Regularity dimension of sequences and its application to phylogenetic tree reconstruction |
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| Authors: | Tuan D. Pham |
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| Affiliation: | 1. Department of Veterinary Surgery and Animal Reproduction, School of Veterinary Medicine and Animal Science – São Paulo State University (UNESP), Botucatu, Brazil;2. Department of Physics and Biophysics, Institute of Biosciences – São Paulo State University (UNESP), Botucatu, Brazil;1. State Key Laboratory for Manufacturing Systems Engineering, Systems Engineering Institute, Xi’an Jiaotong University, Xi’an, Shaanxi, China;2. Vision Microsystems Co., Ltd, Shanghai, China;1. Centro Universitario de la Defensa de San Javier (University Centre of Defence at the Spanish Air Force Academy), MDE-UPCT, C/ Coronel López Peña s/n, 30720 Santiago de la Ribera, Murcia, Spain;2. Universidad Politécnica de Cartagena, Industrial & Medical Electronics Research Group, Campus Antiguo Hospital de Marina, Muralla del Mar, s/n, 30202 Cartagena, Murcia, Spain;1. School of Information and Communications, Gwangju Institute of Science and Technology (GIST), Gwangju, Republic of Korea;2. Department of Neuroscience, Brown University, RI, USA;1. Future Technology Research Center, College of Future, National Yunlin University of Science and Technology, Douliou, Taiwan, ROC;2. School of Science, Engineering and Environment, University of Salford, UK;3. School of Computer Science and Electronic Engineering, University of Essex, UK;4. School of Informatics, University of Edinburgh, UK |
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| Abstract: | 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. |
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