Hyper-cores promote localization and efficient seeding in higher-order processes.

Going beyond networks, to include higher-order interactions of arbitrary sizes, is a major step to better describe complex systems. In the resulting hypergraph representation, tools to identify structures and central nodes are scarce. We consider the decomposition of a hypergraph in hyper-cores, subsets of nodes connected by at least a certain number of hyperedges of at least a certain size. We show that this provides a fingerprint for data described by hypergraphs and suggests a novel notion of centrality, the hypercoreness. We assess the role of hyper-cores and nodes with large hypercoreness in higher-order dynamical processes: such nodes have large spreading power and spreading processes are localized in central hyper-cores. Additionally, in the emergence of social conventions very few committed individuals with high hypercoreness can rapidly overturn a majority convention. Our work opens multiple research avenues, from comparing empirical data to model validation and study of temporally varying hypergraphs.

Distinguishing Simple and Complex Contagion Processes on Networks.

Contagion processes on networks, including disease spreading, information diffusion, or social behaviors propagation, can be modeled as simple contagion, i.e., as a contagion process involving one connection at a time, or as complex contagion, in which multiple interactions are needed for a contagion event. Empirical data on spreading processes, however, even when available, do not easily allow us to uncover which of these underlying contagion mechanisms is at work. We propose a strategy to discriminate between these mechanisms upon the observation of a single instance of a spreading process. The strategy is based on the observation of the order in which network nodes are infected, and on its correlations with their local topology: these correlations differ between processes of simple contagion, processes involving threshold mechanisms, and processes driven by group interactions (i.e., by "higher-order" mechanisms). Our results improve our understanding of contagion processes and provide a method using only limited information to distinguish between several possible contagion mechanisms.

Inferring cell cycle phases from a partially temporal network of protein interactions.

The temporal organization of biological systems is key for understanding them, but current methods for identifying this organization are often ad hoc and require prior knowledge. We present Phasik, a method that automatically identifies this multiscale organization by combining time series data (protein or gene expression) and interaction data (protein-protein interaction network). Phasik builds a (partially) temporal network and uses clustering to infer temporal phases. We demonstrate the method's effectiveness by recovering well-known phases and sub-phases of the cell cycle of budding yeast and phase arrests of mutants. We also show its general applicability using temporal gene expression data from circadian rhythms in wild-type and mutant mouse models. We systematically test Phasik's robustness and investigate the effect of having only partial temporal information. As time-resolved, multiomics datasets become more common, this method will allow the study of temporal regulation in lesser-known biological contexts, such as development, metabolism, and disease.

Modeling framework unifying contact and social networks.

Temporal networks of face-to-face interactions between individuals are useful proxies of the dynamics of social systems on fast timescales. Several empirical statistical properties of these networks have been shown to be robust across a large variety of contexts. To better grasp the role of various mechanisms of social interactions in the emergence of these properties, models in which schematic implementations of such mechanisms can be carried out have proven useful. Here, we put forward a framework to model temporal networks of human interactions based on the idea of a coevolution and feedback between (i) an observed network of instantaneous interactions and (ii) an underlying unobserved social bond network: Social bonds partially drive interaction opportunities and in turn are reinforced by interactions and weakened or even removed by the lack of interactions. Through this coevolution, we also integrate in the model well-known mechanisms such as triadic closure, but also the impact of shared social context and nonintentional (casual) interactions, with several tunable parameters. We then propose a method to compare the statistical properties of each version of the model with empirical face-to-face interaction data sets to determine which sets of mechanisms lead to realistic social temporal networks within this modeling framework.

Contact networks have small metric backbones that maintain community structure and are primary transmission subgraphs.

The structure of social networks strongly affects how different phenomena spread in human society, from the transmission of information to the propagation of contagious diseases. It is well-known that heterogeneous connectivity strongly favors spread, but a precise characterization of the redundancy present in social networks and its effect on the robustness of transmission is still lacking. This gap is addressed by the metric backbone, a weight- and connectivity-preserving subgraph that is sufficient to compute all shortest paths of weighted graphs. This subgraph is obtained via algebraically-principled axioms and does not require statistical sampling based on null-models. We show that the metric backbones of nine contact networks obtained from proximity sensors in a variety of social contexts are generally very small, 49% of the original graph for one and ranging from about 6% to 20% for the others. This reflects a surprising amount of redundancy and reveals that shortest paths on these networks are very robust to random attacks and failures. We also show that the metric backbone preserves the full distribution of shortest paths of the original contact networks-which must include the shortest inter- and intra-community distances that define any community structure-and is a primary subgraph for epidemic transmission based on pure diffusion processes. This suggests that the organization of social contact networks is based on large amounts of shortest-path redundancy which shapes epidemic spread in human populations. Thus, the metric backbone is an important subgraph with regard to epidemic spread, the robustness of social networks, and any communication dynamics that depend on complex network shortest paths.

