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The accurate modeling of individual movement in cities has significant implications for policy decisions across various sectors. Existing research emphasizes the universality of human mobility, positing that simple models can capture population-level movements. However, population-level accuracy does not guarantee consistent performance across all individuals. By overlooking individual differences, universality laws may accurately describe certain groups while less precisely representing others, resulting in aggregate accuracy from a balance of discrepancies. Using large-scale mobility data, we assess individual-level accuracy of a universal model, the Exploration and Preferential Return (EPR), by examining deviations from expected behavior in two scaling laws - one related to exploration and the other to return patterns. Our findings reveal that, while the model can describe population-wide movement patterns, it displays widespread deviations linked to individuals' behavioral traits, socioeconomic status, and lifestyles, contradicting model assumptions like non-bursty exploration and preferential return. Specifically, individuals poorly represented by the EPR model tend to visit routine locations in sequences, exploring rarely but in a bursty manner when they do. Among socioeconomic factors, income most strongly correlates with significant deviations. Consequently, spatial inhomogeneity emerges in model accuracy, with lower performance concentrated in urbanized, densely populated areas, underscoring policy implications. Our results show that emphasizing population-wide models can propagate socioeconomic inequalities by poorly representing vulnerable population sectors.

Behavioral adoptions are influenced by peers in different ways. While some individuals may change after a single incoming influence, others need multiple cumulated attempts. These two mechanism, known as the simple and the complex contagions, often occur together in social phenomena alongside personal factors determining individual adoptions. Here we aim to identify, which of these contagion mechanism dominate a spreading process propagated by time-varying interactions. We consider three types of spreading scenarios: ones pre-dominated by simple or complex contagion, and mixed dynamics where the dominant mechanism changes during the unfolding of the spreading process. We propose different methods to analytically identify the transitions between these three scenarios and compare them with numerical simulations. This work offers new insights into social contagion dynamics on temporal networks, without assuming prior knowledge about individual's contagion mechanism driving their adoption decisions., Comment: 14 pages, 7 figures

Climate change is altering the frequency and intensity of wildfires, leading to increased evacuation events that disrupt human mobility and socioeconomic structures. These disruptions affect access to resources, employment, and housing, amplifying existing vulnerabilities within communities. Understanding the interplay between climate change, wildfires, evacuation patterns, and socioeconomic factors is crucial for developing effective mitigation and adaptation strategies. To contribute to this challenge, we use high-definition mobile phone records to analyse evacuation patterns during the wildfires in Valpara\'iso, Chile, that took place between February 2-3, 2024. This data allows us to track the movements of individuals in the disaster area, providing insight into how people respond to large-scale evacuations in the context of severe wildfires. We apply a causal inference approach that combines regression discontinuity and difference-in-differences methodologies to observe evacuation behaviours during wildfires, with a focus on socioeconomic stratification. This approach allows us to isolate the impact of the wildfires on different socioeconomic groups by comparing the evacuation patterns of affected populations before and after the event, while accounting for underlying trends and discontinuities at the threshold of the disaster. We find that many people spent nights away from home, with those in the lowest socioeconomic segment stayed away the longest. In general, people reduced their travel distance during the evacuation, and the lowest socioeconomic group moved the least. Initially, movements became more random, as people sought refuge in a rush, but eventually gravitated towards areas with similar socioeconomic status. Our results show that socioeconomic differences play a role in evacuation dynamics, providing useful insights for response planning., Comment: 31 pages, 15 figures, 11 tables

We study stationary epidemic processes in scale-free networks with local awareness behavior adopted by only susceptible, only infected, or all nodes. We find that while the epidemic size in the susceptible-aware and the all-aware scenarios scales linearly with the network size, the scaling becomes sublinear in the infected-aware scenario, suggesting that fewer aware nodes may reduce the epidemic size more effectively. We explain this paradox via numerical and theoretical analysis, and highlight the role of influential nodes and their disassortativity to raise awareness in epidemic scenarios.

Poverty map inference has become a critical focus of research, utilizing both traditional and modern techniques, ranging from regression models to convolutional neural networks applied to tabular data, satellite imagery, and networks. While much attention has been given to validating models during the training phase, the final predictions have received less scrutiny. In this study, we analyze the International Wealth Index (IWI) predicted by Lee and Braithwaite (2022) and Esp\'in-Noboa et al. (2023), alongside the Relative Wealth Index (RWI) inferred by Chi et al. (2022), across six Sub-Saharan African countries. Our analysis reveals trends and discrepancies in wealth predictions between these models. In particular, significant and unexpected discrepancies between the predictions of Lee and Braithwaite and Esp\'in-Noboa et al., even after accounting for differences in training data. In contrast, the shape of the wealth distributions predicted by Esp\'in-Noboa et al. and Chi et al. are more closely aligned, suggesting similar levels of skewness. These findings raise concerns about the validity of certain models and emphasize the importance of rigorous audits for wealth prediction algorithms used in policy-making. Continuous validation and refinement are essential to ensure the reliability of these models, particularly when they inform poverty alleviation strategies., Comment: 14 pages (main + references) + 8 pages (appendix). Accepted at the 9th Workshop on Data Science for Social Good, SoGood 2024, held in conjunction with ECML PKDD 2024, at Vilnius, Lithuania

