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Like approximate entropy (ApEn), Sample entropy (SampEn) is a measure of complexity. [1] But it does not include self-similar patterns as ApEn does. For a given embedding dimension, tolerance and number of data points, SampEn is the negative natural logarithm of the probability that if two sets of simultaneous data points of length have distance < then two sets of simultaneous data points of ...
In the context of rainfall forecasting, wavelet packet decomposition proves valuable for capturing the complex and multi-scale patterns in precipitation data. It can decompose the original monthly rainfall time series into various sub-series corresponding to different frequency.
As an example for the method of multiple-scale analysis, consider the undamped and unforced Duffing equation: [1] + + =, =, =, which is a second-order ordinary differential equation describing a nonlinear oscillator.
The inspiration for adopting the word entropy in information theory came from the close resemblance between Shannon's formula and very similar known formulae from statistical mechanics. In statistical thermodynamics the most general formula for the thermodynamic entropy S of a thermodynamic system is the Gibbs entropy
Multiscale decision-making draws upon the analogies between physical systems and complex man-made systems. [citation needed] In meteorology, multiscale modeling is the modeling of the interaction between weather systems of different spatial and temporal scales that produces the weather that we experience.
In statistics, an approximate entropy (ApEn) is a technique used to quantify the amount of regularity and the unpredictability of fluctuations over time-series data. [1] For example, consider two series of data:
Equivalently, the min-entropy () is the largest real number b such that all events occur with probability at most . The name min-entropy stems from the fact that it is the smallest entropy measure in the family of Rényi entropies. In this sense, it is the strongest way to measure the information content of a discrete random variable.
Brought up by Ginestra Bianconi in 2007, the entropy of a network ensemble measures the level of the order or uncertainty of a network ensemble. [24] The entropy is the logarithm of the number of graphs. [25] Entropy can also be defined in one network. Basin entropy is the logarithm of the attractors in one Boolean network. [26]