynamic programming, and how the maximal span-cores can be profitably exploited to significantly speed-up the basic algorithm., Comment: ACM Transactions on Knowledge Discovery from Data (TKDD), 2020. arXiv admin note: substantial text overlap with arXiv:1808.09376

Low-dimensional vector representations of network nodes have proven successful to feed graph data to machine learning algorithms and to improve performance across diverse tasks. Most of the embedding techniques, however, have been developed with the goal of achieving dense, low-dimensional encoding of network structure and patterns. Here, we present a node embedding technique aimed at providing low-dimensional feature vectors that are informative of dynamical processes occurring over temporal networks -- rather than of the network structure itself -- with the goal of enabling prediction tasks related to the evolution and outcome of these processes. We achieve this by using a modified supra-adjacency representation of temporal networks and building on standard embedding techniques for static graphs based on random-walks. We show that the resulting embedding vectors are useful for prediction tasks related to paradigmatic dynamical processes, namely epidemic spreading over empirical temporal networks. In particular, we illustrate the performance of our approach for the prediction of nodes' epidemic states in a single instance of a spreading process. We show how framing this task as a supervised multi-label classification task on the embedding vectors allows us to estimate the temporal evolution of the entire system from a partial sampling of nodes at random times, with potential impact for nowcasting infectious disease dynamics., Comment: updated version with additional results

The use of public transportation or simply moving about in streets are gendered issues. Women and girls often engage in multi-purpose, multi-stop trips in order to do household chores, work, and study ('trip chaining'). Women-headed households are often more prominent in urban settings and they tend to work more in low-paid/informal jobs than men, with limited access to transportation subsidies. Here we present recent results on urban mobility from a gendered perspective by uniquely combining a wide range of datasets, including commercial sources of telecom and open data. We explored urban mobility of women and men in the greater metropolitan area of Santiago, Chile, by analyzing the mobility traces extracted from the Call Detail Records (CDRs) of a large cohort of anonymized mobile phone users over a period of 3 months. We find that, taking into account the differences in users' calling behaviors, women move less than men, visiting less unique locations and distributing their time less equally among such locations. By mapping gender differences in mobility over the 52 comunas of Santiago, we find a higher mobility gap to be correlated with socio-economic indicators, such as a lower average income, and with the lack of public and private transportation options. Such results provide new insights for policymakers to design more gender inclusive transportation plans in the city of Santiago., Comment: 32 pages, 4 figures

Psychological, political, cultural, and even societal factors are entangled in the reasoning and decision-making process towards vaccination, rendering vaccine hesitancy a complex issue. Here, administering a series of surveys via a Facebook-hosted application, we study the worldviews of people that "Liked" supportive or vaccine resilient Facebook Pages. In particular, we assess differences in political viewpoints, moral values, personality traits, and general interests, finding that those sceptical about vaccination, appear to trust less the government, are less agreeable, while they are emphasising more on anti-authoritarian values. Exploring the differences in moral narratives as expressed in the linguistic descriptions of the Facebook Pages, we see that pages that defend vaccines prioritise the value of the family while the vaccine hesitancy pages are focusing on the value of freedom. Finally, creating embeddings based on the health-related likes on Facebook Pages, we explore common, latent interests of vaccine-hesitant people, showing a strong preference for natural cures. This exploratory analysis aims at exploring the potentials of a social media platform to act as a sensing tool, providing researchers and policymakers with insights drawn from the digital traces, that can help design communication campaigns that build confidence, based on the values that also appeal to the socio-moral criteria of people.