The adoption of individual behavioural patterns is largely determined by stimuli arriving from peers via social interactions or from external sources. Based on these influences, individuals are commonly assumed to follow simple or complex adoption rules, inducing social contagion processes. In reality, multiple adoption rules may coexist even within the same social contagion process, introducing additional complexity into the spreading phenomena. Our goal is to understand whether coexisting adoption mechanisms can be distinguished from a microscopic view, at the egocentric network level, without requiring global information about the underlying network, or the unfolding spreading process. We formulate this question as a classification problem, and study it through a Bayesian likelihood approach and with random forest classifiers in various synthetic and data-driven experiments. This study offers a novel perspective on the observations of propagation processes at the egocentric level and a better understanding of landmark contagion mechanisms from a local view., Comment: 25 pages, 11 figures

Behavior-disease models suggest that if individuals are aware and take preventive actions when the prevalence of the disease increases among their close contacts, then the pandemic can be contained in a cost-effective way. To measure the true impact of local awareness behavior on epidemic spreading, we propose an efficient approach to identify superspreading events and assign corresponding Event Containment Scores (ECSs) in clinical genetic sequence data. We validate ECS as a measure of local awareness in simulation experiments, and we find that ECS was correlated positively with policy stringency during the COVID-19 pandemic. Finally, we observe a temporary drop in ECS during the Omicron wave in most European countries, matching a survey experiment we carried out at the same time. Our findings bring important insight into the field of awareness modeling through the analysis of large-scale genetic sequence data, one of the most promising data sources in epidemics research.

The metaverse promises a shift in the way humans interact with each other, and with their digital and physical environments. The lack of geographical boundaries and travel costs in the metaverse prompts us to ask if the fundamental laws that govern human mobility in the physical world apply. We collected data on avatar movements, along with their network mobility extracted from NFT purchases. We find that despite the absence of commuting costs, an individuals inclination to explore new locations diminishes over time, limiting movement to a small fraction of the metaverse. We also find a lack of correlation between land prices and visitation, a deviation from the patterns characterizing the physical world. Finally, we identify the scaling laws that characterize meta mobility and show that we need to add preferential selection to the existing models to explain quantitative patterns of metaverse mobility. Our ability to predict the characteristics of the emerging meta mobility network implies that the laws governing human mobility are rooted in fundamental patterns of human dynamics, rather than the nature of space and cost of movement., Comment: 4 figures

Fully decentralised federated learning enables collaborative training of individual machine learning models on a distributed network of communicating devices while keeping the training data localised on each node. This approach avoids central coordination, enhances data privacy and eliminates the risk of a single point of failure. Our research highlights that the effectiveness of decentralised federated learning is significantly influenced by the network topology of connected devices and the learning models' initial conditions. We propose a strategy for uncoordinated initialisation of the artificial neural networks based on the distribution of eigenvector centralities of the underlying communication network, leading to a radically improved training efficiency. Additionally, our study explores the scaling behaviour and the choice of environmental parameters under our proposed initialisation strategy. This work paves the way for more efficient and scalable artificial neural network training in a distributed and uncoordinated environment, offering a deeper understanding of the intertwining roles of network structure and learning dynamics.

Socioeconomic segregation patterns in networks usually evolve gradually, yet they can change abruptly in response to external shocks. The recent COVID-19 pandemic and the subsequent government policies induced several interruptions in societies, potentially disadvantaging the socioeconomically most vulnerable groups. Using large-scale digital behavioral observations as a natural laboratory, here we analyze how lockdown interventions lead to the reorganization of socioeconomic segregation patterns simultaneously in communication and mobility networks in Sierra Leone. We find that while segregation in mobility clearly increased during lockdown, the social communication network reorganized into a less segregated configuration as compared to reference periods. Moreover, due to differences in adaption capacities, the effects of lockdown policies varied across socioeconomic groups, leading to different or even opposite segregation patterns between the lower and higher socioeconomic classes. Such secondary effects of interventions need to be considered for better and more equitable policies.

Federated Learning (FL) is a well-known framework for successfully performing a learning task in an edge computing scenario where the devices involved have limited resources and incomplete data representation. The basic assumption of FL is that the devices communicate directly or indirectly with a parameter server that centrally coordinates the whole process, overcoming several challenges associated with it. However, in highly pervasive edge scenarios, the presence of a central controller that oversees the process cannot always be guaranteed, and the interactions (i.e., the connectivity graph) between devices might not be predetermined, resulting in a complex network structure. Moreover, the heterogeneity of data and devices further complicates the learning process. This poses new challenges from a learning standpoint that we address by proposing a communication-efficient Decentralised Federated Learning (DFL) algorithm able to cope with them. Our solution allows devices communicating only with their direct neighbours to train an accurate model, overcoming the heterogeneity induced by data and different training histories. Our results show that the resulting local models generalise better than those trained with competing approaches, and do so in a more communication-efficient way., Comment: Supported by the H2020 HumaneAI Net (#952026), H2020 INFRAIA-01-2018-2019 SoBigData++ (#871042), and by the CHIST-ERA-19-XAI010 SAI projects, FWF (grant No. I 5205). Also funded by PNRR MUR Partenariato Esteso PE00000013 FAIR, PNRR MUR Partenariato Esteso PE00000001 - "RESTART"