Minimising school disruption under high incidence conditions due to the Omicron variant in France, Switzerland, Italy, in January 2022.

BackgroundAs record cases of Omicron variant were registered in Europe in early 2022, schools remained a vulnerable setting undergoing large disruption.AimThrough mathematical modelling, we compared school protocols of reactive screening, regular screening, and reactive class closure implemented in France, in Baselland (Switzerland), and in Italy, respectively, and assessed them in terms of case prevention, testing resource demand, and schooldays lost.MethodsWe used a stochastic agent-based model of SARS-CoV-2 transmission in schools accounting for within- and across-class contacts from empirical contact data. We parameterised it to the Omicron BA.1 variant to reproduce the French Omicron wave in January 2022. We simulated the three protocols to assess their costs and effectiveness for varying peak incidence rates in the range experienced by European countries.ResultsWe estimated that at the high incidence rates registered in France during the Omicron BA.1 wave in January 2022, the reactive screening protocol applied in France required higher test resources compared with the weekly screening applied in Baselland (0.50 vs 0.45 tests per student-week), but achieved considerably lower control (8% vs 21% reduction of peak incidence). The reactive class closure implemented in Italy was predicted to be very costly, leading to > 20% student-days lost.ConclusionsAt high incidence conditions, reactive screening protocols generate a large and unplanned demand in testing resources, for marginal control of school transmissions. Comparable or lower resources could be more efficiently used through weekly screening. Our findings can help define incidence levels triggering school protocols and optimise their cost-effectiveness.

Impact of contact data resolution on the evaluation of interventions in mathematical models of infectious diseases.

Computational models offer a unique setting to test strategies to mitigate the spread of infectious diseases, providing useful insights to applied public health. To be actionable, models need to be informed by data, which can be available at different levels of detail. While high-resolution data describing contacts between individuals are increasingly available, data gathering remains challenging, especially during a health emergency. Many models thus use synthetic data or coarse information to evaluate intervention protocols. Here, we evaluate how the representation of contact data might affect the impact of various strategies in models, in the realm of COVID-19 transmission in educational and work contexts. Starting from high-resolution contact data, we use detailed to coarse data representations to inform a model of SARS-CoV-2 transmission and simulate different mitigation strategies. We find that coarse data representations estimate a lower risk of superspreading events. However, the rankings of protocols according to their efficiency or cost remain coherent across representations, ensuring the consistency of model findings to inform public health advice. Caution should be taken, however, on the quantitative estimations of those benefits and costs triggering the adoption of protocols, as these may depend on data representation.

Screening and vaccination against COVID-19 to minimise school closure: a modelling study.

BACKGROUND: Schools were closed extensively in 2020-21 to counter SARS-CoV-2 spread, impacting students' education and wellbeing. With highly contagious variants expanding in Europe, safe options to maintain schools open are urgently needed. By estimating school-specific transmissibility, our study evaluates costs and benefits of different protocols for SARS-CoV-2 control at school. METHODS: We developed an agent-based model of SARS-CoV-2 transmission in schools. We used empirical contact data in a primary and a secondary school and data from pilot screenings in 683 schools during the alpha variant (B.1.1.7) wave in March-June, 2021, in France. We fitted the model to observed school prevalence to estimate the school-specific effective reproductive number for the alpha (Ralpha) and delta (B.1.617.2; Rdelta) variants and performed a cost-benefit analysis examining different intervention protocols. FINDINGS: We estimated Ralpha to be 1·40 (95% CI 1·35-1·45) in the primary school and 1·46 (1·41-1·51) in the secondary school during the spring wave, higher than the time-varying reproductive number estimated from community surveillance. Considering the delta variant and vaccination coverage in Europe as of mid-September, 2021, we estimated Rdelta to be 1·66 (1·60-1·71) in primary schools and 1·10 (1·06-1·14) in secondary schools. Under these conditions, weekly testing of 75% of unvaccinated students (PCR tests on saliva samples in primary schools and lateral flow tests in secondary schools), in addition to symptom-based testing, would reduce cases by 34% (95% CI 32-36) in primary schools and 36% (35-39) in secondary schools compared with symptom-based testing alone. Insufficient adherence was recorded in pilot screening (median ≤53%). Regular testing would also reduce student-days lost up to 80% compared with reactive class closures. Moderate vaccination coverage in students would still benefit from regular testing for additional control-ie, weekly testing 75% of unvaccinated students would reduce cases compared with symptom-based testing only, by 23% in primary schools when 50% of children are vaccinated. INTERPRETATION: The COVID-19 pandemic will probably continue to pose a risk to the safe and normal functioning of schools. Extending vaccination coverage in students, complemented by regular testing with good adherence, are essential steps to keep schools open when highly transmissible variants are circulating. FUNDING: EU Framework Programme for Research and Innovation Horizon 2020, Horizon Europe Framework Programme, Agence Nationale de la Recherche, ANRS-Maladies Infectieuses Émergentes.

