Power law temporal auto-correlations in day-long records of human physical activity and their alteration with disease

¹ Department of Chemical Engineering, Northwestern University Evanston, IL 60208, USA
² International Center for Complex Systems and Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte - Natal, Brazil
³ Center for Polymer Studies and Department of Physics, Boston University Boston, MA 02215, USA
⁴ Department of Psychosomatic Medicine, The University of Tokyo Hospital Tokyo 113-8655, Japan
⁵ Educational Physiology Laboratory, Graduate School of Education The University of Tokyo - Tokyo 113-0033, Japan
⁶ PRESTO, Japan Science and Technology Corporation - Saitama 332-0012, Japan

Received: 4 November 2003
Accepted: 3 March 2004

Abstract

We investigate long-duration time series of human physical activity under three different conditions: healthy individuals in i) a constant routine protocol and ii) in regular daily routine, and iii) individuals diagnosed with multiple chemical sensitivities. We find that in all cases human physical activity displays power law decaying temporal auto-correlations. Moreover, we find that under regular daily routine, time correlations of physical activity are significantly different during diurnal and nocturnal periods but that no difference exists under constant routine conditions. Finally, we find significantly different auto-correlations for diurnal records of patients with multiple chemical sensitivities.