Theil Entropy as a Non-Lineal Analysis for Spectral Inequality of Physiological Oscillations

Abstract

Theil entropy is a statistical measure used in economics to quantify income inequalities. However, it can be applied to any data distribution including biological signals. In this work, we applied different spectral methods on heart rate variability signals and cellular calcium oscillations previously to Theil entropy analysis. The behavior of Theil entropy and its decomposable property was investigated using exponents in the range of [−1, 2], on the spectrum of synthetic and physiological signals. Our results suggest that the best spectral decomposition method to analyze the spectral inequality of physiological oscillations is the Lomb–Scargle method, followed by Theil entropy analysis. Moreover, our results showed that the exponents that provide more information to describe the spectral inequality in the tested signals were zero, one, and two. It was also observed that the intra-band component is the one that contributes the most to total inequality for the studied oscillations. More in detail, we found that in the state of mental stress, the inequality determined by the Theil entropy analysis of heart rate increases with respect to the resting state. Likewise, the same analytical approach shows that cellular calcium oscillations present on developing interneurons display greater inequality distribution when inhibition of a neurotransmitter system is in place. In conclusion, we propose that Theil entropy is useful for analyzing spectral inequality and to explore its origin in physiological signals.

Spatiotemporal Differences in Marine Environment Quality in China and the Influencing Factors

“…Due to its good decomposability, the Theil index has been extended from its early use in studying income inequality to other fields, such as economics and ecology. It is mainly used to analyze regional overall differences, inter-regional and intra-regional differences, and the contribution of intra-group and inter-group differences to the total gap [48]. We used the Theil index to calculate the degree of difference in regional MEQ, and the specific formula is as follows:…”

Determinants of Inclusive Economic Growth in Latin America

“…Also, there are other indicators, such as the Theil index, proposed by Henry Theil in 1967, which measures inequality, having as an advantage that it can be broken down into subgroups; this is because it takes the basis of the concept of entropy; also, this index "complies with the additive decomposition property," characteristic that differentiates it from other indices by allowing "to know what percentage of inequality is explained by the inequality that is generated between the groups formed and which one comes from the differences of income within them," [39], (p. 18). Finally, Carrazana, Sánchez & Ávila, [40], conclude that the entropy of Theil presents desirable characteristics as an indicator of inequality, among them that it is independent of population size and scale and can be broken down into each of its elements. In this line, according to INEI, [41], Latin American countries have very high rates of exclusion generated by inequality in income distribution and poverty; because of this, these countries are characterized by their disintegrated and fragmented societies.…”