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Entropy02:39

Entropy

33.7K
Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy01:18

Entropy

3.3K
The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
3.3K
Distribution and Dispersion00:54

Distribution and Dispersion

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To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
23.6K
Coefficient of Variation01:10

Coefficient of Variation

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The coefficient of variation measures the dispersion of the data points or distribution around the mean. Using the coefficient of variation, we can compare two data series with drastically different means or different units of measurement. The coefficient of variation for a sample and a population is expressed as a percentage of the ratio of standard deviation to the mean.
The coefficient of variation is a practical statistical tool in finance. It allows investors to assess the volatility or...
7.6K
Variability: Analysis01:11

Variability: Analysis

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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
323
Standard Deviation01:10

Standard Deviation

25.5K
The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
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Related Experiment Video

Updated: Nov 27, 2025

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
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Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy

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Amplitude- and Fluctuation-Based Dispersion Entropy.

Hamed Azami1, Javier Escudero1

  • 1School of Engineering, Institute for Digital Communications, University of Edinburgh, Edinburgh EH9 3FB, UK.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

Dispersion entropy (DispEn) quantifies time series uncertainty. This study explores its mapping effects and noise sensitivity, introducing fluctuation-based DispEn (FDispEn) for enhanced time series analysis.

Keywords:
dispersion entropyfluctuation-based dispersion entropyforbidden patternsnonlinear analysispermutation entropy

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Area of Science:

  • * Time series analysis and complexity.
  • * Signal processing and entropy measures.

Background:

  • * Dispersion entropy (DispEn) is a novel, efficient metric for time series uncertainty quantification.
  • * The impact of different mapping strategies within DispEn remains underexplored.
  • * Sensitivity to noise and the potential for fluctuation-based measures require investigation.

Purpose of the Study:

  • * To investigate the influence of linear and nonlinear mapping on DispEn performance.
  • * To assess DispEn's parameter sensitivity to noise.
  • * To introduce and evaluate fluctuation-based DispEn (FDispEn) and forbidden dispersion patterns for time series discrimination.

Main Methods:

  • * Comparative analysis of linear and nonlinear mapping techniques in DispEn.
  • * Sensitivity analysis of DispEn parameters against varying noise levels.
  • * Development of fluctuation-based DispEn (FDispEn) and forbidden dispersion patterns.
  • * Performance evaluation against permutation entropy, sample entropy, and Lempel-Ziv complexity on physiological datasets.

Main Results:

  • * DispEn demonstrates high consistency in distinguishing dynamics within biomedical signals.
  • * FDispEn offers a robust approach for analyzing time series fluctuations.
  • * Forbidden dispersion patterns effectively differentiate deterministic from stochastic time series.
  • * DispEn and FDispEn outperform other methods in characterizing physiological data complexity.

Conclusions:

  • * DispEn and FDispEn offer significant advantages over existing entropy methods for time series analysis.
  • * These novel methods are well-suited for characterizing diverse real-world time series, particularly in biomedical applications.
  • * The study provides valuable insights into optimizing DispEn and its novel variants for complex data analysis.