Related Experiment Video
Updated: Jul 10, 2026
09:55
Troubleshooting and Quality Assurance in Hyperpolarized Xenon Magnetic Resonance Imaging: Tools for High-Quality Image Acquisition
Published on: January 5, 2024
Distinguishing noise from chaos.
O A Rosso1, H A Larrondo, M T Martin
1Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia.
Physical Review Letters
|November 13, 2007
Summary
This study introduces a new complexity-entropy causality plane to differentiate chaotic and stochastic systems. The method uses entropy and statistical complexity measures derived from time series data.
Area of Science:
- Complex Systems Science
- Nonlinear Dynamics
- Information Theory
Background:
- Chaotic systems and stochastic processes exhibit similar properties, making them difficult to distinguish.
- Traditional methods struggle to differentiate between these two types of time series.
- Understanding the underlying dynamics of time series is crucial in various scientific fields.
Purpose of the Study:
- To introduce a novel representation space, the complexity-entropy causality plane.
- To develop a method for clearly distinguishing between chaotic and stochastic time series.
- To provide a new tool for analyzing and classifying complex systems.
Main Methods:
- Assigning probability distribution functions to time series using the Bandt-Pompe method.
- Calculating system entropy and statistical complexity measures.
- Utilizing these measures as coordinates in the complexity-entropy causality plane.
Main Results:
- Demonstrated the ability to clearly distinguish between chaotic and stochastic time series within the new representation space.
- Successfully analyzed well-known model-generated time series of both chaotic and stochastic nature.
- The complexity-entropy causality plane effectively separates systems based on their underlying dynamics.
Conclusions:
- The complexity-entropy causality plane offers a powerful new approach for differentiating chaotic and stochastic systems.
- This method overcomes the limitations of existing techniques in distinguishing similar time series.
- The findings have significant implications for time series analysis and dynamical system characterization.
Related Concept Videos
00:53Sound Waves: Interference
Sound waves can be modeled either as longitudinal waves, wherein the molecules of the medium oscillate around an equilibrium position, or as pressure waves. When two identical waves from the same source superimpose on each other, the combination of two crests or two troughs results in amplitude reinforcement known as constructive interference. If two identical waves, that are initially in phase, become out of phase because of different path lengths, the combination of crests with troughs...
01:05Difference from Background: Limit of Detection
The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...
The LOD indicates the presence or absence...
01:09Beats
The study of music provides many examples of the superposition of waves and the constructive and destructive interference that occurs. Very few examples of music being performed consist of a single source playing a single frequency for an extended period of time. A single frequency of sound for an extended period might be monotonous to the point of irritation, similar to the unwanted drone of an aircraft engine or a loud fan. Music is pleasant and exciting due to mixing the changing frequencies...
01:10Interference: Path Lengths
Consider two sources of sound, that may or may not be in phase, emitting waves at a single frequency, and consider the frequencies to be the same.
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
Two special sources may be considered when they are in phase. This can be easily achieved by feeding the two sources from the same source. An example would be synchronizing the two speakers by feeding them with the same source, such as the sound waves produced by a tuning fork. This setup ensures that the two sources have the same frequency and are...
01:21Entropy 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...
01:18Aliasing
Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original signal...