Fluctuation scaling in complex systems: Taylor's law and beyond

Complex systems consist of many interacting elements which participate in some dynamical process. The activity of various elements is often different and the fluctuation in the activity of an element grows monotonically with the average activity. This relationship is often of the form "$fluctuations \approx const.\times average^\alpha$", where the exponent $\alpha$ is predominantly in the range $[1/2, 1]$. This power law has been observed in a very wide range of disciplines, ranging from population dynamics through the Internet to the stock market and it is often treated under the names \emph{Taylor's law} or \emph{fluctuation scaling}. This review attempts to show how general the above scaling relationship is by surveying the literature, as well as by reporting some new empirical data and model calculations. We also show some basic principles that can underlie the generality of the phenomenon. This is followed by a mean-field framework based on sums of random variables. In this context the emergence of fluctuation scaling is equivalent to some corresponding limit theorems. In certain physical systems fluctuation scaling can be related to finite size scaling.Comment: 33 pages, 20 figures, 2 tables, submitted to Advances in Physic

Functional independence in the Finnish spinal cord injury population

Abstract Study design: A cross-sectional survey of the Finnish population with spinal cord injury (FinSCI database). Objectives: To describe the functional independence of the population with spinal cord injury (SCI) in Finland and to identify how generic and lesion characteristics affect their functional independence. Setting: The participants were recruited from the registers of three SCI outpatient clinics responsible for lifelong follow-up and care for people with SCI in Finland. Methods: The data were retrieved from FinSCI (n = 1772). The response rate was 50% (n = 884). The Spinal Cord Independence Measure-Self Report (SCIM-SR) was used. The data were analyzed with univariate testing, factor analyses, and multiple linear regression models. Results: The median (percentiles 25; 75) SCIM-SR total score was 76.0 (58.8; 89.0), and the score was 18.0 (13.0; 20:0) for the self-care sub-scale, 33.0 (25.0; 39.0) for the respiration and sphincter management sub-scale and 29.0 (16.0; 36.8) for the mobility sub-scale. The higher the neurological level in groups AIS A, B, and C, the lower the functional ability. Group AIS D at any injury level had the highest level of functional ability. Age and the number of years since injury negatively influenced the SCIM-SR scores for every sub-scale. Conclusion: Based on the International Spinal Cord Injury Core Data Set, the severity of SCI can differentiate persons with SCI according to their functional ability. The results suggest that SCI affects individuals’ health more than ageing alone does, thereby reducing the functional ability and independence of persons with SCI over time