Transition from simple to complex contagion in collective decision-making.

How does the spread of behavior affect consensus-based collective decision-making among animals, humans or swarming robots? In prior research, such propagation of behavior on social networks has been found to exhibit a transition from simple contagion-i.e, based on pairwise interactions-to a complex one-i.e., involving social influence and reinforcement. However, this rich phenomenology appears so far limited to threshold-based decision-making processes with binary options. Here, we show theoretically, and experimentally with a multi-robot system, that such a transition from simple to complex contagion can also bed observed in an archetypal model of distributed decision-making devoid of any thresholds or nonlinearities. Specifically, we uncover two key results: the nature of the contagion-simple or complex-is tightly related to the intrinsic pace of the behavior that is spreading, and the network topology strongly influences the effectiveness of the behavioral transmission in ways that are reminiscent of threshold-based models. These results offer new directions for the empirical exploration of behavioral contagions in groups, and have significant ramifications for the design of cooperative and networked robot systems.

From temporal network data to the dynamics of social relationships.

Networks are well-established representations of social systems, and temporal networks are widely used to study their dynamics. However, going from temporal network data (i.e. a stream of interactions between individuals) to a representation of the social group's evolution remains a challenge. Indeed, the temporal network at any specific time contains only the interactions taking place at that time and aggregating on successive time-windows also has important limitations. Here, we present a new framework to study the dynamic evolution of social networks based on the idea that social relationships are interdependent: as the time we can invest in social relationships is limited, reinforcing a relationship with someone is done at the expense of our relationships with others. We implement this interdependence in a parsimonious two-parameter model and apply it to several human and non-human primates' datasets to demonstrate that this model detects even small and short perturbations of the networks that cannot be detected using the standard technique of successive aggregated networks. Our model solves a long-standing problem by providing a simple and natural way to describe the dynamic evolution of social networks, with far-reaching consequences for the study of social networks and social evolution.

Building surrogate temporal network data from observed backbones.

Many systems of socioeconomic interests find a convenient representation in the form of temporal networks, i.e., sets of nodes and interactions occurring at specified times. In the corresponding data sets, however, crucial elements coexist with nonessential ones and noise. Several methods have thus been proposed to extract a "network backbone," i.e., the set of most important links in a network data set. The outcome of such methods can be seen as compressed versions of the original data. However, the question of how to practically use such reduced views of the data has not been tackled: for instance, using them directly in numerical simulations of processes on networks might lead to important biases. Overall, such reduced views of the data might not be actionable without an adequate decompression method. Here, we address this issue by putting forward and exploring several systematic procedures to build surrogate data from various kinds of temporal network backbones. In particular, we explore how much information about the original data needs to be retained alongside the backbone so that the surrogate data can be used in data-driven numerical simulations of spreading processes on a wide range of spreading parameters. We illustrate our results using empirical temporal networks with a broad variety of structures and properties. Our results give hints on how to best summarize complex data sets so that they remain actionable. Moreover, they show how ensembles of surrogate data with similar properties can be obtained from an original single data set, without any modeling assumptions.

Anatomy of digital contact tracing: Role of age, transmission setting, adoption, and case detection.

The efficacy of digital contact tracing against coronavirus disease 2019 (COVID-19) epidemic is debated: Smartphone penetration is limited in many countries, with low coverage among the elderly, the most vulnerable to COVID-19. We developed an agent-based model to precise the impact of digital contact tracing and household isolation on COVID-19 transmission. The model, calibrated on French population, integrates demographic, contact and epidemiological information to describe exposure and transmission of COVID-19. We explored realistic levels of case detection, app adoption, population immunity, and transmissibility. Assuming a reproductive ratio R = 2.6 and 50% detection of clinical cases, a ~20% app adoption reduces peak incidence by ~35%. With R = 1.7, >30% app adoption lowers the epidemic to manageable levels. Higher coverage among adults, playing a central role in COVID-19 transmission, yields an indirect benefit for the elderly. These results may inform the inclusion of digital contact tracing within a COVID-19 response plan.

On the Challenges and Potential of Using Barometric Sensors to Track Human Activity.