External shocks embody an unexpected and disruptive impact on the regular life of people. This was the case during the COVID-19 outbreak that rapidly led to changes in the typical mobility patterns in urban areas. In response, people reorganised their daily errands throughout space. However, these changes might not have been the same across socioeconomic classes leading to possibile additional detrimental effects on inequality due to the pandemic. In this paper we study the reorganisation of mobility segregation networks due to external shocks and show that the diversity of visited places in terms of locations and socioeconomic status is affected by the enforcement of mobility restriction during pandemic. We use the case of COVID-19 as a natural experiment in several cities to observe not only the effect of external shocks but also its mid-term consequences and residual effects. We build on anonymised and privacy-preserved mobility data in four cities: Bogota, Jakarta, London, and New York. We couple mobility data with socioeconomic information to capture inequalities in mobility among different socioeconomic groups and see how it changes dynamically before, during, and after different lockdown periods. We find that the first lockdowns induced considerable increases in mobility segregation in each city, while loosening mobility restrictions did not necessarily diminished isolation between different socioeconomic groups, as mobility mixing has not recovered fully to its pre-pandemic level even weeks after the interruption of interventions. Our results suggest that a one fits-all policy does not equally affect the way people adjust their mobility, which calls for socioeconomically informed intervention policies in the future., Comment: 27 pages, 14 figures

The socioeconomic background of people and how they use standard forms of language are not independent, as demonstrated in various sociolinguistic studies. However, the extent to which these correlations may be influenced by the mixing of people from different socioeconomic classes remains relatively unexplored from a quantitative perspective. In this work we leverage geotagged tweets and transferable computational methods to map deviations from standard English on a large scale, in seven thousand administrative areas of England and Wales. We combine these data with high-resolution income maps to assign a proxy socioeconomic indicator to home-located users. Strikingly, across eight metropolitan areas we find a consistent pattern suggesting that the more different socioeconomic classes mix, the less interdependent the frequency of their departures from standard grammar and their income become. Further, we propose an agent-based model of linguistic variety adoption that sheds light on the mechanisms that produce the observations seen in the data.

Pairwise temporal interactions between entities can be represented as temporal networks, which code the propagation of processes such as epidemic spreading or information cascades, evolving on top of them. The largest outcome of these processes is directly linked to the structure of the underlying network. Indeed, a node of a network at given time cannot affect more nodes in the future than it can reach via time-respecting paths. This set of nodes reachable from a source defines an out-component, which identification is costly. In this paper, we propose an efficient matrix algorithm to tackle this issue and show that it outperforms other state-of-the-art methods. Secondly, we propose a hashing framework to coarsen large temporal networks into smaller proxies on which out-components are easier to estimate, and then recombined to obtain the initial components. Our graph hashing solution has implications in privacy respecting representation of temporal networks., Comment: 17 pages, 8 figures

Individuals socio-demographic and economic characteristics crucially shape the spread of an epidemic by largely determining the exposure level to the virus and the severity of the disease for those who got infected. While the complex interplay between individual characteristics and epidemic dynamics is widely recognized, traditional mathematical models often overlook these factors. In this study, we examine two important aspects of human behavior relevant to epidemics: contact patterns and vaccination uptake. Using data collected during the Covid-19 pandemic in Hungary, we first identify the dimensions along which individuals exhibit the greatest variation in their contact patterns and vaccination attitudes. We find that generally privileged groups of the population have higher number of contact and a higher vaccination uptake with respect to disadvantaged groups. Subsequently, we propose a data-driven epidemiological model that incorporates these behavioral differences. Finally, we apply our model to analyze the fourth wave of Covid-19 in Hungary, providing valuable insights into real-world scenarios. By bridging the gap between individual characteristics and epidemic spread, our research contributes to a more comprehensive understanding of disease dynamics and informs effective public health strategies., Comment: 33 pages, 22 figures

Temporal networks are commonly used to represent dynamical complex systems like social networks, simultaneous firing of neurons, human mobility or public transportation. Their dynamics may evolve on multiple time scales characterising for instance periodic activity patterns or structural changes. The detection of these time scales can be challenging from the direct observation of simple dynamical network properties like the activity of nodes or the density of links. Here we propose two new methods, which rely on already established static representations of temporal networks, namely supra-adjacency matrices and temporal event graphs. We define dissimilarity metrics extracted from these representations and compute their Fourier Transform to effectively identify dominant periodic time scales characterising the original temporal network. We demonstrate our methods using synthetic and real-world data sets describing various kinds of temporal networks. We find that while in all cases the two methods outperform the reference measures, the supra-adjacency based method identifies more easily periodic changes in network density, while the temporal event graph based method is better suited to detect periodic changes in the group structure of the network. Our methodology may provide insights into different phenomena occurring at multiple time-scales in systems represented by temporal networks., Comment: 19 pages, 11 figures

