- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2012 (2012), Article ID 439089, 13 pages
Shannon Information and Power Law Analysis of the Chromosome Code
Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
Received 8 June 2012; Revised 17 August 2012; Accepted 21 August 2012
Academic Editor: Dumitru Bǎleanu
Copyright © 2012 J. A. Tenreiro Machado. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- R. T. Schuh and A. V. Z. Brower, Biological Systematics: Principles and Applications, Cornell University Press, 2nd edition, 2009.
- H. Seitz, Analytics of Protein-DNA Interactions, Advances in Biochemical Engineering Biotechnology, Springer, 2007.
- H. Pearson, “What is a gene?” Nature, vol. 441, no. 7092, pp. 398–401, 2006.
- UCSC Genome Bioinformatics, http://hgdownload.cse.ucsc.edu/downloads.html.
- G. E. Sims, S. R. Jun, G. A. Wu, and S. H. Kim, “Alignment-free genome comparison with feature frequency profiles (FFP) and optimal resolutions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 106, no. 8, pp. 2677–2682, 2009.
- W. J. Murphy, T. H. Pringle, T. A. Crider, M. S. Springer, and W. Miller, “Using genomic data to unravel the root of the placental mammal phylogeny,” Genome Research, vol. 17, no. 4, pp. 413–421, 2007.
- H. Zhao and G. Bourque, “Recovering genome rearrangements in the mammalian phylogeny,” Genome Research, vol. 19, no. 5, pp. 934–942, 2009.
- A. B. Prasad, M. W. Allard, and E. D. Green, “Confirming the phylogeny of mammals by use of large comparative sequence data sets,” Molecular Biology and Evolution, vol. 25, no. 9, pp. 1795–1808, 2008.
- I. Ebersberger, P. Galgoczy, S. Taudien, S. Taenzer, M. Platzer, and A. Von Haeseler, “Mapping human genetic ancestry,” Molecular Biology and Evolution, vol. 24, no. 10, pp. 2266–2276, 2007.
- C. W. Dunn, A. Hejnol, D. Q. Matus et al., “Broad phylogenomic sampling improves resolution of the animal tree of life,” Nature, vol. 452, no. 7188, pp. 745–749, 2008.
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Fractional dynamics in DNA,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 2963–2969, 2011.
- A. M. Costa, J. T. Machado, and M. D. Quelhas, “Histogram-based DNA analysis for the visualization of chromosome, genome and species information,” Bioinformatics, vol. 27, no. 9, pp. 1207–1214, 2011.
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Entropy analysis of the DNA code dynamics in human chromosomes,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1612–1617, 2011.
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Analysis and visualization of chromosome information,” Gene, vol. 491, no. 1, pp. 81–87, 2012.
- M. Kimura, The Neutral Theory of Molecular Evolution, Cambridge University Press, Cambridge, Mass, USA, 1983.
- P. J. Deschavanne, A. Giron, J. Vilain, G. Fagot, and B. Fertit, “Genomic signature: characterization and classification of species assessed by chaos game representation of sequences,” Molecular Biology and Evolution, vol. 16, no. 10, pp. 1391–1399, 1999.
- M. Lynch, “The frailty of adaptive hypotheses for the origins of organismal complexity,” Proceedings of the National Academy of Sciences of the United States of America, vol. 104, no. 1, pp. 8597–8604, 2007.
- G. Albrecht-Buehler, “Asymptotically increasing compliance of genomes with Chargaff's second parity rules through inversions and inverted transpositions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 103, no. 47, pp. 17828–17833, 2006.
- D. Mitchell and R. Bridge, “A test of Chargaff's second rule,” Biochemical and Biophysical Research Communications, vol. 340, no. 1, pp. 90–94, 2006.
- B. R. Powdel, S. S. Satapathy, A. Kumar et al., “A study in entire chromosomes of violations of the intra-strand parity of complementary nucleotides (Chargaff's Second Parity Rule),” DNA Research, vol. 16, no. 6, pp. 325–343, 2009.
- C. T. Zhang, R. Zhang, and H. Y. Ou, “The Z curve database: a graphic representation of genome sequences,” Bioinformatics, vol. 19, no. 5, pp. 593–599, 2003.
- P. Bak, K. Chen, and C. Tang, “A forest-fire model and some thoughts on turbulence,” Physics Letters A, vol. 147, no. 5-6, pp. 297–300, 1990.
- N. E. Israeloff, M. Kagalenko, and K. Chan, “Can Zipf distinguish language from noise in noncoding DNA?” Physical Review Letters, vol. 76, pp. 1976–1979, 1995.
- R. N. Mantegna and H. E. Stanley, “Scaling behaviour in the dynamics of an economic index,” Nature, vol. 376, no. 6535, pp. 46–49, 1995.
- L. A. Adamic and B. A. Huberman, “Zipfs law and the Internet,” Glottometrics, vol. 3, pp. 143–150, 2002.
