We analyze general trends and pattern in time series that characterize the dynamics of collective attention to social media services and Web-based businesses. Our study is based on search frequency data available from Google Trends and considers 175 different services. For each service, we collect data from 45 different countries as well as global averages. This way, we obtain more than 8,000 time series which we analyze using diffusion models from the economic sciences. We find that these models accurately characterize the empirical data and our analysis reveals that collective attention to social media grows and subsides in a highly regular and predictable manner. Regularities persist across regions, cultures, and topics and thus hint at general mechanisms that govern the adoption of Web-based services. We discuss several cases in detail to highlight interesting findings. Our methods are of economic interest as they may inform investment decisions and can help assessing at what stage of the general life-cycle a Web service is at.
While attention dynamics on shorter time scales have been modeled using random fields @cite_15 , structured models @cite_12 , or differential equations @cite_22 , long term temporal dynamics of collective attention have previously been modeled using mixtures of power-law and Poisson distributions @cite_4 or systems of differential equations @cite_30 @cite_25 which were inspired by techniques from the area of epidemic modeling @cite_26 @cite_9 . In this context, we note that the diffusion models considered in this paper also allow for interpretations in terms of the dynamics of elementary differential equations. For instance, the Weibull model in can be expressed as @math which hints at a similarity in spirit between economic diffusion and established epidemic models that seems to merit further research.
@cite_30 @cite_26 @cite_4 @cite_22 @cite_9 @cite_15 @cite_25 @cite_12
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Many cultural traits exhibit volatile dynamics, commonly dubbed fashions or fads. Here we show that realistic fashion-like dynamics emerge spontaneously if individuals can copy others' preferences for cultural traits as well as traits themselves. We demonstrate this dynamics in simple mathematical models of the diffusion, and subsequent abandonment, of a single cultural trait which individuals may or may not prefer. We then simulate the coevolution between many cultural traits and the associated preferences, reproducing power-law frequency distributions of cultural traits (most traits are adopted by few individuals for a short time, and very few by many for a long time), as well as correlations between the rate of increase and the rate of decrease of traits (traits that increase rapidly in popularity are also abandoned quickly and vice versa). We also establish that alternative theories, that fashions result from individuals signaling their social status, or from individuals randomly copying each other, do not satisfactorily reproduce these empirical observations. This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases. We study the relaxation response of a social system after endogenous and exogenous bursts of activity using the time series of daily views for nearly 5 million videos on YouTube. We find that most activity can be described accurately as a Poisson process. However, we also find hundreds of thousands of examples in which a burst of activity is followed by an ubiquitous power-law relaxation governing the timing of views. We find that these relaxation exponents cluster into three distinct classes and allow for the classification of collective human dynamics. This is consistent with an epidemic model on a social network containing two ingredients: a power-law distribution of waiting times between cause and action and an epidemic cascade of actions becoming the cause of future actions. This model is a conceptual extension of the fluctuation-dissipation theorem to social systems [Ruelle, D (2004) Phys Today 57:48–53] and [Roehner BM, et al, (2004) Int J Mod Phys C 15:809–834], and provides a unique framework for the investigation of timing in complex systems. Tracking new topics, ideas, and "memes" across the Web has been an issue of considerable interest. Recent work has developed methods for tracking topic shifts over long time scales, as well as abrupt spikes in the appearance of particular named entities. However, these approaches are less well suited to the identification of content that spreads widely and then fades over time scales on the order of days - the time scale at which we perceive news and events. We develop a framework for tracking short, distinctive phrases that travel relatively intact through on-line text; developing scalable algorithms for clustering textual variants of such phrases, we identify a broad class of memes that exhibit wide spread and rich variation on a daily basis. As our principal domain of study, we show how such a meme-tracking approach can provide a coherent representation of the news cycle - the daily rhythms in the news media that have long been the subject of qualitative interpretation but have never been captured accurately enough to permit actual quantitative analysis. We tracked 1.6 million mainstream media sites and blogs over a period of three months with the total of 90 million articles and we find a set of novel and persistent temporal patterns in the news cycle. In particular, we observe a typical lag of 2.5 hours between the peaks of attention to a phrase in the news media and in blogs respectively, with divergent behavior around the overall peak and a "heartbeat"-like pattern in the handoff between news and blogs. We also develop and analyze a mathematical model for the kinds of temporal variation that the system exhibits. User generated information in online communities has been characterized with the mixture of a text stream and a network structure both changing over time. A good example is a web-blogging community with the daily blog posts and a social network of bloggers. An important task of analyzing an online community is to observe and track the popular events, or topics that evolve over time in the community. Existing approaches usually focus on either the burstiness of topics or the evolution of networks, but ignoring the interplay between textual topics and network structures. In this paper, we formally define the problem of popular event tracking in online communities (PET), focusing on the interplay between texts and networks. We propose a novel statistical method that models the the popularity of events over time, taking into consideration the burstiness of user interest, information diffusion on the network structure, and the evolution of textual topics. Specifically, a Gibbs Random Field is defined to model the influence of historic status and the dependency relationships in the graph; thereafter a topic model generates the words in text content of the event, regularized by the Gibbs Random Field. We prove that two classic models in information diffusion and text burstiness are special cases of our model under certain situations. Empirical experiments with two different communities and datasets (i.e., Twitter and DBLP) show that our approach is effective and outperforms existing approaches. We present an analysis of a person-to-person recommendation network, consisting of 4 million people who made 16 million recommendations on half a million products. We observe the propagation of recommendations and the cascade sizes, which we explain by a simple stochastic model. We then establish how the recommendation network grows over time and how effective it is from the viewpoint of the sender and receiver of the recommendations. While on average recommendations are not very effective at inducing purchases and do not spread very far, we present a model that successfully identifies product and pricing categories for which viral marketing seems to be very effective.