Scaled Shannon entropy

We now offer a way to independently determine the scaling exponent from the time series data using the Shannon entropy for a diffusive process p(x, t) ... 

It follows from Eq. (87) that the information (configuration) Shannon entropy, Hs ln), of a fractal set depends on the scale / ... 

We will describe below the SE formalism in detail and explain how it can be used to estimate chemical information content based on histogram representations of feature value distributions. Examples from our work and studies by others will be used to illustrate key aspects of chemical information content analysis. Although we focus on the Shannon entropy concept, other measures of information content will also be discussed, albeit briefly. We will also explain why it has been useful to extend the Shannon entropy concept by introducing differential Shannon entropy (DSE) to facilitate large-scale analysis and comparison of chemical features. The DSE formalism has ultimately led to the introduction of the SE-DSE metric. 

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