Patterns of deliberate human activity and behavior are of utmost importance in areas as diverse as disease spread, resource allocation, and emergency response. Because of its widespread availability and use, e-mail correspondence provides an attractive proxy for studying human activity. Recently, it was reported that the probability density for the inter-event time between consecutively sent e-mails decays asymptotically as ؊␣ , with ␣ Ϸ 1. The slower-than-exponential decay of the inter-event time distribution suggests that deliberate human activity is inherently non-Poissonian. Here, we demonstrate that the approximate power-law scaling of the inter-event time distribution is a consequence of circadian and weekly cycles of human activity. We propose a cascading nonhomogeneous Poisson process that explicitly integrates these periodic patterns in activity with an individual's tendency to continue participating in an activity. Using standard statistical techniques, we show that our model is consistent with the empirical data. Our findings may also provide insight into the origins of heavy-tailed distributions in other complex systems.complex systems ͉ human activity ͉ hypothesis testing ͉ point process T he analysis of social and economic data has a long and illustrious history (1-3). Despite their idiosyncratic complexity, a number of striking statistical regularities are known to describe individual and societal human behavior (4-7). These regularities are of enormous practical importance because they provide insight into how individual behaviors influence social and economic outcomes. Indeed, much of the current research on complex systems aims to quantify the impact of individual agents on the organization and dynamics of the system as a whole (8, 9). Before we can predict how individuals affect, for example, the organization of systems, it is paramount to understand the behavior of the individual agents.The current availability of digital records has made it much easier for researchers to quantitatively investigate various aspects of human behavior (10-21). In particular, e-mail communication records are attracting much attention as a proxy for quantifying deliberate human behavior because of the omnipresence of e-mail communication and availability of e-mail records (13,14,16,18). The data, however, do not provide a detailed record of all of the activities in which each individual participates; we do not know, for instance, when an individual is sleeping, eating, walking, or even browsing the web. The resulting uncertainty in deliberate human activity thus poses a fundamental challenge to quantifying and modeling of human behavior.Researchers commonly account for uncertainty or lack of information through stochastic models. One of the simplest stochastic models for human activity is a point process in which independent events occur at a constant rate . Such processes are referred to as homogeneous Poisson processes, and they are used to describe a large class of phenomena, including some aspects of human act...
Identifying and modeling patterns of human activity has important ramifications in applications ranging from predicting disease spread to optimizing resource allocation. Because of its relevance and availability, written correspondence provides a powerful proxy for studying human activity. One school of thought is that human correspondence is driven by responses to received correspondence, a view that requires distinct response mechanism to explain e-mail and letter correspondence observations. Here, we demonstrate that, like e-mail correspondence, the letter correspondence patterns of 16 writers, performers, politicians, and scientists are well-described by the circadian cycle, task repetition and changing communication needs. We confirm the universality of these mechanisms by properly rescaling letter and e-mail correspondence statistics to reveal their underlying similarity.Power-law statistics are a hallmark of critical phenomena. A less obvious characteristic of crit-1
Studying the interaction between a system's components and the temporal evolution of the system are two common ways to uncover and characterize its internal workings. Recently, several maps from a time series to a network have been proposed with the intent of using network metrics to characterize time series. Although these maps demonstrate that different time series result in networks with distinct topological properties, it remains unclear how these topological properties relate to the original time series. Here, we propose a map from a time series to a network with an approximate inverse operation, making it possible to use network statistics to characterize time series and time series statistics to characterize networks. As a proof of concept, we generate an ensemble of time series ranging from periodic to random and confirm that application of the proposed map retains much of the information encoded in the original time series (or networks) after application of the map (or its inverse). Our results suggest that network analysis can be used to distinguish different dynamic regimes in time series and, perhaps more importantly, time series analysis can provide a powerful set of tools that augment the traditional network analysis toolkit to quantify networks in new and useful ways.
The role of mentorship in protégé performance is a matter of importance to academic, business and governmental organizations. Although the benefits of mentorship for protégés, mentors and their organizations are apparent, the extent to which protégés mimic their mentors' career choices and acquire their mentorship skills is unclear. The importance of a science, technology, engineering and mathematics workforce to economic growth and the role of effective mentorship in maintaining a 'healthy' such workforce demand the study of the role of mentorship in academia. Here we investigate one aspect of mentor emulation by studying mentorship fecundity-the number of protégés a mentor trains-using data from the Mathematics Genealogy Project, which tracks the mentorship record of thousands of mathematicians over several centuries. We demonstrate that fecundity among academic mathematicians is correlated with other measures of academic success. We also find that the average fecundity of mentors remains stable over 60 years of recorded mentorship. We further discover three significant correlations in mentorship fecundity. First, mentors with low mentorship fecundities train protégés that go on to have mentorship fecundities 37% higher than expected. Second, in the first third of their careers, mentors with high fecundities train protégés that go on to have fecundities 29% higher than expected. Finally, in the last third of their careers, mentors with high fecundities train protégés that go on to have fecundities 31% lower than expected.
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