Social media in scientific research offer a unique digital observatory of human behaviours and hence great opportunities to conduct research at large scale answering complex sociodemographic questions. We focus on the identification and assessment of biases in social media administered surveys. This study aims to shed light on population, self-selection and behavioural biases, empirically comparing the consistency between self-reported information collected traditionally versus social media administered questionnaires, including demographic and psychometric attributes. We engaged a demographically representative cohort of young adults in Italy (approximately 4,000 participants) in taking a traditionally administered online survey and then, after one year, we invited them to use our ad hoc Facebook application (988 accepted) where they filled in part of the initial survey. We assess the statistically significant differences indicating population, self-selection, and behavioural biases due to the different context in which the questionnaire is administered. Our findings suggest that surveys administered on Facebook do not exhibit major biases with respect to traditionally administered surveys neither in terms of demographics, nor personality traits. Loyalty, authority, and social binding values were higher in the Facebook platform, probably due to the platform's intrinsic social character. We conclude, that Facebook apps are valid research tools for administering demographic and psychometric surveys provided that the entailed biases are taken into consideration. We contribute to the characterisation of Facebook apps as a valid scientific tool to administer demographic and psychometric surveys, and to the assessment of population, self-selection, and behavioural biases in the collected data.

Over the past several decades, naturally occurring and man-made mass casualty incidents (MCI) have increased in frequency and number, worldwide. To test the impact of such event on medical resources, simulations can provide a safe, controlled setting while replicating the chaotic environment typical of an actual disaster. A standardised method to collect and analyse data from mass casualty exercises is needed, in order to assess preparedness and performance of the healthcare staff involved. We report on the use of wearable proximity sensors to measure proximity events during a MCI simulation. We investigated the interactions between medical staff and patients, to evaluate the time dedicated by the medical staff with respect to the severity of the injury of the victims depending on the roles. We estimated the presence of the patients in the different spaces of the field hospital, in order to study the patients' flow. Data were obtained and collected through the deployment of wearable proximity sensors during a mass casualty incident functional exercise. The scenario included two areas: the accident site and the Advanced Medical Post (AMP), and the exercise lasted 3 hours. A total of 238 participants simulating medical staff and victims were involved. Each participant wore a proximity sensor and 30 fixed devices were placed in the field hospital. The contact networks show a heterogeneous distribution of the cumulative time spent in proximity by participants. We obtained contact matrices based on cumulative time spent in proximity between victims and the rescuers. Our results showed that the time spent in proximity by the healthcare teams with the victims is related to the severity of the patient's injury. The analysis of patients' flow showed that the presence of patients in the rooms of the hospital is consistent with triage code and diagnosis, and no obvious bottlenecks were found.

When analyzing temporal networks, a fundamental task is the identification of dense structures (i.e., groups of vertices that exhibit a large number of links), together with their temporal span (i.e., the period of time for which the high density holds). We tackle this task by introducing a notion of temporal core decomposition where each core is associated with its span: we call such cores span-cores. As the total number of time intervals is quadratic in the size of the temporal domain $T$ under analysis, the total number of span-cores is quadratic in $|T|$ as well. Our first contribution is an algorithm that, by exploiting containment properties among span-cores, computes all the span-cores efficiently. Then, we focus on the problem of finding only the maximal span-cores, i.e., span-cores that are not dominated by any other span-core by both the coreness property and the span. We devise a very efficient algorithm that exploits theoretical findings on the maximality condition to directly compute the maximal ones without computing all span-cores. Experimentation on several real-world temporal networks confirms the efficiency and scalability of our methods. Applications on temporal networks, gathered by a proximity-sensing infrastructure recording face-to-face interactions in schools, highlight the relevance of the notion of (maximal) span-core in analyzing social dynamics and detecting/correcting anomalies in the data.

The social inclusion aspects of shopping malls and their effects on our understanding of urban spaces have been a controversial argument largely discussed in the literature. Shopping malls offer an open, safe and democratic version of the public space. Many of their detractors suggest that malls target their customers in subtle ways, promoting social exclusion. In this work, we analyze whether malls offer opportunities for social mixing by analyzing the patterns of shopping mall visits in a large Latin-American city: Santiago de Chile. We use a large XDR (Data Detail Records) dataset from a telecommunication company to analyze the mobility of $387,152$ cell phones around $16$ large malls in Santiago de Chile during one month. We model the influx of people to malls in terms of a gravity model of mobility, and we are able to predict the customer profile distribution of each mall, explaining it in terms of mall location, the population distribution, and mall size. Then, we analyze the concept of social attraction, expressed as people from low and middle classes being attracted by malls that target high-income customers. We include a social attraction factor in our model and find that it is negligible in the process of choosing a mall. We observe that social mixing arises only in peripheral malls located farthest from the city center, which both low and middle class people visit. Using a co-visitation model we show that people tend to choose a restricted profile of malls according to their socio-economic status and their distance from the mall. We conclude that the potential for social mixing in malls could be capitalized by designing public policies regarding transportation and mobility., Comment: submitted to peer review

