Regularity dimension of sequences and its application to phylogenetic tree reconstruction

The concept of dimension is a central development of chaos theory for studying nonlinear dynamical systems. Different types of dimensions have been derived to interpret different geometrical or physical observations. Approximate entropy and its modified methods have been introduced for studying regularity and complexity of time-series data in physiology and biology. Here, the concept of power laws and entropy measure are adopted to develop the regularity dimension of sequences to model a mathematical relationship between the frequency with which information about signal regularity changes in various scales. The proposed regularity dimension is applied to reconstruct phylogenetic trees using mitochondrial DNA (mtDNA) sequences for the family Hominidae, which can be validated according to the hypothesized evolutionary relationships between organisms.