Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching...
Approximate Entropy and Sample Entropy are two algorithms for determining the regularity of series of data based on the existence of patterns. Despite their similarities, the theoretical ideas behind those techniques are different but usually ignored...
Computational textual aesthetics aims at studying observable differences between aesthetic categories of text. We use Approximate Entropy to measure the (un)predictability in two aesthetic text categories, i.e., canonical fiction (‘classics&rsq...
Approximate entropy (ApEn) is used as a nonlinear measure of heart-rate variability (HRV) in the analysis of ECG time-series recordings. Previous studies have reported that HRV can differentiate between frail and pre-frail people. In this study, EEGs...
The classification recognition rate of motor imagery is a key factor to improve the performance of brain–computer interface (BCI). Thus, we propose a feature extraction method based on discrete wavelet transform (DWT), empirical mode decomposit...
Neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS), Parkinson’s diseases (PD), and Huntington’s disease (HD) are not rare neurological diseases. They affect different neurological systems and present various characteri...
Chatter is a complex dynamic instability in machining processes and presents nonlinear and nonstationary behavior. Detection of this phenomenon before a catastrophic failure occurs has great importance in the industry today. This behavior demands onl...
Wind energy is a clean, sustainable, and renewable source. It is receiving a large amount of attention from governments and energy companies worldwide as it plays a significant role as an alternative source of energy in reducing carbon emissions. How...
Given the chaotic characteristics of the time series of landslides, a new method based on modified ensemble empirical mode decomposition (MEEMD), approximate entropy and the weighted least square support vector machine (WLS-SVM) was proposed. The met...
Dissolved gas analysis (DGA) in transformer oil, which analyzes its gas content, is valuable for promptly detecting potential faults in oil-immersed transformers. Given the limitations of traditional transformer fault diagnostic methods, such as insu...
Evaluating brain function through biosignals remains challenging. Quantitative electroencephalography (qEEG) outcomes have emerged as a potential intermediate biomarker for diagnostic clarification in psychological disorders. The Test of Variables of...
The present study aimed at testing the hypothesis that application of multiscale cross-approximate entropy (MCAE) analysis in the study of nonlinear coupling behavior of two synchronized time series of different natures [i.e., R-R interval (RRI) and...
The suboesophageal ganglion (SOG), which connects to both central and peripheral nerves, is the primary taste-processing center in the Drosophila’s brain. The neural oscillation in this center may be of great research value yet it is rarely reported....
Approximate entropy (ApEn) and sample entropy (SampEn) are statistical indices designed to quantify the regularity or predictability of time-series data. Although ApEn has been a prominent choice in analyzing non-linear data, it is currently unclear...
Many regional hydrological regime changes are complex under the influences of climate change and human activities, which make it difficult to understand the regional or basin al hydrological status. To investigate the complexity of precipitation and...
Existing works have paid scant attention to the multivariate entropy of complex data. Thus, existing methods perform poorly in fully exposing the nature of complex data. To mine a rich vein of data features, this paper applies a shuffle and surrogate...
Self-organized criticality theory proved that information transmission and computational performances of neural networks are optimal in critical state. By using recordings of the spontaneous activity originated by dissociated neuronal assemblies coup...
A rolling bearing early fault diagnosis method is proposed in this paper, which is derived from a refined composite multi-scale approximate entropy (RCMAE) and improved coyote optimization algorithm based probabilistic neural network (ICOA-PNN) algor...
Partial discharge (PD) fault diagnosis is of great importance for ensuring the safe and stable operation of power transformers. To address the issues of low accuracy in traditional PD fault diagnostic methods, this paper proposes a novel method for t...
Obstructive sleep apnea (OSA) is a fatal respiratory disease occurring in sleep. OSA can induce declined heart rate variability (HRV) and was reported to have autonomic nerve system (ANS) dysfunction. Variance delay fuzzy approximate entropy (VD_fApE...
To eliminate the influence of white noise in partial discharge (PD) detection, we propose a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and approximate entropy (ApEn). By introducing adaptive noi...
In this paper, we investigate a lossy source coding problem, where an upper limit on the permitted distortion is defined for every dataset element. It can be seen as an alternative approach to rate distortion theory where a bound on the allowed avera...
Approximation of entropies of various types using machine learning (ML) regression methods are shown for the first time. The ML models presented in this study define the complexity of the short time series by approximating dissimilar entropy techniqu...
The empirical entropy is a key statistical measure of data frequency vectors, enabling one to estimate how diverse the data are. From the computational point of view, it is important to quickly compute, approximate, or bound the entropy. In a distrib...
Cardiac autonomic neuropathy (CAN) is a common complication of diabetes mellitus, and can be assessed using heart rate variability (HRV) and the correlations between systolic blood pressure (SBP) and ECG R-R intervals (RRIs), namely baroreflex sensit...