Novel digital data sources and tools like machine learning (ML) and artificial intelligence (AI) have the potential to revolutionize data about development and can contribute to monitoring and mitigating humanitarian problems. The potential of applying novel technologies to solving some of humanity's most pressing issues has garnered interest outside the traditional disciplines studying and working on international development. Today, scientific communities in fields like Computational Social Science, Network Science, Complex Systems, Human Computer Interaction, Machine Learning, and the broader AI field are increasingly starting to pay attention to these pressing issues. However, are sophisticated data driven tools ready to be used for solving real-world problems with imperfect data and of staggering complexity? We outline the current state-of-the-art and identify barriers, which need to be surmounted in order for data-driven technologies to become useful in humanitarian and development contexts. We argue that, without organized and purposeful efforts, these new technologies risk at best falling short of promised goals, at worst they can increase inequality, amplify discrimination, and infringe upon human rights., Comment: 15 pages, 2 figures

Contact matrices have become a key ingredient of modern epidemic models. They account for the stratification of contacts for the age of individuals and, in some cases, the context of their interactions. However, age and context are not the only factors shaping contact structures and affecting the spreading of infectious diseases. Socio-economic status (SES) variables such as wealth, ethnicity, and education play a major role as well. Here, we introduce generalized contact matrices capable of stratifying contacts across any number of dimensions including any SES variable. We derive an analytical expression for the basic reproductive number of an infectious disease unfolding on a population characterized by such generalized contact matrices. Our results, on both synthetic and real data, show that disregarding higher levels of stratification might lead to the under-estimation of the reproductive number and to a mis-estimation of the global epidemic dynamics. Furthermore, including generalized contact matrices allows for more expressive epidemic models able to capture heterogeneities in behaviours such as different levels of adoption of non-pharmaceutical interventions across different groups. Overall, our work contributes to the literature attempting to bring socio-economic, as well as other dimensions, to the forefront of epidemic modeling. Tackling this issue is crucial for developing more precise descriptions of epidemics, and thus to design better strategies to contain them.

Representing social systems as networks, starting from the interactions between individuals, sheds light on the mechanisms governing their dynamics. However, networks encode only pairwise interactions, while most social interactions occur among groups of individuals, requiring higher-order network representations. Despite the recent interest in higher-order networks, little is known about the mechanisms that govern the formation and evolution of groups, and how people move between groups. Here, we leverage empirical data on social interactions among children and university students to study their temporal dynamics at both individual and group levels, characterising how individuals navigate groups and how groups form and disaggregate. We find robust patterns across contexts and propose a dynamical model that closely reproduces empirical observations. These results represent a further step in understanding social systems, and open up research directions to study the impact of group dynamics on dynamical processes that evolve on top of them., Comment: 16 pages, 5 figures, Supplementary Material (15 pages, 25 figures)

Poverty maps are essential tools for governments and NGOs to track socioeconomic changes and adequately allocate infrastructure and services in places in need. Sensor and online crowd-sourced data combined with machine learning methods have provided a recent breakthrough in poverty map inference. However, these methods do not capture local wealth fluctuations, and are not optimized to produce accountable results that guarantee accurate predictions to all sub-populations. Here, we propose a pipeline of machine learning models to infer the mean and standard deviation of wealth across multiple geographically clustered populated places, and illustrate their performance in Sierra Leone and Uganda. These models leverage seven independent and freely available feature sources based on satellite images, and metadata collected via online crowd-sourcing and social media. Our models show that combined metadata features are the best predictors of wealth in rural areas, outperforming image-based models, which are the best for predicting the highest wealth quintiles. Our results recover the local mean and variation of wealth, and correctly capture the positive yet non-monotonous correlation between them. We further demonstrate the capabilities and limitations of model transfer across countries and the effects of data recency and other biases. Our methodology provides open tools to build towards more transparent and interpretable models to help governments and NGOs to make informed decisions based on data availability, urbanization level, and poverty thresholds., Comment: 12 pages. In Proceedings of the ACM Web Conference 2023 (WWW'23)

Near-real time estimations of the effective reproduction number are among the most important tools to track the progression of a pandemic and to inform policy makers and the general public. However, these estimations rely on reported case numbers, commonly recorded with significant biases. The epidemic outcome is strongly influenced by the dynamics of social contacts, which are neglected in conventional surveillance systems as their real-time observation is challenging. Here, we propose a concept using online and offline behavioral data, recording age-stratified contact matrices at a daily rate. Modeling the epidemic using the reconstructed matrices we dynamically estimate the effective reproduction number during the two first waves of the COVID-19 pandemic in Hungary. Our results demonstrate how behavioral data can be used to build alternative monitoring systems complementing the established public health surveillance. They can identify and provide better signals during periods when official estimates appear unreliable due to observational biases.