Personal electronic devices including smartphones give access to behavioural signals that can be used to learn about the characteristics and preferences of individuals. In this study, we explore the connection between demographic and psychological attributes and the digital behavioural records, for a cohort of 7,633 people, closely representative of the US population with respect to gender, age, geographical distribution, education, and income. Along with the demographic data, we collected self-reported assessments on validated psychometric questionnaires for moral traits and basic human values and combined this information with passively collected multi-modal digital data from web browsing behaviour and smartphone usage. A machine learning framework was then designed to infer both the demographic and psychological attributes from the behavioural data. In a cross-validated setting, our models predicted demographic attributes with good accuracy as measured by the weighted AUROC score (Area Under the Receiver Operating Characteristic), but were less performant for the moral traits and human values. These results call for further investigation since they are still far from unveiling individuals' psychological fabric. This connection, along with the most predictive features that we provide for each attribute, might prove useful for designing personalised services, communication strategies, and interventions, and can be used to sketch a portrait of people with a similar worldview.

Recent advances in data collection have facilitated the access to time-resolved human proximity data that can conveniently be represented as temporal networks of contacts between individuals. While this type of data is fundamental to investigate how information or diseases propagate in a population, it often suffers from incompleteness, which possibly leads to biased conclusions. A major challenge is thus to estimate the outcome of spreading processes occurring on temporal networks built from partial information. To cope with this problem, we devise an approach based on Non-negative Tensor Factorization (NTF) -- a dimensionality reduction technique from multi-linear algebra. The key idea is to learn a low-dimensional representation of the temporal network built from partial information, to adapt it to take into account temporal and structural heterogeneity properties known to be crucial for spreading processes occurring on networks, and to construct in this way a surrogate network similar to the complete original network. To test our method, we consider several human-proximity networks, on which we simulate a loss of data. Using our approach on the resulting partial networks, we build a surrogate version of the complete network for each. We then compare the outcome of a spreading process on the complete networks (non altered by a loss of data) and on the surrogate networks. We observe that the epidemic sizes obtained using the surrogate networks are in good agreement with those measured on the complete networks. Finally, we propose an extension of our framework when additional data sources are available to cope with the missing data problem.

The problem of mapping human close-range proximity networks has been tackled using a variety of technical approaches. Wearable electronic devices, in particular, have proven to be particularly successful in a variety of settings relevant for research in social science, complex networks and infectious diseases dynamics. Each device and technology used for proximity sensing (e.g., RFIDs, Bluetooth, low-power radio or infrared communication, etc.) comes with specific biases on the close-range relations it records. Hence it is important to assess which statistical features of the empirical proximity networks are robust across different measurement techniques, and which modeling frameworks generalize well across empirical data. Here we compare time-resolved proximity networks recorded in different experimental settings and show that some important statistical features are robust across all settings considered. The observed universality calls for a simplified modeling approach. We show that one such simple model is indeed able to reproduce the main statistical distributions characterizing the empirical temporal networks.

Data describing human interactions often suffer from incomplete sampling of the underlying population. As a consequence, the study of contagion processes using data-driven models can lead to a severe underestimation of the epidemic risk. Here we present a systematic method to alleviate this issue and obtain a better estimation of the risk in the context of epidemic models informed by high-resolution time-resolved contact data. We consider several such data sets collected in various contexts and perform controlled resampling experiments. We show how the statistical information contained in the resampled data can be used to build a series of surrogate versions of the unknown contacts. We simulate epidemic processes on the resulting reconstructed data sets and show that it is possible to obtain good estimates of the outcome of simulations performed using the complete data set. We discuss limitations and potential improvements of our method.