Multiscale cross-approximate entropy (MC-ApEn) between two different physiological signals could evaluate cardiovascular health in diabetes. Whether MC-ApEn analysis between two similar signals such as photoplethysmographic (PPG) pulse amplitudes of...
We propose a minimum variance unbiased approximation to the conditional relative entropy of the distribution induced by the observed frequency estimates, for multi-classification tasks. Such approximation is an extension of a decomposable scoring cri...
In the present paper, we propose a large sample asymptotic approximation for the sampling and posterior distributions of differential entropy when the sample is composed of independent and identically distributed realization of a multivariate normal...
In through wall imaging, clutter plays an important role in the detection of objects behind the wall. In the literature, extensive studies have been carried out to eliminate clutter in the case of targets with the same dielectric. Existing clutter re...
Human brain, a dynamic complex system, can be studied with different approaches, including linear and nonlinear ones. One of the nonlinear approaches widely used in electroencephalographic (EEG) analyses is the entropy, the measurement of disorder in...
This study discusses the calculation of entropy of discrete-time stochastic biological systems. First, measurement methods of the system entropy of discrete-time linear stochastic networks are introduced. The system entropy is found to be characteriz...
The body’s postural control system is responsible for responding to perturbations of balance and keeping the body upright. During quiet standing, the center of pressure oscillates about the center of mass, counteracting imbalances. These oscill...
To avoid structural failures it is of critical importance to detect, locate and quantify impact damage as soon as it occurs. This can be achieved by impact identification methodologies, which continuously monitor the structure, detecting, locating, a...
Sandwich structures are very attractive due to their high strength at a minimum weight, and, therefore, there has been a rapid increase in their applications. Nevertheless, these structures may present imperfect bonding or debonding between the skins...
This paper is devoted to the experimental study of the integral approximation method in entropy optimization problems arising from the application of the Randomized Machine Learning method. Entropy-optimal probability density functions contain normal...
Approximate Entropy and especially Sample Entropy are recently frequently used algorithms for calculating the measure of complexity of a time series. A lesser known fact is that there are also accelerated modifications of these two algorithms, namely...
Heart rate variability (HRV) analysis is a non-invasive tool for assessing cardiac health. Entropy measures quantify the chaotic properties of HRV, but they are sensitive to the choice of their required parameters. Previous studies therefore have per...
Heart rate variability (HRV) is a non-invasive measurement based on the intervals between normal heart beats that characterize cardiac autonomic function. Decreased HRV is associated with increased risk of cardiovascular events. Characterizing HRV us...
The volatility analysis of stock returns data is paramount in financial studies. We investigate the dynamics of volatility and randomness of the Pakistan Stock Exchange (PSX-100) and obtain insights into the behavior of investors during and before th...
Measures of predictability in physiological signals using entropy measures have been widely applied in many areas of research. Multiscale entropy expresses different levels of either approximate entropy or sample entropy by means of multiple factors...
In this paper, under the symmetric entropy and the scale squared error loss functions, we consider the maximum likelihood (ML) estimation and Bayesian estimation of the Shannon entropy and Rényi entropy of the two-parameter inverse Weibull dis...
Nonlinear dynamical analysis is a powerful approach to understanding biological systems. One of the most used metrics of system complexities is the Kolmogorov entropy. Long input signals without noise are required for the calculation, which are very...
Rheoencephalography (REG) is a simple and inexpensive technique that intends to monitor cerebral blood flow (CBF), but its ability to reflect CBF changes has not been extensively proved. Based on the hypothesis that alterations in CBF during apnea sh...
In the diagnosis of neurological diseases and assessment of brain function, entropy measures for quantifying electroencephalogram (EEG) signals are attracting ever-increasing attention worldwide. However, some entropy measures, such as approximate en...
Research in computational textual aesthetics has shown that there are textual correlates of preference in prose texts. The present study investigates whether textual correlates of preference vary across different time periods (contemporary texts vers...
Body temperature is usually employed in clinical practice by strict binary thresholding, aiming to classify patients as having fever or not. In the last years, other approaches based on the continuous analysis of body temperature time series have eme...
Entropy measures have been extensively used to assess heart rate variability (HRV), a noninvasive marker of cardiovascular autonomic regulation. It is yet to be elucidated whether those entropy measures can sensitively respond to changes of autonomic...
In the literature, we can find several blind adaptive deconvolution algorithms based on closed-form approximated expressions for the conditional expectation (the expectation of the source input given the equalized or deconvolutional output), involvin...
The study on the complexity of streamflow has guiding significance for hydrologic simulation, hydrologic prediction, water resources planning and management. Utilizing monthly streamflow data from four hydrologic control stations in the mainstream of...
Approximate entropy (ApEn) and sample entropy (SampEn) are widely used for temporal complexity analysis of real-world phenomena. However, their relationship with the Hurst exponent as a measure of self-similarity is not widely studied. Additionally,...
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