Many countries have secured larger quantities of COVID-19 vaccines than their populace is willing to take. This abundance and variety of vaccines created a historical moment to understand vaccine hesitancy better. Never before were more types of vaccines available for an illness and the intensity of vaccine-related public discourse is unprecedented. Yet, the heterogeneity of hesitancy by vaccine types has been neglected so far, even though factual or believed vaccine characteristics and patient attributes are known to influence acceptance. We address this problem by analysing acceptance and assessment of five vaccine types using information collected with a nationally representative survey at the end of the third wave of the COVID-19 pandemic in Hungary, where a unique portfolio of vaccines were available to the public in large quantities. Our special case enables us to quantify revealed preferences across vaccine types since one could evaluate a vaccine unacceptable and even could reject an assigned vaccine to wait for another type. We find that the source of information that respondents trust characterizes their attitudes towards vaccine types differently and leads to divergent vaccine hesitancy. Believers of conspiracy theories were significantly more likely to evaluate the mRNA vaccines (Pfizer and Moderna) unacceptable while those who follow the advice of politicians evaluate vector-based (AstraZeneca and Sputnik) or whole-virus vaccines (Sinopharm) acceptable with higher likelihood. We illustrate that the rejection of non-desired and re-selection of preferred vaccines fragments the population by the mRNA versus other type of vaccines while it generally improves the assessment of the received vaccine. These results highlight that greater variance of available vaccine types and individual free choice are desirable conditions that can widen the acceptance of vaccines in societies., Comment: 29 pages, 9 figures

The event graph representation of temporal networks suggests that the connectivity of temporal structures can be mapped to a directed percolation problem. However, similar to percolation theory on static networks, this mapping is valid under the approximation that the structure and interaction dynamics of the temporal network are determined by its local properties, and otherwise, it is maximally random. We challenge these conditions and demonstrate the robustness of this mapping in case of more complicated systems. We systematically analyze random and regular network topologies and heterogeneous link-activation processes driven by bursty renewal or self-exciting processes using numerical simulation and finite-size scaling methods. We find that the critical percolation exponents characterizing the temporal network are not sensitive to many structural and dynamical network heterogeneities, while they recover known scaling exponents characterizing directed percolation on low dimensional lattices. While it is not possible to demonstrate the validity of this mapping for all temporal network models, our results establish the first batch of evidence supporting the robustness of the scaling relationships in the limited-time reachability of temporal networks., Comment: Implementation available at https://doi.org/10.5281/zenodo.5570746

Urban areas serve as melting pots of people with diverse socioeconomic backgrounds, who may not only be segregated but have characteristic mobility patterns in the city. While mobility is driven by individual needs and preferences, the specific choice of venues to visit is usually constrained by the socioeconomic status of people. The complex interplay between people and places they visit, given their personal attributes and homophily leaning, is a key mechanism behind the emergence of socioeconomic stratification patterns ultimately leading to urban segregation at large. Here we investigate mixing patterns of mobility in the twenty largest cities of the United States by coupling individual check-in data from the social location platform Foursquare with census information from the American Community Survey. We find strong signs of stratification indicating that people mostly visit places in their own socioeconomic class, occasionally visiting locations from higher classes. The intensity of this `upwards bias' increases with socioeconomic status and correlates with standard measures of racial residential segregation. Our results indicate an even stronger socioeconomic segregation in individual mobility than one would expect from system-level distributions, shedding further light on uneven mobility mixing patterns in cities., Comment: 27 pages, 21 figures

Connectivity and reachability on temporal networks, which can describe the spreading of a disease, decimation of information or the accessibility of a public transport system over time, have been among the main contemporary areas of study in complex systems for the last decade. However, while isotropic percolation theory successfully describes connectivity in static networks, a similar description has not been yet developed for temporal networks. Here address this problem and formalize a mapping of the concept of temporal network reachability to percolation theory. We show that the limited-waiting-time reachability, a generic notion of constrained connectivity in temporal networks, displays directed percolation phase transition in connectivity. Consequently, the critical percolation properties of spreading processes on temporal networks can be estimated by a set of known exponents characterising the directed percolation universality class. This result is robust across a diverse set of temporal network models with different temporal and topological heterogeneities, while by using our methodology we uncover similar reachability phase transitions in real temporal networks too. These findings open up an avenue to apply theory, concepts and methodology from the well-developed directed percolation literature to temporal networks., Comment: Implementation available at https://doi.org/10.5281/zenodo.5570746

It is a fundamental question in disease modelling how the initial seeding of an epidemic, spreading over a network, determines its final outcome. Research in this topic has primarily concentrated on finding the seed configuration which infects the most individuals. Although these optimal configurations give insight into how the initial state affects the outcome of an epidemic, they are unlikely to occur in real life. In this paper we identify two important seeding scenarios, both motivated by historical data, that reveal a new complex phenomenon. In one scenario, the seeds are concentrated on the central nodes of a network, while in the second, they are spread uniformly in the population. Comparing the final size of the epidemic started from these two initial conditions through data-driven and synthetic simulations on real and modelled geometric metapopulation networks, we find evidence for a switchover phenomenon: When the basic reproduction number $R_0$ is close to its critical value, more individuals become infected in the first seeding scenario, but for larger values of $R_0$, the second scenario is more dangerous. We find that the switchover phenomenon is amplified by the geometric nature of the underlying network, and confirm our results via mathematically rigorous proofs, by mapping the network epidemic processes to bond percolation. Our results expand on the previous finding that in case of a single seed, the first scenario is always more dangerous, and further our understanding why the sizes of consecutive waves can differ even if their epidemic characters are similar., Comment: 29 pages, 6 figures