The customary perspective to reason about epidemic mitigation in temporal networks hinges on the identification of nodes with specific features or network roles. The ensuing individual-based control strategies, however, are difficult to carry out in practice and ignore important correlations between topological and temporal patterns. Here we adopt a mesoscopic perspective and present a principled framework to identify collective features at multiple scales and rank their importance for epidemic spread. We use tensor decomposition techniques to build an additive representation of a temporal network in terms of mesostructures, such as cohesive clusters and temporally-localized mixing patterns. This representation allows to determine the impact of individual mesostructures on epidemic spread and to assess the effect of targeted interventions that remove chosen structures. We illustrate this approach using high-resolution social network data on face-to-face interactions in a school and show that our method affords the design of effective mesoscale interventions.

School environments are thought to play an important role in the community spread of airborne infections (e.g., influenza) because of the high mixing rates of school children. The closure of schools has therefore been proposed as efficient mitigation strategy, with however high social and economic costs: alternative, less disruptive interventions are highly desirable. The recent availability of high-resolution contact networks in school environments provides an opportunity to design micro-interventions and compare the outcomes of alternative mitigation measures. We consider mitigation measures that involve the targeted closure of school classes or grades based on readily available information such as the number of symptomatic infectious children in a class. We focus on the case of a primary school for which we have high-resolution data on the close-range interactions of children and teachers. We simulate the spread of an influenza-like illness in this population by using an SEIR model with asymptomatics and compare the outcomes of different mitigation strategies. We find that targeted class closure affords strong mitigation effects: closing a class for a fixed period of time -equal to the sum of the average infectious and latent durations- whenever two infectious individuals are detected in that class decreases the attack rate by almost 70% and strongly decreases the probability of a severe outbreak. The closure of all classes of the same grade mitigates the spread almost as much as closing the whole school. Targeted class closure strategies based on readily available information on symptomatic subjects and on limited information on mixing patterns, such as the grade structure of the school, can be almost as effective as whole-school closure, at a much lower cost. This may inform public health policies for the management and mitigation of influenza-like outbreaks in the community.

Contacts between patients, patients and health care workers (HCWs) and among HCWs represent one of the important routes of transmission of hospital-acquired infections (HAI). A detailed description and quantification of contacts in hospitals provides key information for HAIs epidemiology and for the design and validation of control measures. We used wearable sensors to detect close-range interactions ("contacts") between individuals in the geriatric unit of a university hospital. Contact events were measured with a spatial resolution of about 1.5 meters and a temporal resolution of 20 seconds. The study included 46 HCWs and 29 patients and lasted for 4 days and 4 nights. 14037 contacts were recorded. The number and duration of contacts varied between mornings, afternoons and nights, and contact matrices describing the mixing patterns between HCW and patients were built for each time period. Contact patterns were qualitatively similar from one day to the next. 38% of the contacts occurred between pairs of HCWs and 6 HCWs accounted for 42% of all the contacts including at least one patient, suggesting a population of individuals who could potentially act as super-spreaders. Wearable sensors represent a novel tool for the measurement of contact patterns in hospitals. The collected data provides information on important aspects that impact the spreading patterns of infectious diseases, such as the strong heterogeneity of contact numbers and durations across individuals, the variability in the number of contacts during a day, and the fraction of repeated contacts across days. This variability is associated with a marked statistical stability of contact and mixing patterns across days. Our results highlight the need for such measurement efforts in order to correctly inform mathematical models of HAIs and use them to inform the design and evaluation of prevention strategies.

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.

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.

