Derangetropy in Probability Distributions and Information Dynamics.

We introduce derangetropy, which is a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation that captures the dispersion of information across the entire support of a distribution. By incorporating self-referential and periodic properties, it provides insights into information dynamics governed by differential equations and equilibrium states.

Theory of Lehmer transform and its applications in identifying the electroencephalographic signature of major depressive disorder.

We propose a novel transformation called Lehmer transform and establish a theoretical framework used to compress and characterize large volumes of highly volatile time series data. The proposed method is a powerful data-driven approach for analyzing extreme events in non-stationary and highly oscillatory stochastic processes like biological signals. The proposed Lehmer transform decomposes the information contained in a function of the data sample into a domain of some statistical moments.