Ending poverty in all its forms everywhere is the number one Sustainable Development Goal of the UN 2030 Agenda. To monitor the progress towards such an ambitious target, reliable, up-to-date and fine-grained measurements of socioeconomic indicators are necessary. When it comes to socioeconomic development, novel digital traces can provide a complementary data source to overcome the limits of traditional data collection methods, which are often not regularly updated and lack adequate spatial resolution. In this study, we collect publicly available and anonymous advertising audience estimates from Facebook to predict socioeconomic conditions of urban residents, at a fine spatial granularity, in four large urban areas: Atlanta (USA), Bogot\'a (Colombia), Santiago (Chile), and Casablanca (Morocco). We find that behavioral attributes inferred from the Facebook marketing platform can accurately map the socioeconomic status of residential areas within cities, and that predictive performance is comparable in both high and low-resource settings. We also show that training a model on attributes of adult Facebook users, aged more than 25, leads to a more accurate mapping of socioeconomic conditions in all cities. Our work provides additional evidence of the value of social advertising media data to measure human development.

Millions commute to work every day in cities and interact with colleagues, customers, providers, friends, and strangers. Commuting facilitates the mixing of people from distant and diverse neighborhoods, but whether this has an imprint on social inclusion or instead, connections remain assortative is less explored. In this paper, we aim to better understand income sorting in social networks inside cities and investigate how commuting distance conditions the online social ties of Twitter users in the 50 largest metropolitan areas of the United States. Home and work locations are identified from geolocated tweets that enable us to infer the socio-economic status of individuals. Our results show that an above-median commuting distance in cities is associated with more diverse individual networks in terms of connected peers and their income. The degree that distant commutes link neighborhoods of different socio-economic backgrounds greatly varies by city size and structure. However, we find that above-median commutes are associated with a nearly uniform, moderate reduction of social tie assortativity across the top 50 US cities suggesting a universal role of commuting in integrating disparate social networks in cities. Our results inform policy that facilitating access across distant neighborhoods can advance the social inclusion of low-income groups.

The unprecedented behavioural responses of societies have been evidently shaping the COVID-19 pandemic, yet it is a significant challenge to accurately monitor the continuously changing social mixing patterns in real-time. Contact matrices, usually stratified by age, summarise interaction motifs efficiently, but their collection relies on conventional representative survey techniques, which are expensive and slow to obtain. Here we report a data collection effort involving over $2.3\%$ of the Hungarian population to simultaneously record contact matrices through a longitudinal online and sequence of representative phone surveys. To correct non-representative biases characterising the online data, by using census data and the representative samples we develop a reconstruction method to provide a scalable, cheap, and flexible way to dynamically obtain closer-to-representative contact matrices. Our results demonstrate the potential of combined online-offline data collections to understand the changing behavioural responses determining the future evolution of the outbreak, and inform epidemic models with crucial data., Comment: 17 pages, 5 figures

Human social interactions in local settings can be experimentally detected by recording the physical proximity and orientation of people. Such interactions, approximating face-to-face communications, can be effectively represented as time varying social networks with links being unceasingly created and destroyed over time. Traditional analyses of temporal networks have addressed mostly pairwise interactions, where links describe dyadic connections among individuals. However, many network dynamics are hardly ascribable to pairwise settings but often comprise larger groups, which are better described by higher-order interactions. Here we investigate the higher-order organizations of temporal social networks by analyzing three publicly available datasets collected in different social settings. We find that higher-order interactions are ubiquitous and, similarly to their pairwise counterparts, characterized by heterogeneous dynamics, with bursty trains of rapidly recurring higher-order events separated by long periods of inactivity. We investigate the evolution and formation of groups by looking at the transition rates between different higher-order structures. We find that in more spontaneous social settings, group are characterized by slower formation and disaggregation, while in work settings these phenomena are more abrupt, possibly reflecting pre-organized social dynamics. Finally, we observe temporal reinforcement suggesting that the longer a group stays together the higher the probability that the same interaction pattern persist in the future. Our findings suggest the importance of considering the higher-order structure of social interactions when investigating human temporal dynamics.

Burstiness, the tendency of interaction events to be heterogeneously distributed in time, is critical to information diffusion in physical and social systems. However, an analytical framework capturing the effect of burstiness on generic dynamics is lacking. We develop a master equation formalism to study cascades on temporal networks with burstiness modelled by renewal processes. Supported by numerical and data-driven simulations, we describe the interplay between heterogeneous temporal interactions and models of threshold-driven and epidemic spreading. We find that increasing interevent time variance can both accelerate and decelerate spreading for threshold models, but can only decelerate epidemic spreading. When accounting for the skewness of different interevent time distributions, spreading times collapse onto a universal curve. Our framework uncovers a deep yet subtle connection between generic diffusion mechanisms and underlying temporal network structures that impacts on a broad class of networked phenomena, from spin interactions to epidemic contagion and language dynamics., Comment: 27 pages, 12 figures

Urbanisation is a great challenge for modern societies, promising better access to economic opportunities while widening socioeconomic inequalities. Accurately tracking how this process unfolds has been challenging for traditional data collection methods, while remote sensing information offers an alternative to gather a more complete view on these societal changes. By feeding a neural network with satellite images one may recover the socioeconomic information associated to that area, however these models lack to explain how visual features contained in a sample, trigger a given prediction. Here we close this gap by predicting socioeconomic status across France from aerial images and interpreting class activation mappings in terms of urban topology. We show that the model disregards the spatial correlations existing between urban class and socioeconomic status to derive its predictions. These results pave the way to build interpretable models, which may help to better track and understand urbanisation and its consequences., Comment: 19 pages, 17 figures

