Research Article: Stationarity of the inter-event power-law distributions

Date Published: March 27, 2017

Publisher: Public Library of Science

Author(s): Yerali Gandica, João Carvalho, Fernando Sampaio dos Aidos, Renaud Lambiotte, Timoteo Carletti, Enrico Scalas.

http://doi.org/10.1371/journal.pone.0174509

Abstract

A number of human activities exhibit a bursty pattern, namely periods of very high activity that are followed by rest periods. Records of these processes generate time series of events whose inter-event times follow a probability distribution that displays a fat tail. The grounds for such phenomenon are not yet clearly understood. In the present work we use the freely available Wikipedia’s editing records to unravel some features of this phenomenon. We show that even though the probability to start editing is conditioned by the circadian 24 hour cycle, the conditional probability for the time interval between successive edits at a given time of the day is independent from the latter. We confirm our findings with the activity of posting on the social network Twitter. Our results suggest that there is an intrinsic humankind scheduling pattern: after overcoming the encumbrance of starting an activity, there is a robust distribution of new related actions, which does not depend on the time of day at which the activity started.

Partial Text

The digital media are an important component of our lives. Nowadays, digital records of human activity of different sorts are systematically stored and made accessible for academic research. Hence a huge amount of data has become available throughout the past couple of decades, which allows for a quantitative study of human behaviour. For a long time, scholars from different backgrounds have been studying this field. However, some interesting and basic properties have still been outside the reach of researchers, mainly for lack of large amounts of reliable data. The increasing amount of data that is being gathered in this digital age is progressively opening up new possibilities for quantitative studies of these features. One such aspect, detected by means of data-gathering, is human bursty behaviour, which is an activity characterized by intervals of rapidly occurring events separated by long periods of inactivity [1]. The dynamics of a wide range of systems in nature displays such a behaviour [2].

Our study explores the editing activity of the super-editors (defined hereafter) in four separate Wikipedias (WP) [13], written in four different languages: English (EN-WP), Spanish (ES-WP), French (FR-WP) and Portuguese (PT-WP). In all cases, the data span a period of about ten years, ending between 2010 and 2011 (depending on the language). Each entry in the database contains the edited WP page name, the time stamp of the saving and the identification of the editor who performed the changes. Moreover, we discarded entries associated to IPs and bots, thus considering only editors who login before editing, so that the editor is univocally identified.

In [15] we have shown that WP editing is strongly influenced by the circadian cycle, as reported before by Yasseri et al. [16]. Here we analyze whether these circadian patterns have consequences on the inter-event probability distribution, namely we check whether the time between edits depends on the hour of the day at which the first edit has been carried out. To perform such an analysis we compute the conditional probability distribution for the inter-event time, considering that the first event has taken place within a specific hour of the day. If this conditional probability depends on that hour of the day, then we can conclude that circadian cycles have an influence on the human inter-event time and thus the origin of burstiness can possibly be ascribed to this dependence. In the opposite case we can conclude that burstiness in WP editing does not depend on the periodically changing conditions.

To summarize, in this work we provide numerical evidence that the conditional probability, P(τ|n ≤ t < n + 1), to have an inter-event of duration τ after an edit of WP registered at time t, such that n ≤ t < n + 1 is mainly independent from n. Moreover, this probability is fat-tailed and well described by a power law. It could be related to some sort of queuing process, but we prefer to see it as due to a resource allocation (attention, time, energy) process, which exhibits a broad distribution: shorter activities are more likely to be executed next than the longer ones, which ultimately may be responsible for the bursty nature of human behaviour.   Source: http://doi.org/10.1371/journal.pone.0174509

 

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