Random heterogeneity outperforms design in network synchronization

A widely held assumption on network dynamics is that similar components are more likely to exhibit similar behavior than dissimilar ones and that generic differences among them are necessarily detrimental to synchronization. Here, we show that this assumption does not generally hold in oscillator networks when communication delays are present. We demonstrate, in particular, that random parameter heterogeneity among oscillators can consistently rescue the system from losing synchrony. This finding is supported by electrochemical-oscillator experiments performed on a multielectrode array network. Remarkably, at intermediate levels of heterogeneity, random mismatches are more effective in promoting synchronization than parameter assignments specifically designed to facilitate identical synchronization. Our results suggest that, rather than being eliminated or ignored, intrinsic disorder in technological and biological systems can be harnessed to help maintain coherence required for function.

Self-Evaluation, Differential Item Functioning, and Longitudinal Anchoring Vignettes

Anchoring vignettes are a powerful instrument to detect systematic differences in the use of self-reported ordinal survey responses. Not taking into account the (non-random) heterogeneity in reporting styles across different respondents may systematically bias the measurement of the variables of interest. The presence of such individual heterogeneity leads respondents to interpret, understand, or use the response categories for the same question differently. This phenomenon is defined as differential item functioning (DIF) in the psychometric literature. A growing amount of cross-sectional studies apply the anchoring vignette approach to tackle this issue but its use is still limited in the longitudinal context. This chapter introduces longitudinal anchoring vignettes for DIF correction, as well as the statistical approaches available when working with such data and how to investigate stability over time of individual response scales.