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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 ...
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
The scale space representation of a signal obtained by Gaussian smoothing satisfies a number of special properties, scale-space axioms, which make it into a special form of multi-scale representation.
A new approach to the problem of entropy evaluation is to compare the expected entropy of a sample of random sequence with the calculated entropy of the sample. The method gives very accurate results, but it is limited to calculations of random sequences modeled as Markov chains of the first order with small values of bias and correlations ...
Entropy is a scientific concept that is most commonly associated with a state of disorder, ... a sample of the substance is cooled as close to absolute zero as ...
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.
Despite the foregoing, there is a difference between the two quantities. The information entropy Η can be calculated for any probability distribution (if the "message" is taken to be that the event i which had probability p i occurred, out of the space of the events possible), while the thermodynamic entropy S refers to thermodynamic probabilities p i specifically.
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.