Measurable Notions of Complexity and Their Relationship to Biological Complexity

Abstract

Complexity is often invoked as a motivation for a systems approach to biology. We review three measurable notions of complexity from the areas of computation and data analysis. These measures have each led to mathematical theory and to further insight on the complexity of objects, demonstrating the benefits of having a well-defined measure of complexity. Each measure is applicable in the study of particular biological systems; however, none is satisfactory to serve as a universal measure of biological complexity. The study of biological systems will likely require numerous measures of complexity, each appropriate for analysis in specific settings.

Characterization of early partial seizure onset: Frequency, complexity and entropy

“…There are many definitions for both entropy and complexity and potential classifications of these methods were introduced by Wackerbauer (Wackerbauer et al, 1994) and Rapp (Rapp and Schmah, 1996). Attempts to compare the theoretical and applied advantages of those measures have grown over the last decade (Jimenez-Montano et al, 2002; Rosso et al, 2003; Ferenets et al, 2006; Adeli et al, 2007; Brooks, 2007; Hornero et al, 2008; Chen et al, 2009; Sabeti et al, 2009). The most common entropy measures are distribution-determined and provide a quantitative determination of the relative frequency of a specific event but are insensitive to the sequence of events.…”

“…We focus our study on the relationships between the most commonly used spectral features and the measures of entropy and complexity for biological signals and their comparative efficiency when dealing with real world cases of seizure detection. Computation of several complexity measures rather than relying on a single measurement can provide a more comprehensive overview of the underlying processes (Bhattacharya, 2000; Watanabe et al, 2003; Brooks, 2007). All the measures investigated here are single channel analyses and focus on the pair of electrodes closest to the seizure focus.…”