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Related Concept Videos

Entropy02:39

Entropy

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...
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...

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Related Experiment Video

Updated: Jul 3, 2026

Applications of EEG Neuroimaging Data: Event-related Potentials, Spectral Power, and Multiscale Entropy
11:15

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

Published on: June 27, 2013

Measuring Complexity and Predictability of Time Series with Flexible Multiscale Entropy for Sensor Networks.

Renjie Zhou1,2, Chen Yang3,4, Jian Wan5,6

  • 1School of Computer Science and Technology, Hangzhou Dianzi University, Hangzhou 310018, China. renjie_zhou@163.com.

Sensors (Basel, Switzerland)
|April 7, 2017
PubMed
Summary
This summary is machine-generated.

Flexible multiscale entropy (FMSE) enhances time series complexity measurement. This new method improves reliability and stability, especially for short time series, benefiting sensor network analysis.

Keywords:
complexityflexible multiscale entropyflexible similarity criterionsample entropysensor network controllingsensor network organizingtime series

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Area of Science:

  • Complex systems analysis
  • Information theory
  • Network science

Background:

  • Time series complexity and predictability are crucial for sensor network topology and congestion control.
  • Multiscale entropy (MSE) is a common method, but its component, sample entropy, has limitations with short time series.
  • Existing methods like MSE and Composite Multiscale Entropy (CMSE) exhibit sudden changes in entropy values due to their similarity measurement.

Purpose of the Study:

  • To introduce Flexible Multiscale Entropy (FMSE) as a more reliable and stable method for measuring time series complexity.
  • To address the limitations of sample entropy in existing multiscale entropy methods, particularly for short time series.
  • To enhance the performance of time series analysis for applications in sensor networks.

Main Methods:

  • Developed Flexible Multiscale Entropy (FMSE) by introducing a novel similarity function.
  • The new similarity function measures subsequence similarity with values ranging from zero to one, unlike the binary output of sample entropy.
  • Evaluated FMSE on synthetic (white noise, 1/f noise) and real-world (vibration signals) time series data.

Main Results:

  • FMSE demonstrates significant improvements in the reliability and stability of time series complexity measurement compared to MSE and CMSE.
  • These improvements are particularly notable when analyzing short time series.
  • FMSE provides more accurate complexity assessments, avoiding sudden changes in entropy values.

Conclusions:

  • FMSE offers a more robust and stable approach to measuring time series complexity, especially for short datasets.
  • The enhanced reliability of FMSE can lead to improved performance in sensor network applications, including topology and traffic congestion control.
  • Flexible Multiscale Entropy represents a significant advancement in time series analysis techniques.