Universal Scaling Law in Human Behavioral Organization Toru Nakamura, 1 Ken Kiyono, 2 Kazuhiro Yoshiuchi, 3 Rika Nakahara, 4 Zbigniew R. Struzik, 5 and Yoshiharu Yamamoto 5, * 1 The Center for Advanced Medical Engineering and Informatics, Osaka University, 1–3 Machikaneyama, Toyonaka-shi, Osaka 560 –8531, Japan 2 College of Engineering, Nihon University, 1 Naka-gawara, Tokusada, Tamura-machi, Koriyama City, Fukushima, 963–8642, Japan 3 Department of Psychosomatic Medicine, Graduate School of Medicine, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo 113–8655, Japan 4 Department of Psychiatry, Teikyo University Mizonokuchi Hospital, 3–8–3 Mizonokuchi, Takatsu-ku, Kawasaki, Kanagawa 213–8507, Japan 5 Educational Physiology Laboratory, Graduate School of Education, The University of Tokyo, 7–3–1 Hongo, Bunkyo-ku, Tokyo 113–0033, Japan (Received 29 April 2007; published 28 September 2007) We describe the nature of human behavioral organization, specifically how resting and active periods are interwoven throughout daily life. Active period durations with physical activity count successively above a predefined threshold, when rescaled with individual means, follow a universal stretched exponential (gamma-type) cumulative distribution with characteristic time, both in healthy individuals and in patients with major depressive disorder. On the other hand, resting period durations below the threshold for both groups obey a scale-free power-law cumulative distribution over two decades, with significantly lower scaling exponents in the patients. We thus find universal distribution laws governing human behavioral organization, with a parameter altered in depression. DOI: 10.1103/PhysRevLett.99.138103 PACS numbers: 87.19.St, 05.40.a, 89.75.Da Universality in waiting time distributions is abundant in a wide range of complex systems: e.g., earthquake occur- rences [1,2], human communication [3,4], and in neuronal avalanches [5], where it has been associated with critical branching processes [6] and systems showing (on-off) intermittent dynamics [7]. In models of human dynamics at a macroscopic level of interhuman communication, a phenomenological priority concept has been suggested [3,4] to account for the non- Poisson statistics and universal scaling. Yet, the origins of the universality and the emergence of an apparent physical law of human communication dynamics are, to date, not evident. It is intriguing to observe that waiting time dis- tributions at microscopic scales of neuronal avalanches in neurocortical circuits [5] exhibit universality of an analog- ical class to that of decision making based human commu- nication dynamics, successfully modeled by a critical branching process [6]. However, a hierarchical distance in these multiscale human dynamics between the local neuronal circuits and social interactions is large. In this Letter, we reveal an analogical universality class in human behavior at an intermediate scale. By studying quantitatively how periods of lower levels of activity are interwoven with those of higher levels of activity through- out daily life, we identify the underlying criticality signa- ture of human behavioral organization governing the onset and termination of movement and its alterations in clinical depression [8]. We analyze so-called locomotor activity data in humans, capturing even slight bodily acceleration counts in a con- tinuous fashion (Fig. 1) and report a robust statistical law governing the temporal organization of periods of lower levels of activity (resting periods) and higher levels of activity (active periods). We find that the cumulative probability distribution of resting periods with lower levels of activity takes a power-law form over two decades, while the cumulative distribution of active periods with higher activity levels takes a stretched exponential form. Surprisingly, these statistical laws, after being rescaled by the mean waiting times, are not affected by altering the threshold value to calculate the waiting times. They share the distribution form for individuals considerably different in their daily living, and regardless of whether healthy or suffering from major depression, therefore suggesting the presence of universal laws governing human behavioral organization. Locomotor activity data, defined as counts of events in which an acceleration signal crosses zero-level within a predefined time, were acquired from 14 patients with major depressive disorder (age: 32:9  5:9 years; mean  S:D:) and 11 age-matched healthy control subjects (age: 32:7  15:7 years)[11]. Zero-crossing counts were accumulated for every 1 min, both in the patients and in the healthy controls. The activity sensors have the capability of detect- ing small changes in wrist acceleration (up to 0:01g) so that even slight movements of the subjects, ranging from, e.g., writing or working on a computer to physical exercise, are registered. Examples of locomotor activity data for a control sub- ject and a depression patient over 5 consecutive days (Fig. 1) show a clear circadian rest-activity cycle in the control subject, while in the patient, such a rhythmic pattern is much disrupted, reflecting the reported chrono- biological abnormality in depression [15 –17]. During the PRL 99, 138103 (2007) PHYSICAL REVIEW LETTERS week ending 28 SEPTEMBER 2007 0031-9007= 07=99(13)=138103(4) 138103-1  2007 The American Physical Society