Physical aging in article page views

Yeseul Kim,∗ Kun Cho,∗ and Byung Mook Weon†

Soft Matter Physics Laboratory, School of Advanced Materials Science and Engineering,SKKU Advanced Institute of Nanotechnology (SAINT),

Sungkyunkwan University, Suwon 440-746, Korea(Dated: November 6, 2018)

Statistics of article page views is useful for measuring the impact of individual articles. Analyzingthe temporal evolution of article page views, we find that article page views usually decay over timeafter reaching a peak, especially exhibiting relaxation with nonexponentiality. This finding suggeststhat relaxation in article page views resembles physical aging as frequently found in complex systems.

Keywords: Statistics, Article page views, Physical aging, Relaxation

INTRODUCTION

Nowadays, many scientific journals promote onlinepublication, which is efficient in distributing research im-pact through web-based communities. Once a researcharticle is published online on a journal website, the publiccan access the article immediately [1]. Counting articlepage views is an alternative method to measure the im-pact of individual articles, instead of the journal impactfactor [2–5]. Empirically, when an article receives at-tention, its daily page views will reach a peak and thenshould decay with time, which is similar to a physical re-laxation process. A recent study raised the possibility ofa universal decay pattern in article page views, based onobservations from six different PLoS journals [1]. How-ever, it remains unclear what mathematical model is ap-propriate for statistics in article page views.

Physical aging is the spontaneous temporal evolutionof out-of-equilibrium systems [6]. Glasses, for instance,usually show relaxation toward equilibrium, which iscommonly referred to as physical aging [7]. Nonexponen-tial relaxation is ubiquitous in complex systems. Nonex-ponentiality in relaxation is frequently described by thestretched exponential [8–10] or the Kohlrausch-Williams-Watts (KWW) decay function [11, 12] (also known as theWeibull function [13]): s = exp[−(t/α)β ], where the char-acteristic lifetime α corresponds to the specific lifetimefor s = exp(−1) and the stretched exponent β reflects thenonexponentiality. The simple exponential decay corre-sponds to β = 1 and the classical stretched exponentialdecay to 0 < β < 1 (classically β is invariant). Particu-larly, the stretched exponent is associated with a cascademechanism of relaxation [7].

In this study, we utilize reliable statistical data of ar-ticle page views that are available in Scientific Reportsfor articles published after 1 January 2012. Data fordaily page views including HTML views and PDF down-loads are offered 48 hours after online publication andupdated daily. Here, we suggest a useful methodology forevaluating the nonexponentiality in article page views byadopting a modified stretched exponential function [14–18]. This study shows the possibility that relaxation in

article page views resembles physical aging as frequentlyfound in complex systems.

RESULTS

We selected two datasets: the first comprised 42 ar-ticles from Scientific Reports published in 2012 and thesecond comprised 19 articles published between Januaryand May in 2015, showing more than 1,000 daily pageviews in a few days after online publication.

First, we counted the number of page views (pt) attime t (days) normalized by the number of initially max-imized page views (p0). The attention rate can be definedas s = pt/p0 and usually decreases with time from theinitial peak. Empirically, there would be three types ofpublic attention: initial attention at time t0, irregularattention at time t, and no attention (for insignificantp0). For demonstration, the normalized page views forthe two datasets are illustrated by the normal scales inFig 1A-B. As illustrated, the maximum peak can existat the origin of time, indicating the initial attention, anda few peaks can exist in the middle stage, indicating ir-regular attention. To examine whether the normalizedpage views have power-law time dependencies, we de-picted the log-log plots in Fig 1C-D by simply rescalingFig 1A-B. Here the straightness in the log-log plots isnot manifested, which means that the power-law scalingof s vs t is invalid. Such a temporal behavior in s vs t isrepeatable for both datasets.

Next, we tested the nonexponentiality in the normal-ized page views. A convenient methodology is the adop-tion of a modified stretched exponential function. Thisfunction is described as s = exp[−(t/α)β ] with the char-acteristic lifetime α and the stretched exponent β, espe-cially where β varies with time [14, 15]. This functionwas originally adopted to describe complicated biologicalsurvival curves [16–18]. The stretched exponent is calcu-lated as β = ln[− ln(s)]/ ln(t/α) from the α values. Thecharacteristic lifetime α can be measured by detectingthe interception point between s(t) and s(α) = exp(−1).The rough α estimate can be obtained from a linear re-

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FIG. 1: Statistics of article page views after onlinepublication. The first dataset (A,C,E) contains 42 articlesselected from Scientific Reports published in 2012 and the sec-ond dataset (B,D,F) contains 19 articles published betweenJanuary and May in 2015, showing more than 1,000 viewsat the early stage of online publication. The normalized pageviews over time are described by normal scales (A,B) and log-arithmic scales (C,D). The temporal evolution of stretched ex-ponents is obtained from the normalized page views, showingnonexponentiality in relaxation for both cases. As a guide,srep00223 (A,C,D) and srep07971 (B,E,F) are marked withbold solid lines.

gression from two data points that exist just above (+1p)and just below (−1p) the exp(−1) point for each s vs tcurve [18]. Here the stretched exponent is a good measurefor testing the nonexponentiality of a decay curve and isrelevant to an asymmetrical broadening of the relaxationtime distribution [9].

As illustrated in Fig 1E-F, we are able to see the non-exponentiality of the normalized page views for the twodifferent datasets published in Scientific Reports. In-terestingly, the stretched exponents behave irregularlyover a short period (shorter than 10 days approximately)and then gradually decrease with time over a long period(longer than 10 days).

DISCUSSION

Our finding from the page view statistics suggests thatpublic attention in research is similar to physical relax-ation processes in complex systems. Social media areindeed complex systems that actively connect people ev-ery day. Interestingly, the temporal evolution of thestretched exponents in the normalized page views is iden-tical to that of luminescence decays: the stretched expo-nents become smaller than unity and gradually decreasewith time (see refs. [14, 15]). Public attention and phys-ical perturbation would be alike in terms of the time evo-lution of impact and information propagation. A stochas-tic model for information propagation would be relevantto the nonexponentiality of page view statistics [1]. Fur-ther studies would be necessary on statistical analysesfor a universal decay pattern in page views with widedatasets.

In summary, we present a novel statistical approach forarticle page views for online published articles. A signifi-cant finding is obtained: article page views usually decayover time after reaching a peak, especially exhibiting non-exponentiality. A feasible methodology is suggested forevaluation of the nonexponentiality. Our study showsthat article page views follow nonexponential decay aspublic attention propagates through web-based commu-nities, as frequently found in complex systems.

Acknowledgments

This work was supported by Sungkyun Research Fund,Sungkyunkwan University, 2014.

∗ These authors contributed equally to this article.† Electronic address: B.M.W. (bmweon@skku.edu)

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