Detection and characterization of dynamical heterogeneity in an event series using wavelet correlation

A method that combines wavelet-based multiscale decomposition with correlation statistical analysis to extract, detect, and characterize time-dependent variations in the spectral response of a system has been developed. The approach is independent of the distribution of the observable and does not rely on any presumed kinetic model for the system's dynamical response. It provides a quantitative and objective framework for studies of complex systems exhibiting dynamics that are nonuniform in time. Applying this method to computer simulated data, it is shown that the wavelet correlation approach is capable of resolving the size fluctuations in a single nanostructure by single-molecule tracking spectroscopy.