Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind

Impact of environmental changes on the dynamics of temporal networks

Dynamics of complex social systems has often been described in the framework of temporal networks, where links are considered to exist only at the moment of interaction between nodes. Such interaction patterns are not only driven by internal interaction mechanisms, but also affected by environmental changes. To investigate the impact of the environmental changes on the dynamics of temporal networks, we analyze several face-to-face interaction datasets using the multiscale entropy (MSE) method to find that the observed temporal correlations can be categorized according to the environmental similarity of datasets such as classes and break times in schools. By devising and studying a temporal network model considering a periodically changing environment as well as a preferential activation mechanism, we numerically show that our model could successfully reproduce various empirical results by the MSE method in terms of multiscale temporal correlations. Our results demonstrate that the environmental changes can play an important role in shaping the dynamics of temporal networks when the interactions between nodes are influenced by the environment of the systems.

Rényi entropy yields artificial biases not in the data and incorrect updating due to the finite-size data

We show that the Rényi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite size of the data despite being additive. It is demonstrated that this is so because it does not conform to the system and subset independence axioms of Shore and Johnson [J. IEEE Trans. Inf. Theory 26, 26 (1980)IETTAW0018-944810.1109/TIT.1980.1056144]. We finally show that the escort averaged constraints do not remedy the situation.

Bi-dimensional multiscale entropy: Relation with discrete Fourier transform and biomedical application

The multiscale entropy (MSE_1D) measure is now widely used to quantify the complexity of time series. The development of complexity measures for images is also a long-standing goal. Recently, the bi-dimensional version of MSE_1D has been proposed (MSE_2D) to analyze images. The interpretation of MSE_2D curves and the applications to real data are still emergent. Because the coarse-graining step in the MSE_2D computation changes the frequency content of the image, we hypothesized a possible dependence between MSE_2D and the discrete Fourier transform (DFT). To analyze this dependence, synthetic as well as biomedical images are analyzed. Our results reveal that i) the profile of MSE_2D is sensitive to both the amplitude and phase of the DFT; ii) MSE_2D could find applications in the biomedical field. This work brings valuable information for MSE_2D interpretation and opens possibilities to study images from an entropy point of view through spatial scales.