Two types of densification scaling in the evolution of temporal networks

Many real-world social networks constantly change their global properties over time, such as the number of edges, size and density. While temporal and local properties of social networks have been extensively studied, the origin of their dynamical nature is not yet well understood. Networks may grow or shrink if a) the total population of nodes changes and/or b) the chance of two nodes being connected varies over time. Here, we develop a method that allows us to classify the source of time-varying nature of temporal networks. In doing so, we first show empirical evidence that real-world dynamical systems could be categorized into two classes, the difference of which is characterized by the way the number of edges grows with the number of active nodes, i.e., densification scaling. We develop a dynamic hidden-variable model to formally characterize the two dynamical classes. The model is fitted to the empirical data to identify whether the origin of scaling comes from a changing population in the system or shifts in the connecting probabilities.Comment: 12 pages, 6 figures (plus 7 figures in SI

Can co-location be used as a proxy for face-to-face contacts?

Technological advances have led to a strong increase in the number of data collection efforts aimed at measuring co-presence of individuals at different spatial resolutions. It is however unclear how much co-presence data can inform us on actual face-to-face contacts, of particular interest to study the structure of a population in social groups or for use in data-driven models of information or epidemic spreading processes. Here, we address this issue by leveraging data sets containing high resolution face-to-face contacts as well as a coarser spatial localisation of individuals, both temporally resolved, in various contexts. The co-presence and the face-to-face contact temporal networks share a number of structural and statistical features, but the former is (by definition) much denser than the latter. We thus consider several down-sampling methods that generate surrogate contact networks from the co-presence signal and compare them with the real face-to-face data. We show that these surrogate networks reproduce some features of the real data but are only partially able to identify the most central nodes of the face-to-face network. We then address the issue of using such down-sampled co-presence data in data-driven simulations of epidemic processes, and in identifying efficient containment strategies. We show that the performance of the various sampling methods strongly varies depending on context. We discuss the consequences of our results with respect to data collection strategies and methodologies

Temporal Gillespie algorithm: Fast simulation of contagion processes on time-varying networks

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.Comment: Minor changes and updates to reference

How memory generates heterogeneous dynamics in temporal networks

Empirical temporal networks display strong heterogeneities in their dynamics, which profoundly affect processes taking place on these networks, such as rumor and epidemic spreading. Despite the recent wealth of data on temporal networks, little work has been devoted to the understanding of how such heterogeneities can emerge from microscopic mechanisms at the level of nodes and links. Here we show that long-term memory effects are present in the creation and disappearance of links in empirical networks. We thus consider a simple generative modeling framework for temporal networks able to incorporate these memory mechanisms. This allows us to study separately the role of each of these mechanisms in the emergence of heterogeneous network dynamics. In particular, we show analytically and numerically how heterogeneous distributions of contact durations, of inter-contact durations and of numbers of contacts per link emerge. We also study the individual effect of heterogeneities on dynamical processes, such as the paradigmatic Susceptible-Infected epidemic spreading model. Our results confirm in particular the crucial role of the distributions of inter-contact durations and of the numbers of contacts per link

The switching mechanisms of social network densification

Densification and sparsification of temporal networks are attributed to two fundamental mechanisms: a change in the population in the system and/or a change in the chances that nodes in the system are connected. In theory, each of these mechanisms generates a distinctive type of densification scaling, but in reality both types are generally mixed. Here, we develop a Bayesian statistical method to identify the extent to which each of these mechanisms is at play at a given point in time, taking the mixed densification scaling as input. We apply the method to networks of face-to-face interactions of individuals and reveal that the main mechanism that causes densification and sparsification occasionally switches, the frequency of which depending on the social context. The proposed method uncovers an inherent regime-switching property of network dynamics, which will provide a new insight into the mechanics behind evolving social interactions.Comment: 12 pages, 6 figures + S

Combining Surveys and Sensors to Explore Student Behaviour

Student belongingness is important for successful study paths, and group work forms an important part of modern university physics education. To study the group dynamics of introductory physics students at the University of Helsinki, we collected network data from seven laboratory course sections of approximately 20 students each for seven consecutive weeks. The data was collected via the SocioPatterns platform, and supplemented with students’ major subject, year of study and gender. We also collected the Mechanics Baseline Test to measure physics knowledge and the Colorado Learning Attitudes about Science Survey to measure attitudes. We developed metrics for studying the small networks of the laboratory sessions by using connections of the teaching assistant as a constant. In the network, we found both demographically homogeneous and heterogeneous groups that are stable. While some students are consistently loosely connected to their networks, we were not able to identify risk factors. Based on our results, the physics laboratory course is equally successful in building strongly connected groups regardless of student demographics in the sections or the formed small groups. SocioPatterns supplemented with surveys thus provides an opportunity to look into the dynamics of students’ social networks

Combining Surveys and Sensors to Explore Student Behaviour

Student belongingness is important for successful study paths, and group work forms an important part of modern university physics education. To study the group dynamics of introductory physics students at the University of Helsinki, we collected network data from seven laboratory course sections of approximately 20 students each for seven consecutive weeks. The data was collected via the SocioPatterns platform, and supplemented with students’ major subject, year of study and gender. We also collected the Mechanics Baseline Test to measure physics knowledge and the Colorado Learning Attitudes about Science Survey to measure attitudes. We developed metrics for studying the small networks of the laboratory sessions by using connections of the teaching assistant as a constant. In the network, we found both demographically homogeneous and heterogeneous groups that are stable. While some students are consistently loosely connected to their networks, we were not able to identify risk factors. Based on our results, the physics laboratory course is equally successful in building strongly connected groups regardless of student demographics in the sections or the formed small groups. SocioPatterns supplemented with surveys thus provides an opportunity to look into the dynamics of students’ social networks

Compensating for population sampling in simulations of epidemic spread on temporal contact networks

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

Metal enrichment in a semi-analytical model, fundamental scaling relations, and the case of Milky Way galaxies

Gas flows play a fundamental role in galaxy formation and evolution, providing the fuel for the star formation process. These mechanisms leave an imprint in the amount of heavy elements. Thus, the analysis of this metallicity signature provides additional constraint on the galaxy formation scenario. We aim to discriminate between four different galaxy formation models based on two accretion scenarios and two different star formation recipes. We address the impact of a bimodal accretion scenario and a strongly regulated star formation recipe. We present a new extension of the eGalICS model, which allows us to track the metal enrichment process. Our new chemodynamical model is applicable for situations ranging from metal-free primordial accretion to very enriched interstellar gas contents. We use this new tool to predict the metallicity evolution of both the stellar populations and gas phase. We also address the evolution of the gas metallicity with the star formation rate (SFR). We then focus on a sub-sample of Milky Way-like galaxies. We compare both the cosmic stellar mass assembly and the metal enrichment process of such galaxies with observations and detailed chemical evolution models. Our models, based on a strong star formation regulation, allow us to reproduce well the stellar mass to gas-phase metallicity relation observed in the local universe. However, we observe a systematic shift towards high masses. Our $Mstar-Zg-SFR relation is in good agreement with recent measurements: our best model predicts a clear dependence with the SFR. Both SFR and metal enrichment histories of our Milky Way-like galaxies are consistent with observational measurements and detailed chemical evolution models. We finally show that Milky Way progenitors start their evolution below the observed main sequence and progressively reach this observed relation at z = 0.Comment: 22 pages, 11 figure