[show abstract][hide abstract] ABSTRACT: 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.
PLoS ONE 01/2014; 9(1):e86028. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: Thanks to recent technological advances, measuring real-world interactions using mobile devices and wearable sensors has become possible, allowing researchers to gather data on human social interactions in a variety of contexts with a high spatial and temporal resolution. Empirical data describing contact networks reach thus a high level of detail that may yield bring new insights into the dynamics of infection transmission between individuals. At the same time, such data bring forth new challenges related to their statistical description and analysis and to their use in mathematical models. In particular, the integration of highly detailed empirical data in computational frameworks designed to model the spread of infectious diseases raises the issue of assessing which representations of the raw data work best to inform the models. There is an emerging need to strike a balance between simplicity and detail in order to ensure both generalizability and accuracy of predictions. Here, we review recent work on the collection and analysis of highly detailed data on temporal networks of face-to-face human proximity, carried out in the context of the SocioPatterns collaboration. We discuss the various levels of coarse-graining that can be used to represent the data in order to inform models of infectious diseases transmission. We moreover discuss several limitations of the data and future avenues for data collection and modeling efforts in the field of infectious diseases. This article is protected by copyright. All rights reserved.
Clinical Microbiology and Infection 11/2013; · 4.58 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
Journal of Theoretical Biology 07/2013; · 2.35 Impact Factor
[show abstract][hide abstract] ABSTRACT: We investigate gender homophily in the spatial proximity of children (6 to 12
years old) in a French primary school, using time-resolved data on face-to-face
proximity recorded by means of wearable sensors. For strong ties, i.e., for
pairs of children who interact more than a defined threshold, we find
statistical evidence of gender preference that increases with grade. For weak
ties, conversely, gender homophily is negatively correlated with grade for
girls, and positively correlated with grade for boys. This different evolution
with grade of weak and strong ties exposes a contrasted picture of gender
[show abstract][hide abstract] ABSTRACT: 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.
Temporal Networks, Understanding Complex Systems. ISBN 978-3-642-36460-0. Springer-Verlag Berlin Heidelberg, 2013, p. 191. 05/2013;
[show abstract][hide abstract] ABSTRACT: BACKGROUND: The integration of empirical data in computational frameworks designed to model the spread of infectious diseases poses a number of challenges that are becoming more 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, designing containment strategies, and evaluating outcomes. However, the integration of highly detailed data sources yields models that are less transparent and general in their applicability. Hence, given a specific disease model, it is crucial to assess which representations of the raw data work best to inform the model, striking a balance between simplicity and detail. METHODS: We consider high-resolution data on the face-to-face interactions of individuals in a pediatric 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 empirical contact patterns. At the most detailed level, we take into account all contacts between individuals and their exact timing and order. Then, we build a hierarchy of coarse-grained representations of the contact patterns that preserve only partially the temporal and structural information available in the data. We compare the dynamics of the SEIR model across these representations. RESULTS: We show that a contact matrix that only contains average contact durations between role classes fails to reproduce the size of the epidemic obtained using the high-resolution contact data and also fails 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, in the case study presented, this representation yields a good approximation of the epidemic spreading properties obtained by using the high-resolution data. CONCLUSIONS: Our results mark a first 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 in a typical case of a structured population that this novel kind of representation can preserve in simulation quantitative features of the epidemics that are crucial for their study and management.
[show abstract][hide abstract] ABSTRACT: Mobile devices and wearable sensors are making available records of human mobility and proximity with unprecedented levels of detail. Here we focus on close-range human proximity networks measured by means of wireless wearable sensors in a variety of real-world environments. We show that simple dynamical processes computed over the time-varying proximity networks can uncover important features of the interaction patterns that go beyond standard statistical indicators of heterogeneity and burstiness, and can tell apart datasets that would otherwise look statistically similar. We show that, due to the intrinsic temporal heterogeneity of human dynamics, the characterization of spreading processes over time-varying networks of human contact may benefit from abandoning the notion of wall-clock time in favor of a node-specific notion of time based on the contact activity of individual nodes.
PerMoby 2013: International workshop on the impact of human mobility in pervasive systems and applications; 03/2013
[show abstract][hide abstract] ABSTRACT: The ever increasing adoption of mobile technologies and ubiquitous services allows to sense human behavior at unprecedented level of details and scale. Wearable sensors, in particular, open up a new window on human mobility and proximity in a variety of indoor environments. Here we review stylized facts on the structural and dynamical properties of empirical networks of human face-to-face proximity, measured in three different real-world contexts: an academic conference, a hospital ward, and a museum exhibition. First, we discuss the structure of the aggregated contact networks, that project out the detailed ordering of contact events while preserving temporal heterogeneities in their weights. We show that the structural properties of aggregated networks highlight important differences and unexpected similarities across contexts, and discuss the additional complexity that arises from attributes that are typically associated with nodes in real-world interaction networks, such as role classes in hospitals. We then consider the empirical data at the finest level of detail, i.e., we consider time-dependent networks of face-to-face proximity between individuals. To gain insights on the effects that causal constraints have on spreading processes, we simulate the dynamics of a simple susceptible-infected model over the empirical time-resolved contact data. We show that the spreading pathways for the epidemic process are strongly affected by the temporal structure of the network data, and that the mere knowledge of static aggregated networks leads to erroneous conclusions about the transmission paths on the corresponding dynamical networks.
