Diagnostics of the Synchronization of Self-Oscillatory Systems by an External Force with Varying Frequency with the Use of Wavelet Analysis

A diagnostics method based on a continuous wavelet transform is proposed. This method makes it possible to diagnose the presence of synchronization of the oscillations of a self-excited oscillator locked by an external force with a linearly modulated frequency and to distinguish such a situation from the case when an external signal leaks into self-oscillations; i.e., the signals are summed without a change in the self-oscillation frequency. The method's efficiency is shown with the use of a Van der Pol generator and experimental physiological data as examples.Comment: 11 pages, 9 figure

Novel approach to analysing large data sets of personal sun exposure measurements

Personal sun exposure measurements provide important information to guide the development of sun awareness and disease prevention campaigns. We assess the scaling properties of personal ultraviolet radiation (pUVR) sun exposure measurements using the wavelet transform (WT) spectral analysis to process long-range, high-frequency personal recordings collected by electronic UVR dosimeters designed to measure erythemal UVR exposure. We analysed the sun exposure recordings of school children, farmers, marathon runners and outdoor workers in South Africa, and construction workers and work site supervisors in New Zealand. We found scaling behaviour in all the analysed pUVR data sets. We found that the observed scaling changes from uncorrelated to long-range correlated with increasing duration of sun exposure. Peaks in the WT spectra that we found suggest the existence of characteristic times in sun exposure behaviour that were to some extent universal across our data set. Our study also showed that WT measures enable group classification, as well as distinction between individual UVR exposures, otherwise unattainable by conventional statistical methods

Operator hyperreflexivity of subspace lattices

Abstract. We introduce and study the notion of operator hyperreflexivity of subspace lattices. This notion is a natural analogue of the operator reflexivity and is related to hyperreflexivity of subspace lattices introduced by Davidson and Harrison. 1