Network science has become a powerful tool to describe the structure and dynamics of real-world complex physical, biological, social, and technological systems. Largely built on empirical observations to tackle heterogeneous, temporal, and adaptive patterns of interactions, its intuitive and flexible nature has contributed to the popularity of the field. With pioneering work on the evolution of random graphs, graph theory is often cited as the mathematical foundation of network science. Despite this narrative, the two research communities are still largely disconnected. In this Commentary we discuss the need for further cross-pollination between fields -- bridging the gap between graphs and networks -- and how network science can benefit from such influence. A more mathematical network science may clarify the role of randomness in modeling, hint at underlying laws of behavior, and predict yet unobserved complex networked phenomena in nature., Comment: 7 pages, 1 figure. To appear in Communications Physics as an Invited Commentary

The times of temporal-network events and their correlations contain information on the function of the network and they influence dynamical processes taking place on it. To extract information out of correlated event times, techniques such as the analysis of temporal motifs have been developed. We discuss a recently-introduced, more general framework that maps temporal-network structure into static graphs while retaining information on time-respecting paths and the time differences between their consequent events. This framework builds on weighted temporal event graphs: directed, acyclic graphs (DAGs) that contain a superposition of all temporal paths. We introduce the reader to the temporal event-graph mapping and associated computational methods and illustrate its use by applying the framework to temporal-network percolation.

Network embedding techniques are powerful to capture structural regularities in networks and to identify similarities between their local fabrics. However, conventional network embedding models are developed for static structures, commonly consider nodes only and they are seriously challenged when the network is varying in time. Temporal networks may provide an advantage in the description of real systems, but they code more complex information, which could be effectively represented only by a handful of methods so far. Here, we propose a new method of event embedding of temporal networks, called weg2vec, which builds on temporal and structural similarities of events to learn a low dimensional representation of a temporal network. This projection successfully captures latent structures and similarities between events involving different nodes at different times and provides ways to predict the final outcome of spreading processes unfolding on the temporal structure.

Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These dynamics can be described as limited waiting-time processes, and they are particularly important for systems modelled as temporal networks. These processes have been studied via simulations, which is equivalent to repeatedly finding all limited-waiting time temporal paths from a source node and time. We propose a method yielding orders of magnitude more efficient way of tracking the reachability of such temporal paths. Our method gives simultaneous estimates of the in- or out-reachability (with any chosen waiting-time limit) from every possible starting point and time. It works on very large temporal networks with hundreds of millions of events on current commodity computing hardware. This opens up the possibility to analyse reachability and dynamics of spreading processes on large temporal networks in completely new ways. For example, one can now compute centralities based on global reachability for all events or can find with high probability the infected node and time, which would lead to the largest epidemic outbreak., Comment: Software implementation available at https://doi.org/10.5281/zenodo.3369893

Twitter may be considered as a decentralized social information processing platform whose users constantly receive their followees' information feeds, which they may in turn dispatch to their followers. This decentralization is not devoid of hierarchy and heterogeneity, both in terms of activity and attention. In particular, we appraise the distribution of attention at the collective and individual level, which exhibits the existence of attentional constraints and focus effects. We observe that most users usually concentrate their attention on a limited core of peers and topics, and discuss the relationship between interactional and informational attention processes -- all of which, we suggest, may be useful to refine influence models by enabling the consideration of differential attention likelihood depending on users, their activity levels and peers' positions., Comment: 16 pages, 6 figures

This thesis summarises my scientific contributions in the domain of network science, human dynamics and computational social science. These contributions are associated to computer science, physics, statistics, and applied mathematics. The goal of this thesis is twofold, on one hand to write a concise summary of my most interesting scientific contributions, and on the other hand to provide an up-to-date view and perspective about my field. I start my dissertation with an introduction to position the reader on the landscape of my field and to put in perspective my contributions. In the second chapter I concentrate on my works on bursty human dynamics, addressing heterogeneous temporal characters of human actions and interactions. Next, I discuss my contributions to the field of temporal networks and give a synthesises of my works on various methods of the representation, characterisation, and modelling of time-varying structures. Finally, I discuss my works on the data-driven observations and modelling of collective social phenomena. There, I summarise studies on the static observations of emergent patterns of socioeconomic inequalities and their correlations with social-communication networks, and with linguistic patterns. I also discuss dynamic observations and modelling of social contagion processes., Comment: Habilitation thesis, ENS Lyon (2019) - 148 pages, 49 figures

The creation of social ties is largely determined by the entangled effects of people's similarities in terms of individual characters and friends. However, feature and structural characters of people usually appear to be correlated, making it difficult to determine which has greater responsibility in the formation of the emergent network structure. We propose \emph{AN2VEC}, a node embedding method which ultimately aims at disentangling the information shared by the structure of a network and the features of its nodes. Building on the recent developments of Graph Convolutional Networks (GCN), we develop a multitask GCN Variational Autoencoder where different dimensions of the generated embeddings can be dedicated to encoding feature information, network structure, and shared feature-network information. We explore the interaction between these disentangled characters by comparing the embedding reconstruction performance to a baseline case where no shared information is extracted. We use synthetic datasets with different levels of interdependency between feature and network characters and show (i) that shallow embeddings relying on shared information perform better than the corresponding reference with unshared information, (ii) that this performance gap increases with the correlation between network and feature structure, and (iii) that our embedding is able to capture joint information of structure and features. Our method can be relevant for the analysis and prediction of any featured network structure ranging from online social systems to network medicine.

