Emergence of long-range correlations and bursty activity patterns in online communication

Burst-tree structure and higher-order temporal correlations

Understanding the characteristics of temporal correlations in a time series is crucial for developing accurate models in natural and social sciences. The burst-tree decomposition method was recently introduced to reveal temporal correlations in a time series in the form of an event sequence, in particular, the hierarchical structure of bursty trains of events for the entire range of timescales [Jo et al., Sci. Rep. 10, 12202 (2020)10.1038/s41598-020-68157-1]. Such structure cannot be solely captured by the interevent time distribution but can show higher-order correlations beyond interevent times. It has been found to be simply characterized by the burst-merging kernel governing which bursts are merged together as the timescale for defining bursts increases. In this work, we study the effects of kernels on the higher-order temporal correlations in terms of burst-size distributions, memory coefficients for bursts, and the autocorrelation function. We employ several kernels, including the constant, sum, product, and diagonal kernels as well as those inspired by empirical results. We generically find that kernels with preferential merging lead to heavy-tailed burst-size distributions, while kernels with assortative merging lead to positive correlations between burst sizes. The decaying exponent of the autocorrelation function depends not only on the kernel but also on the power-law exponent of the interevent time distribution. In addition, thanks to the analogy to the coagulation process, analytical solutions of burst-size distributions for some kernels could be obtained. Our findings may shed light on the role of burst-merging kernels as underlying mechanisms of higher-order temporal correlations in a time series.

Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history

The origin of non-Poissonian or bursty temporal patterns observed in various data sets for human social dynamics has been extensively studied, yet its understanding still remains incomplete. Considering the fact that humans are social beings, a fundamental question arises: Is the bursty human dynamics dominated by individual characteristics or by interaction between individuals? In this paper we address this question by analyzing the Wikipedia edit history to see how spontaneous individual editors are in initiating bursty periods of editing, i.e., individual-driven burstiness, and to what extent such editors' behaviors are driven by interaction with other editors in those periods, i.e., interaction-driven burstiness. We quantify the degree of initiative (DoI) of an editor of interest in each Wikipedia article by using the statistics of bursty periods containing the editor's edits. The integrated value of the DoI over all relevant timescales reveals which is dominant between individual-driven and interaction-driven burstiness. We empirically find that this value tends to be larger for weaker temporal correlations in the editor's editing behavior and/or stronger editorial correlations. These empirical findings are successfully confirmed by deriving an analytic form of the DoI from a model capturing the essential features of the edit sequence. Thus our approach provides a deeper insight into the origin and underlying mechanisms of bursts in human social dynamics.

A comparative study of online communities and popularity of BBS in four Chinese universities

Online forums in Chinese universities play an important role in understanding collective behavior of college students. Of particular interest are community and popularity. We address these two issues by examining data from Bulletin Board Systems (BBSs) of four Chinese universities. To characterize users’ behavior, we introduce a hypothesis test to infer individual preferred boards, which yields a polarization of users. We also perform a multilevel algorithm to detect communities of each BBS network. We measure the similarity between the board-preferred polarization and the algorithmically identified community structure by quantitative and visual tools. The resulting discrepancy indicates that board labels are inadequate to represent underlying communities. To reveal online popularity, we employ latent Dirichlet allocation to mine topics from threads to compare popularity in different universities. Based on which, we implement the Cox-Stuart test to explore the change in popularity over time and reproduce significantly ascending and descending topics around a decade. Finally, we devise a two-step model based on users’ preference and interests to reproduce the observed connectivity patterns.

Correlated bursts in temporal networks slow down spreading

Spreading dynamics has been considered to take place in temporal networks, where temporal interaction patterns between nodes show non-Poissonian bursty nature. The effects of inhomogeneous interevent times (IETs) on the spreading have been extensively studied in recent years, yet little is known about the effects of correlations between IETs on the spreading. In order to investigate those effects, we study two-step deterministic susceptible-infected (SI) and probabilistic SI dynamics when the interaction patterns are modeled by inhomogeneous and correlated IETs, i.e., correlated bursts. By analyzing the transmission time statistics in a single-link setup and by simulating the spreading in Bethe lattices and random graphs, we conclude that the positive correlation between IETs slows down the spreading. We also argue that the shortest transmission time from one infected node to its susceptible neighbors can successfully explain our numerical results.

How Online Communities of People With Long-Term Conditions Function and Evolve: Network Analysis of the Structure and Dynamics of the Asthma UK and British Lung Foundation Online Communities

Background

Self-management support can improve health and reduce health care utilization by people with long-term conditions. Online communities for people with long-term conditions have the potential to influence health, usage of health care resources, and facilitate illness self-management. Only recently, however, has evidence been reported on how such communities function and evolve, and how they support self-management of long-term conditions in practice.

Objective

The aim of this study is to gain a better understanding of the mechanisms underlying online self-management support systems by analyzing the structure and dynamics of the networks connecting users who write posts over time.

Methods

We conducted a longitudinal network analysis of anonymized data from 2 patients’ online communities from the United Kingdom: the Asthma UK and the British Lung Foundation (BLF) communities in 2006-2016 and 2012-2016, respectively.

Results

The number of users and activity grew steadily over time, reaching 3345 users and 32,780 posts in the Asthma UK community, and 19,837 users and 875,151 posts in the BLF community. People who wrote posts in the Asthma UK forum tended to write at an interval of 1-20 days and six months, while those in the BLF community wrote at an interval of two days. In both communities, most pairs of users could reach one another either directly or indirectly through other users. Those who wrote a disproportionally large number of posts (the superusers) represented 1% of the overall population of both Asthma UK and BLF communities and accounted for 32% and 49% of the posts, respectively. Sensitivity analysis showed that the removal of superusers would cause the communities to collapse. Thus, interactions were held together by very few superusers, who posted frequently and regularly, 65% of them at least every 1.7 days in the BLF community and 70% every 3.1 days in the Asthma UK community. Their posting activity indirectly facilitated tie formation between other users. Superusers were a constantly available resource, with a mean of 80 and 20 superusers active at any one time in the BLF and Asthma UK communities, respectively. Over time, the more active users became, the more likely they were to reply to other users’ posts rather than to write new ones, shifting from a help-seeking to a help-giving role. This might suggest that superusers were more likely to provide than to seek advice.

Conclusions

In this study, we uncover key structural properties related to the way users interact and sustain online health communities. Superusers’ engagement plays a fundamental sustaining role and deserves research attention. Further studies are needed to explore network determinants of the effectiveness of online engagement concerning health-related outcomes. In resource-constrained health care systems, scaling up online communities may offer a potentially accessible, wide-reaching and cost-effective intervention facilitating greater levels of self-management.

Modeling correlated bursts by the bursty-get-burstier mechanism

Temporal correlations of time series or event sequences in natural and social phenomena have been characterized by power-law decaying autocorrelation functions with decaying exponent γ. Such temporal correlations can be understood in terms of power-law distributed interevent times with exponent α and/or correlations between interevent times. The latter, often called correlated bursts, has recently been studied by measuring power-law distributed bursty trains with exponent β. A scaling relation between α and γ has been established for the uncorrelated interevent times, while little is known about the effects of correlated interevent times on temporal correlations. In order to study these effects, we devise the bursty-get-burstier model for correlated bursts, by which one can tune the degree of correlations between interevent times, while keeping the same interevent time distribution. We numerically find that sufficiently strong correlations between interevent times could violate the scaling relation between α and γ for the uncorrelated case. A nontrivial dependence of γ on β is also found for some range of α. The implication of our results is discussed in terms of the hierarchical organization of bursty trains at various time scales.