Barometers are among the oldest engineered sensors. Historically, they have been primarily used either as environmental sensors to measure the atmospheric pressure for weather forecasts or as altimeters for aircrafts. With the advent of microelectromechanical system (MEMS)-based barometers and their systematic embedding in smartphones and wearable devices, a vast breadth of new applications for the use of barometers has emerged. For instance, it is now possible to use barometers in conjunction with other sensors to track and identify a wide range of human activity classes. However, the effectiveness of barometers in the growing field of human activity recognition critically hinges on our understanding of the numerous factors affecting the atmospheric pressure, as well as on the properties of the sensor itself-sensitivity, accuracy, variability, etc. This review article thoroughly details all these factors and presents a comprehensive report of the numerous studies dealing with one or more of these factors in the particular framework of human activity tracking and recognition. In addition, we specifically collected some experimental data to illustrate the effects of these factors, which we observed to be in good agreement with the findings in the literature. We conclude this review with some suggestions on some possible future uses of barometric sensors for the specific purpose of tracking human activities.

Relevance of temporal cores for epidemic spread in temporal networks.

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 include influential spreaders.

Measuring social networks in primates: wearable sensors versus direct observations.

Network analysis represents a valuable and flexible framework to understand the structure of individual interactions at the population level in animal societies. The versatility of network representations is moreover suited to different types of datasets describing these interactions. However, depending on the data collection method, different pictures of the social bonds between individuals could a priori emerge. Understanding how the data collection method influences the description of the social structure of a group is thus essential to assess the reliability of social studies based on different types of data. This is however rarely feasible, especially for animal groups, where data collection is often challenging. Here, we address this issue by comparing datasets of interactions between primates collected through two different methods: behavioural observations and wearable proximity sensors. We show that, although many directly observed interactions are not detected by the sensors, the global pictures obtained when aggregating the data to build interaction networks turn out to be remarkably similar. Moreover, sensor data yield a reliable social network over short time scales and can be used for long-term studies, showing their important potential for detailed studies of the evolution of animal social groups.

Dynamic core-periphery structure of information sharing networks in entorhinal cortex and hippocampus.

Neural computation is associated with the emergence, reconfiguration, and dissolution of cell assemblies in the context of varying oscillatory states. Here, we describe the complex spatiotemporal dynamics of cell assemblies through temporal network formalism. We use a sliding window approach to extract sequences of networks of information sharing among single units in hippocampus and entorhinal cortex during anesthesia and study how global and node-wise functional connectivity properties evolve through time and as a function of changing global brain state (theta vs. slow-wave oscillations). First, we find that information sharing networks display, at any time, a core-periphery structure in which an integrated core of more tightly functionally interconnected units links to more loosely connected network leaves. However the units participating to the core or to the periphery substantially change across time windows, with units entering and leaving the core in a smooth way. Second, we find that discrete network states can be defined on top of this continuously ongoing liquid core-periphery reorganization. Switching between network states results in a more abrupt modification of the units belonging to the core and is only loosely linked to transitions between global oscillatory states. Third, we characterize different styles of temporal connectivity that cells can exhibit within each state of the sharing network. While inhibitory cells tend to be central, we show that, otherwise, anatomical localization only poorly influences the patterns of temporal connectivity of the different cells. Furthermore, cells can change temporal connectivity style when the network changes state. Altogether, these findings reveal that the sharing of information mediated by the intrinsic dynamics of hippocampal and entorhinal cortex cell assemblies have a rich spatiotemporal structure, which could not have been identified by more conventional time- or state-averaged analyses of functional connectivity.

Simplicial models of social contagion.

Complex networks have been successfully used to describe the spread of diseases in populations of interacting individuals. Conversely, pairwise interactions are often not enough to characterize social contagion processes such as opinion formation or the adoption of novelties, where complex mechanisms of influence and reinforcement are at work. Here we introduce a higher-order model of social contagion in which a social system is represented by a simplicial complex and contagion can occur through interactions in groups of different sizes. Numerical simulations of the model on both empirical and synthetic simplicial complexes highlight the emergence of novel phenomena such as a discontinuous transition induced by higher-order interactions. We show analytically that the transition is discontinuous and that a bistable region appears where healthy and endemic states co-exist. Our results help explain why critical masses are required to initiate social changes and contribute to the understanding of higher-order interactions in complex systems.

The structured backbone of temporal social ties.

In many data sets, information on the structure and temporality of a system coexists with noise and non-essential elements. In networked systems for instance, some edges might be non-essential or exist only by chance. Filtering them out and extracting a set of relevant connections is a non-trivial task. Moreover, mehods put forward until now do not deal with time-resolved network data, which have become increasingly available. Here we develop a method for filtering temporal network data, by defining an adequate temporal null model that allows us to identify pairs of nodes having more interactions than expected given their activities: the significant ties. Moreover, our method can assign a significance to complex structures such as triads of simultaneous interactions, an impossible task for methods based on static representations. Our results hint at ways to represent temporal networks for use in data-driven models.