Abstract
The distribution of intervals between human actions such as email posts or keyboard strokes demonstrates distinct properties at short versus long timescales. For instance, at long timescales, which are presumably controlled by complex process such as planning and decision making, it has been shown that those interevent intervals follow a scale-invariant (or power-law) distribution. In contrast, at shorter timescales-which are governed by different processes such as sensorimotor skill-they do not follow the same distribution and we know little about how they relate to the scale-invariant pattern. Here, we analyzed 9 million intervals between smartphone screen touches of 84 individuals which span several orders of magnitudes (from milliseconds to hours). To capture these intervals, we extend a priority-based generative model to smartphone touching events. At short timescale, the model is governed by refractory effects, while at longer timescales, the intertouch intervals are governed by the priority difference between smartphone tasks and other tasks. The flexibility of the model allows us to capture interindividual variations at short and long timescales, while its tractability enables efficient model fitting. According to our model, each individual has a specific power-law exponent which is tightly related to the effective refractory time constant suggesting that motor processes which influence the fast actions are related to the higher cognitive processes governing the longer interevent intervals.
Highlights
Human actions such as mail correspondences, library loans, or website visits are not distributed in time but are typically structured in bursts followed by long periods of inactivity [1,2,3]
Priority-based queuing models [4,5,6,7,8,9] rely on one list(s) of tasks to be executed, where each task is associated with a priority level which directly influences the timing of its execution. This class of models have been pioneered by Barabási [4] and generalized to multiple interacting queues [7,9], time-varying priorities [10], or priorities which depend on the position within the list of tasks [11]. Those models provide an interesting interpretation for the origin of the power-law scaling for long intervals but are usually not designed to capture short interevent timings
We found that for each individual the empirical intertouch interval (ITI) distribution [see Fig. 4(a)] is well captured by the model both for the short timescales which is strongly influenced by the refractory kernel r(t ) [see Fig. 4(c)] as well as the longer ITI which has a typical power-law decay
Summary
Human actions such as mail correspondences, library loans, or website visits are not distributed in time but are typically structured in bursts followed by long periods of inactivity [1,2,3]. This class of models have been pioneered by Barabási [4] and generalized to multiple interacting queues [7,9], time-varying priorities [10], or priorities which depend on the position within the list of tasks [11] Those models provide an interesting interpretation for the origin of the power-law scaling for long intervals (they come from prioritizing tasks) but are usually not designed to capture short interevent timings. Our priority-based model does describe long interevent intervals and includes a detailed description of short interevent intervals and thereby overcomes the need to define an arbitrary onset of the powerlaw distribution [20] It assumes that the agent remains in a so-called refractory state during a short time after each event, where the probability of generating a new event is reduced. We found that from those fitted parameters, we can quantify the relative priority placed on smartphone actions
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