- H. Aoyama, Y. Fujiwara, and W. Souma, “Kinematics and dynamics of pareto-zipf's law and gibrat's law,” Physica A, vol. 344, no. 1-2, pp. 117–121, 2004.
- C. Andersson, A. Hellervik, and K. Lindgren, “A spatial network explanation for a hierarchy of urban power laws,” Physica A, vol. 345, no. 1-2, pp. 227–244, 2005.
- A. L. Barabási, “The origin of bursts and heavy tails in human dynamics,” Nature, vol. 435, no. 7039, pp. 207–211, 2005.
- W. Dahui, L. Menghui, and D. Zengru, “True reason for Zipf's law in language,” Physica A, vol. 358, no. 2–4, pp. 545–550, 2005.
- J. M. Sarabia and F. Prieto, “The Pareto-positive stable distribution: a new descriptive model for city size data,” Physica A, vol. 388, no. 19, pp. 4179–4191, 2009.
- T. Fenner, M. Levene, and G. Loizou, “Predicting the long tail of book sales: unearthing the power-law exponent,” Physica A, vol. 389, no. 12, pp. 2416–2421, 2010.
- J. A. T. Machado, A. C. Costa, and M. D. Quelhas, “Shannon, Rényie and Tsallis entropy analysis of DNA using phase plane,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3135–3144, 2011.
- J. A. T. Machado and S. Entropy, “Analysis of the Genome Code,” Mathematical Problems in Engineering, vol. 2012, Article ID 132625, 12 pages, 2012.
- J. T. Machado, “Accessing complexity from genome information,” Communications in Nonlinear Science and Numerical Simulations, vol. 17, no. 6, pp. 2237–2243, 2012.
- R. Hilfer, Applications of Fractional Calculus in Physics, World Scientific, Singapore, 2000.
- D. Baleanu and S. I. Vacaru, “Fractional curve flows and solitonic hierarchies in gravity and geometric mechanics,” Journal of Mathematical Physics, vol. 52, no. 5, Article ID 053514, 15 pages, 2011.
- D. Baleanu, K. Diethelm, E. Scalas, and J. J. Trujillo, Fractional Calculus Models and Numerical Methods, vol. 3 of Complexity, Nonlinearity and Chaos, World Scientific Publishing, 2012.
- C. E. Shannon, “A mathematical theory of communication,” The Bell System Technical Journal, vol. 27, pp. 379–423, 1948.
- E. T. Jaynes, “Information Theory and Statistical Mechanics,” vol. 106, pp. 620–630, 1957.
- A. I. Khinchin, Mathematical foundations of information theory, Dover Publications, New York, NY, USA, 1957.
- A. Plastino and A. R. Plastino, “Tsallis Entropy and Jaynes' information theory formalism,” Brazilian Journal of Physics, vol. 29, no. 1, pp. 50–60, 1999.
- H. J. Haubold, A. M. Mathai, and R. K. Saxena, “Boltzmann-Gibbs entropy versus Tsallis entropy: recent contributions to resolving the argument of Einstein concerning “neither Herr Boltzmann nor Herr Planck has given a definition of W”? Essay review,” Astrophysics and Space Science, vol. 290, no. 3-4, pp. 241–245, 2004.
- A. M. Mathai and H. J. Haubold, “Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy,” Physica A, vol. 375, no. 1, pp. 110–122, 2007.
- T. Carter, An Introduction to Information Theory and Entropy, Complex Systems Summer School, Santa Fe, Mexico, 2007.
- P. N. Rathie and S. Da Silva, “Shannon, Lévy, and Tsallis: a note,” Applied Mathematical Sciences, vol. 2, no. 25–28, pp. 1359–1363, 2008.
- C. Beck, “Generalised information and entropy measures in physics,” Contemporary Physics, vol. 50, no. 4, pp. 495–510, 2009.
- I. J. Taneja, “On measures of information and inaccuracy,” Journal of Statistical Physics, vol. 14, no. 3, pp. 263–270, 1976.
- B. D. Sharma and I. J. Taneja, “Three generalized-additive measures of entropy,” Elektronische Informationsverarbeitung und Kybernetik, vol. 13, no. 7-8, pp. 419–433, 1977.
- A. Wehrl, “General properties of entropy,” Reviews of Modern Physics, vol. 50, no. 2, pp. 221–260, 1978.
- H. D. Chen, C. H. Chang, L. C. Hsieh, and H. C. Lee, “Divergence and Shannon information in genomes,” Physical Review Letters, vol. 94, no. 17, Article ID 178103, 2005.
- R. M. Gray, Entropy and Information Theory, Springer, New York, NY, USA, 1990.
- M. R. Ubriaco, “Entropies based on fractional calculus,” Physics Letters A, vol. 373, no. 30, pp. 2516–2519, 2009.