The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented levels of details and scale. Wearable sensors are opening up a new window on human mobility and proximity at the finest resolution of face-to-face proximity. As a consequence, empirical data describing social and behavioral networks are acquiring a longitudinal dimension that brings forth new challenges for analysis and modeling. Here we review recent work on the representation and analysis of temporal networks of face-to-face human proximity, based on large-scale datasets collected in the context of the SocioPatterns collaboration. We show that the raw behavioral data can be studied at various levels of coarse-graining, which turn out to be complementary to one another, with each level exposing different features of the underlying system. We briefly review a generative model of temporal contact networks that reproduces some statistical observables. Then, we shift our focus from surface statistical features to dynamical processes on empirical temporal networks. We discuss how simple dynamical processes can be used as probes to expose important features of the interaction patterns, such as burstiness and causal constraints. We show that simulating dynamical processes on empirical temporal networks can unveil differences between datasets that would otherwise look statistically similar. Moreover, we argue that, due to the temporal heterogeneity of human dynamics, in order to investigate the temporal properties of spreading processes it may be necessary to abandon the notion of wall-clock time in favour of an intrinsic notion of time for each individual node, defined in terms of its activity level. We conclude highlighting several open research questions raised by the nature of the data at hand., Comment: Chapter of the book "Temporal Networks", Springer, 2013. Series: Understanding Complex Systems. Holme, Petter; Saram\"aki, Jari (Eds.)

Spreading processes represent a very efficient tool to investigate the structural properties of networks and the relative importance of their constituents, and have been widely used to this aim in static networks. Here we consider simple disease spreading processes on empirical time-varying networks of contacts between individuals, and compare the effect of several immunization strategies on these processes. An immunization strategy is defined as the choice of a set of nodes (individuals) who cannot catch nor transmit the disease. This choice is performed according to a certain ranking of the nodes of the contact network. We consider various ranking strategies, focusing in particular on the role of the training window during which the nodes' properties are measured in the time-varying network: longer training windows correspond to a larger amount of information collected and could be expected to result in better performances of the immunization strategies. We find instead an unexpected saturation in the efficiency of strategies based on nodes' characteristics when the length of the training window is increased, showing that a limited amount of information on the contact patterns is sufficient to design efficient immunization strategies. This finding is balanced by the large variations of the contact patterns, which strongly alter the importance of nodes from one period to the next and therefore significantly limit the efficiency of any strategy based on an importance ranking of nodes. We also observe that the efficiency of strategies that include an element of randomness and are based on temporally local information do not perform as well but are largely independent on the amount of information available.

The integration of empirical data in computational frameworks to model the spread of infectious diseases poses challenges that are becoming pressing with the increasing availability of high-resolution information on human mobility and contacts. This deluge of data has the potential to revolutionize the computational efforts aimed at simulating scenarios and designing containment strategies. However, the integration of detailed data sources yields models that are less transparent and general. Hence, given a specific disease model, it is crucial to assess which representations of the raw data strike the best balance between simplicity and detail. We consider high-resolution data on the face-to-face interactions of individuals in a hospital ward, obtained by using wearable proximity sensors. We simulate the spread of a disease in this community by using an SEIR model on top of different mathematical representations of the contact patterns. We show that a contact matrix that only contains average contact durations fails to reproduce the size of the epidemic obtained with the high-resolution contact data and also to identify the most at-risk classes. We introduce a contact matrix of probability distributions that takes into account the heterogeneity of contact durations between (and within) classes of individuals, and we show that this representation yields a good approximation of the epidemic spreading properties obtained by using the high-resolution data. Our results mark a step towards the definition of synopses of high-resolution dynamic contact networks, providing a compact representation of contact patterns that can correctly inform computational models designed to discover risk groups and evaluate containment policies. We show that this novel kind of representation can preserve in simulation quantitative features of the epidemics that are crucial for their study and management.

Micro-blogging systems such as Twitter expose digital traces of social discourse with an unprecedented degree of resolution of individual behaviors. They offer an opportunity to investigate how a large-scale social system responds to exogenous or endogenous stimuli, and to disentangle the temporal, spatial and topical aspects of users' activity. Here we focus on spikes of collective attention in Twitter, and specifically on peaks in the popularity of hashtags. Users employ hashtags as a form of social annotation, to define a shared context for a specific event, topic, or meme. We analyze a large-scale record of Twitter activity and find that the evolution of hastag popularity over time defines discrete classes of hashtags. We link these dynamical classes to the events the hashtags represent and use text mining techniques to provide a semantic characterization of the hastag classes. Moreover, we track the propagation of hashtags in the Twitter social network and find that epidemic spreading plays a minor role in hastag popularity, which is mostly driven by exogenous factors., Comment: 10 pages, 5 figures, 2 tables - To Appear in WWW'12

