We investigated the possibility of estimating network link weights from the multivariate time series of phase oscillators on a complex network. The inverse phase synchronization index of the coupled oscillator network is found to grow in proportion to the corresponding link weight, as network synchronization occurs for a strong coupling strength. This implies that the network link weights can be estimated from the measurement of the inverse phase synchronization indices. By adopting this estimation method, we successfully reconstructed the minimal spanning tree of the original network from the inverse phase synchronization indices. Even for the weak coupling case, the estimation of the network link weights could be improved significantly by taking the average of a sufficiently large number of configurations.

Electricity demand is influenced by atmospheric conditions, and, therefore it is important to quantify their relationships suitably for accurate electricity demand forecasting and the implementation of power-saving policies. However, interdependencies and characteristics of covariance among meteorological variables within the same periodicities hinder the quantification of their direct and indirect impacts on electric power load. To investigate the strength of the direct correlation between atmospheric conditions and electric power load, this study harnessed a new partialization analysis method based on a partial phase synchronization index combined with wavelet transformation. The advantage of the proposed method is that it can be used to evaluate the degree of independent contribution of the variables over different spatiotemporal scales. Compared with traditional statistical analyses, this new partialization analysis shows that air temperature is the principal variable associated directly with electricity demand, but that the strength of the relationship varies with season and time scale. Relative humidity and wind speed have strong direct correlations with electricity in summer and winter, respectively. Insolation is directly coupled to the electric power load only on sub-diurnal time scales. This investigation indicates that for accurate forecasting of electricity demand, changes in the coupling strengths of different atmospheric variables should be incorporated into the electric power load forecasting process. The study shows that a partial phase synchronization index, combined with wavelet transformation, is a useful tool that could be used in other studies to assess complex interacting atmospheric oscillations that cannot be assessed properly by traditional approaches.

Electroencephalography amplitude, phase synchronization, and directionality of phase coupling within and between hemispheres were compared for different frequency components in 27 healthy individuals before and after 5 days of daily 1 Hz repetitive transcranial magnetic stimulation (rTMS), and at 2 weeks after the last session. Instantaneous amplitudes of α (8-13 Hz) and β (13-30 Hz) frequency components were increased after daily rTMS, the effects of which were declining over time, suggesting an adapting response with repeated rTMS sessions. The phase synchronization of electroencephalography increased significantly in the α frequency, especially the upper-α band (11-13 Hz), in both the frontal and the temporal areas, predominantly in the ipsilateral hemisphere. Asymmetric directional interactions of the upper-α band were stronger from the stimulated area to the contralateral hemisphere. No significant differences were found at 2 weeks after rTMS in any of these values. Focal 1 Hz rTMS induces an enhancement in the ipsilateral dominant corticocortical interaction drastically by interhemispheric asymmetric coupling from the stimulated cortical area with an adapting response with repeated sessions. This kind of method can be valuable for possible clinical applications in various neuropsychiatric conditions to study the therapeutic mechanisms of 1 Hz rTMS.