The European Physical Journal Special Topics 01/2013; 222(6):1295-1309. · 1.80 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: 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. 14,037 contacts were recorded overall, 94.1% of which during daytime. 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 can provide 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 however 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.
PLoS ONE 01/2013; 8(9):e73970. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: 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.
[show abstract][hide abstract] ABSTRACT: Mobile, social, real-time: the ongoing revolution in the way people communicate has given rise to a new kind of epidemiology. Digital data sources, when harnessed appropriately, can provide local and timely information about disease and health dynamics in populations around the world. The rapid, unprecedented increase in the availability of relevant data from various digital sources creates considerable technical and computational challenges.
[show abstract][hide abstract] ABSTRACT: Social media have attracted considerable attention because their open-ended nature allows users to create lightweight semantic scaffolding to organize and share content. To date, the interplay of the social and topical components of social media has been only partially explored. Here, we study the presence of homophily in three systems that combine tagging social media with online social networks. We find a substantial level of topical similarity among users who are close to each other in the social network. We introduce a null model that preserves user activity while removing local correlations, allowing us to disentangle the actual local similarity between users from statistical effects due to the assortative mixing of user activity and centrality in the social network. This analysis suggests that users with similar interests are more likely to be friends, and therefore topical similarity measures among users based solely on their annotation metadata should be predictive of social links. We test this hypothesis on several datasets, confirming that social networks constructed from topical similarity capture actual friendship accurately. When combined with topological features, topical similarity achieves a link prediction accuracy of about 92%.
[show abstract][hide abstract] ABSTRACT: The SocioPatterns sensing platform uses wearable electronic badges to sense close-range proximity among individuals. It was used in an experiential exhibit that simulated a virtual epidemic among the visitors of the INFECTIOUS: STAY AWAY exhibition in the Science Gallery in Dublin, Ireland. The collected data was used to generate a high-resolution visualization that illustrates the variation in contact activity over the course of the exhibition.
[show abstract][hide abstract] ABSTRACT: 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
[show abstract][hide abstract] ABSTRACT: In this paper we present an experimental framework to gather data on face-to-face social interactions between individuals, with a high spatial and temporal resolution. We use active Radio Frequency Identification (RFID) devices that assess contacts with one another by exchanging low-power radio packets. When individuals wear the beacons as a badge, a persistent radio contact between the RFID devices can be used as a proxy for a social interaction between individuals. We present the results of a pilot study recently performed during a conference, and a subsequent preliminary data analysis, that provides an assessment of our method and highlights its versatility and applicability in many areas concerned with human dynamics.
[show abstract][hide abstract] ABSTRACT: Little quantitative information is available on the mixing patterns of children in school environments. Describing and understanding contacts between children at school would help quantify the transmission opportunities of respiratory infections and identify situations within schools where the risk of transmission is higher. We report on measurements carried out in a French school (6-12 years children), where we collected data on the time-resolved face-to-face proximity of children and teachers using a proximity-sensing infrastructure based on radio frequency identification devices.
Data on face-to-face interactions were collected on Thursday, October 1(st) and Friday, October 2(nd) 2009. We recorded 77,602 contact events between 242 individuals (232 children and 10 teachers). In this setting, each child has on average 323 contacts per day with 47 other children, leading to an average daily interaction time of 176 minutes. Most contacts are brief, but long contacts are also observed. Contacts occur mostly within each class, and each child spends on average three times more time in contact with classmates than with children of other classes. We describe the temporal evolution of the contact network and the trajectories followed by the children in the school, which constrain the contact patterns. We determine an exposure matrix aimed at informing mathematical models. This matrix exhibits a class and age structure which is very different from the homogeneous mixing hypothesis.
We report on important properties of the contact patterns between school children that are relevant for modeling the propagation of diseases and for evaluating control measures. We discuss public health implications related to the management of schools in case of epidemics and pandemics. Our results can help define a prioritization of control measures based on preventive measures, case isolation, classes and school closures, that could reduce the disruption to education during epidemics.
PLoS ONE 08/2011; 6(8):e23176. · 3.73 Impact Factor
[show abstract][hide abstract] ABSTRACT: The spread of infectious diseases crucially depends on the pattern of contacts between individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. However, there are few empirical studies available that provide estimates of the number and duration of contacts between social groups. Moreover, their space and time resolutions are limited, so that data are not explicit at the person-to-person level, and the dynamic nature of the contacts is disregarded. In this study, we aimed to assess the role of data-driven dynamic contact patterns between individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population.
We considered high-resolution data about face-to-face interactions between the attendees at a conference, obtained from the deployment of an infrastructure based on radiofrequency identification (RFID) devices that assessed mutual face-to-face proximity. The spread of epidemics along these interactions was simulated using an SEIR (Susceptible, Exposed, Infectious, Recovered) model, using both the dynamic network of contacts defined by the collected data, and two aggregated versions of such networks, 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 that retains only the topology of the contact network fails to reproduce the size of the epidemic.
These results have important implications for understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics. Please see related article BMC Medicine, 2011, 9:88.