The spread of infectious diseases crucially depends on the pattern of contacts among individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. Few empirical studies are however available that provide estimates of the number and duration of contacts among social groups. Moreover, their space and time resolution are limited, so that data is not explicit at the person-to-person level, and the dynamical aspect of the contacts is disregarded. Here, we want to assess the role of data-driven dynamic contact patterns among individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population. We consider high resolution data of face-to-face interactions between the attendees of a conference, obtained from the deployment of an infrastructure based on Radio Frequency Identification (RFID) devices that assess mutual face-to-face proximity. The spread of epidemics along these interactions is simulated through an SEIR model, using both the dynamical network of contacts defined by the collected data, and two aggregated versions of such network, in order to assess the role of the data temporal aspects. We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation which retains only the topology of the contact network fails in reproducing the size of the epidemic. These results have important implications in understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics.

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., Comment: A. Panisson et al., On the dynamics of human proximity for data diffusion in ad-hoc networks, Ad Hoc Netw. (2011)

Digital networks, mobile devices, and the possibility of mining the ever-increasing amount of digital traces that we leave behind in our daily activities are changing the way we can approach the study of human and social interactions. Large-scale datasets, however, are mostly available for collective and statistical behaviors, at coarse granularities, while high-resolution data on person-to-person interactions are generally limited to relatively small groups of individuals. Here we present a scalable experimental framework for gathering real-time data resolving face-to-face social interactions with tunable spatial and temporal granularities. We use active Radio Frequency Identification (RFID) devices that assess mutual proximity in a distributed fashion by exchanging low-power radio packets. We analyze the dynamics of person-to-person interaction networks obtained in three high-resolution experiments carried out at different orders of magnitude in community size. The data sets exhibit common statistical properties and lack of a characteristic time scale from 20 seconds to several hours. The association between the number of connections and their duration shows an interesting super-linear behavior, which indicates the possibility of defining super-connectors both in the number and intensity of connections. Taking advantage of scalability and resolution, this experimental framework allows the monitoring of social interactions, uncovering similarities in the way individuals interact in different contexts, and identifying patterns of super-connector behavior in the community. These results could impact our understanding of all phenomena driven by face-to-face interactions, such as the spreading of transmissible infectious diseases and information., Comment: see also http://www.sociopatterns.org

The present work investigates the structural and dynamical properties of aNobii\footnote{http://www.anobii.com/}, a social bookmarking system designed for readers and book lovers. Users of aNobii provide information about their library, reading interests and geographical location, and they can establish typed social links to other users. Here, we perform an in-depth analysis of the system's social network and its interplay with users' profiles. We describe the relation of geographic and interest-based factors to social linking. Furthermore, we perform a longitudinal analysis to investigate the interplay of profile similarity and link creation in the social network, with a focus on triangle closure. We report a reciprocal causal connection: profile similarity of users drives the subsequent closure in the social network and, reciprocally, closure in the social network induces subsequent profile alignment. Access to the dynamics of the social network also allows us to measure quantitative indicators of preferential linking., Comment: http://www.iisocialcom.org/conference/socialcom2010/

The availability of new data sources on human mobility is opening new avenues for investigating the interplay of social networks, human mobility and dynamical processes such as epidemic spreading. Here we analyze data on the time-resolved face-to-face proximity of individuals in large-scale real-world scenarios. We compare two settings with very different properties, a scientific conference and a long-running museum exhibition. We track the behavioral networks of face-to-face proximity, and characterize them from both a static and a dynamic point of view, exposing important differences as well as striking similarities. We use our data to investigate the dynamics of a susceptible-infected model for epidemic spreading that unfolds on the dynamical networks of human proximity. The spreading patterns are markedly different for the conference and the museum case, and they are strongly impacted by the causal structure of the network data. A deeper study of the spreading paths shows that the mere knowledge of static aggregated networks would lead to erroneous conclusions about the transmission paths on the dynamical networks.