Models of threshold driven contagion explain the cascading spread of information, behavior, systemic risk, and epidemics on social, financial and biological networks. At odds with empirical observation, these models predict that single-layer unweighted networks become resistant to global cascades after reaching sufficient connectivity. We investigate threshold driven contagion on weight heterogeneous multiplex networks and show that they can remain susceptible to global cascades at any level of connectivity, and with increasing edge density pass through alternating phases of stability and instability in the form of reentrant phase transitions of contagion. Our results provide a novel theoretical explanation for the observation of large scale contagion in highly connected but heterogeneous networks., Comment: 26 pages, 13 figures

The socioeconomic status of people depends on a combination of individual characteristics and environmental variables, thus its inference from online behavioral data is a difficult task. Attributes like user semantics in communication, habitat, occupation, or social network are all known to be determinant predictors of this feature. In this paper we propose three different data collection and combination methods to first estimate and, in turn, infer the socioeconomic status of French Twitter users from their online semantics. Our methods are based on open census data, crawled professional profiles, and remotely sensed, expert annotated information on living environment. Our inference models reach similar performance of earlier results with the advantage of relying on broadly available datasets and of providing a generalizable framework to estimate socioeconomic status of large numbers of Twitter users. These results may contribute to the scientific discussion on social stratification and inequalities, and may fuel several applications., Comment: Accepted as a full paper in the 2018 IEEE 18th International Conference on Data Mining - IWSC'18 2nd International Workshop on Social Computing

Many dynamical systems can be successfully analyzed by representing them as networks. Empirically measured networks and dynamic processes that take place in these situations show heterogeneous, non-Markovian, and intrinsically correlated topologies and dynamics. This makes their analysis particularly challenging. Randomized reference models (RRMs) have emerged as a general and versatile toolbox for studying such systems. Defined as random networks with given features constrained to match those of an input (empirical) network, they may, for example, be used to identify important features of empirical networks and their effects on dynamical processes unfolding in the network. RRMs are typically implemented as procedures that reshuffle an empirical network, making them very generally applicable. However, the effects of most shuffling procedures on network features remain poorly understood, rendering their use nontrivial and susceptible to misinterpretation. Here we propose a unified framework for classifying and understanding microcanonical RRMs (MRRMs) that sample networks with uniform probability. Focusing on temporal networks, we survey applications of MRRMs found in the literature, and we use this framework to build a taxonomy of MRRMs that proposes a canonical naming convention, classifies them, and deduces their effects on a range of important network features. We furthermore show that certain classes of MRRMs may be applied in sequential composition to generate new MRRMs from the existing ones surveyed in this article. We finally provide a tutorial showing how to apply a series of MRRMs to analyze how different network features affect a dynamic process in an empirical temporal network., Comment: Accepted version

Our usage of language is not solely reliant on cognition but is arguably determined by myriad external factors leading to a global variability of linguistic patterns. This issue, which lies at the core of sociolinguistics and is backed by many small-scale studies on face-to-face communication, is addressed here by constructing a dataset combining the largest French Twitter corpus to date with detailed socioeconomic maps obtained from national census in France. We show how key linguistic variables measured in individual Twitter streams depend on factors like socioeconomic status, location, time, and the social network of individuals. We found that (i) people of higher socioeconomic status, active to a greater degree during the daytime, use a more standard language; (ii) the southern part of the country is more prone to use more standard language than the northern one, while locally the used variety or dialect is determined by the spatial distribution of socioeconomic status; and (iii) individuals connected in the social network are closer linguistically than disconnected ones, even after the effects of status homophily have been removed. Our results inform sociolinguistic theory and may inspire novel learning methods for the inference of socioeconomic status of people from the way they tweet., Comment: In WWW 2018: The Web Conference, 10 pages, 6 figures

Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve heterogeneously over time by alternating between periods of low and high event frequencies. In such systems, bursts are identified as periods in which the events occur with a rapid pace within a short time-interval while these periods are separated by long periods of time with low frequency of events. As such dynamical patterns occur in a wide range of natural phenomena, their observation, characterisation, and modelling have been a long standing challenge in several fields of research. However, due to some recent developments in communication and data collection techniques it has become possible to follow digital traces of actions and interactions of humans from the individual up to the societal level. This led to several new observations of bursty phenomena in the new but largely unexplored area of human dynamics, which called for the renaissance to study these systems using research concepts and methodologies, including data analytics and modelling. As a result, a large amount of new insight and knowledge as well as innovations have been accumulated in the field, which provided us a timely opportunity to write this brief monograph to make an up-to-date review and summary of the observations, appropriate measures, modelling, and applications of heterogeneous bursty patterns occurring in the dynamics of human behaviour., Comment: 99 pages, 17 figures