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

Tumour budding in oral squamous cell carcinoma : a meta-analysis

Background: Tumour budding has been reported as a promising prognostic marker in many cancers. This meta-analysis assessed the prognostic value of tumour budding in oral squamous cell carcinoma (OSCC). Methods: We searched OvidMedline, PubMed, Scopus and Web of Science for articles that studied tumour budding in OSCC. We used reporting recommendations for tumour marker (REMARK) criteria to evaluate the quality of studies eligible for meta-analysis. Results: A total of 16 studies evaluated the prognostic value of tumour budding in OSCC. The meta-analysis showed that tumour budding was significantly associated with lymph node metastasis (odds ratio = 7.08, 95% CI = 1.75-28.73), disease-free survival (hazard ratio = 1.83, 95% CI = 1.34-2.50) and overall survival (hazard ratio = 1.88, 95% CI = 1.25-2.82). Conclusions: Tumour budding is a simple and reliable prognostic marker for OSCC. Evaluation of tumour budding could facilitate personalised management of OSCC.Peer reviewe