Related papers: Confidence Intervals and Hypothesis Testing for th…
Based on the data gained from a full-scale experiment, the order/disorder characteristics of the compartment fire temperatures are analyzed. Among the known permutation/encoding type entropies used to analyze time series, we look for those…
One of epileptology's fundamental aims is the formulation of a universal, internally consistent seizure definition. To assess this aim's feasibility, three signal analysis methods were applied to a seizure time series and performance…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
Permutation patterns-based approaches, such as permutation entropy (PerEn), have been widely and successfully used to analyze data. However, these methods have two main shortcomings. First, when a series is symbolized based on permutation…
Permutation Entropy, introduced by Bandt and Pompe, is a widely used complexity measure for real-valued time series that is based on the relative order of values within consecutive segments of fixed length. After standardizing each segment…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
The goal of animal movement analysis is to understand how organisms explore and exploit the complex and varying environment. Animals usually exhibit varied and complicated movements, from apparently deterministic behaviors to highly random…
Multiscale inherent fuzzy entropy is an objective measurement of electroencephalography (EEG) complexity, reflecting the habituation of brain systems. Entropy dynamics are generally believed to reflect the ability of the brain to adapt to a…
Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…
We study the fiber Lyapunov exponents of step skew-product maps over a complete shift of $N$, $N\ge2$, symbols and with $C^1$ diffeomorphisms of the circle as fiber maps. The systems we study are transitive and genuinely nonhyperbolic,…
Epilepsy, affecting approximately 50 million people globally, is characterized by abnormal brain activity and remains challenging to treat. The diagnosis of epilepsy relies heavily on electroencephalogram (EEG) data, where specialists…
Bandt and Pompe introduced Permutation Entropy in 2002 for Time Series where equal values, xt1 = xt2, t1 = t2, were neglected and only inequalities between the xt were considered. Since then, this measure has been modified and extended, in…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
Estimating the p-th frequency moment of data stream is a very heavily studied problem. The problem is actually trivial when p = 1, assuming the strict Turnstile model. The sample complexity of our proposed algorithm is essentially O(1) near…
Assessing whether two patient populations exhibit comparable event dynamics is essential for evaluating treatment equivalence, pooling data across cohorts, or comparing clinical pathways across hospitals or strategies. We introduce a…
Epilepsy is a brain disorder due to abnormalactivity of neurons and recording of seizures is of primary interest in the evaluation of epileptic patients. A seizureis the phenomenon of rhythmicity discharge from either a local area or the…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
In this paper, we propose a time-series stochastic model based on a scale mixture distribution with Markov transitions to detect epileptic seizures in electroencephalography (EEG). In the proposed model, an EEG signal at each time point is…
Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…
The concept of entropy in statistical physics is related to the existence of irreversible macroscopic processes. In this work, we explore a recently introduced entropy formula for a class of stochastic processes with more than one absorbing…