Entropy analysis of the DNA code dynamics in human chromosomes

Computers and Mathematics with Applications

Volumn 62, Issue 3, 2011, Pages 1612-1617

  MacHado, J A Tenreiro ^a   Costa, António C ^a   Quelhas, Maria Dulce ^b  

^a INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

^b National Health Institute   (Portugal)

Author keywords

Chromosome; DNA; Dynamics; Entropy; Fractional calculus

Indexed keywords

ANALYSIS TOOLS; DNA CODES; ENTROPY ANALYSIS; EXPERIMENTAL METHODS; FRACTIONAL CALCULUS; FRACTIONAL ORDER; GLOBAL PROPERTIES; HUMAN CHROMOSOMES; INFORMATION CONTENTS; NATURAL CONSEQUENCES; SCIENTIFIC KNOWLEDGE; SYSTEM DYNAMICS;

CHROMOSOMES; DNA; ENTROPY; FOURIER TRANSFORMS; ORGANIC ACIDS;

GENE ENCODING;

EID: 79961016271     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2011.03.005     Document Type: Article

References (42)

1. Keith B. Oldham, and Jerome Spanier The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order 1974 Academic Press
2. Stefan G. Samko, Anatoly A. Kilbas, and Oleg I. Marichev Fractional Integrals and Derivatives: Theory and Applications 1993 Gordon and Breach Science Publishers
3. Kenneth S. Miller, and Bertram Ross An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 John Wiley and Sons
4. Alain Oustaloup La Commande CRONE: Commande Robuste d'ordre Non Entier 1991 Hermes
5. Igor Podlubny Fractional Differential Equations 1999 Academic Press San Diego
6. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations North-Holland Mathematics Studies vol. 204 2006 Elsevier
7. Richard L. Magin Fractional Calculus in Bioengineering 2006 Begell House Publishers
8. J. Sabatier, O.P. Agrawal, and J.A. Tenreiro Machado Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering 2007 Springer
9. Francesco Mainardi Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models 2010 Imperial College Press
10. Riccardo Caponetto, Giovanni Dongola, Luigi Fortuna, and Ivo Petrá Fractional Order Systems: Modeling and Control Applications 2010 World Scientific Publishing Company
11. Concepcion Alicia Monje, YangQuan Chen, Blas Manuel Vinagre, Dingyu Xue, and Vicente Feliu Fractional Order Systems and Controls: Fundamentals and Applications Series: Advances in Industrial Control 2010 Springer
12. Kai Diethelm The Analysis of Fractional Differential Equations Lecture Notes in Mathematics Series 2010 Springer
13. J.Tenreiro Machado, Virginia Kiryakova, and Francesco Mainardi Recent History of Fractional Calculus Communications in Nonlinear Science and Numerical Simulations 16 2011 Elsevier 1140 1153
14. C.E. Shannon A mathematical theory of communication Bell System Technical Journal 27 1948 379 423 623656
15. E.T. Jaynes Information theory and statistical mechanics Physical Review 106 1957 620
16. A.I. Khinchin Mathematical Foundations of Information Theory 1957 Dover New York
17. A. Plastino, and A.R. Plastino Tsallis entropy and Jaynes information theory formalism Brazilian Journal of Physics 29 1 1999 50 60
18. X. Li, C. Essex, M. Davison, K.H. Hoffmann, and C. Schulzky Fractional diffusion, irreversibility and entropy Journal of Non-Equilibrium Thermodynamics 28 3 2003 279 291
19. H.J. Haubold, A.M. Mathai, and R.K. Saxena BoltzmannGibbs 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? Astrophysics and Space Science 290 34 2004 241 245 (Pubitemid 38926208)
20. A.M. Mathai, and H.J. Haubold Pathway model, superstatistics, Tsallis statistics, and a generalized measure of entropy Physica A: Statistical Mechanics and its Applications 375 1 2007 110 122 (Pubitemid 44830100)
21. T. Carter, An Introduction to Information Theory and Entropy, Complex Systems Summer School, Santa Fe, 2007.
22. P. Rathie, and S. da Silva Shannon, Levy, and Tsallis: a note Applied Mathematical Science 2 28 2008 1359 1363
23. C. Beck Generalised information and entropy measures in physics Contemporary Physics 50 4 2009 495 510
24. R.M. Gray Entropy and Information Theory 2009 Springer-Verlag
25. M.R. Ubriaco Entropies based on fractional calculus Physics Letters A 373 30 2009 2516 2519
26. I.G. Taneja On measures of information and inaccuracy Journal of Statistical Physics 14 1976 203 270
27. B.D. Sharma, and R.K. Taneja Three generalized additive measures of entropy Elektronische Informationsverarbeitung und Kybernetik (EIK) 13 1977 419 433
28. A. Wehrl General properties of entropy Reviews of Modern Physics 50 1978 221 260
29. David Micklos, and Greg A. Freyer DNA Science: A First Course 2nd ed. 2003 Cold Spring Harbor Laboratory Press
30. James D. Watson DNA: The Secret of Life 2004 Arrow Books Ltd
31. R.T. Schuh, and A.V.Z. Brower Biological Systematics: Principles and Applications 2nd ed. 2009 Cornell University Press
32. Harald Seitz Analytics of ProteinDNA Interactions Advances in Biochemical Engineering Biotechnology 2007 Springer
33. H. Pearson Genetics: what is a gene? Nature 441 7092 2006 398 401
34. UCSC Genome Bioinformatics. http://hgdownload.cse.ucsc.edu/downloads. html.
35. Gregory E. Sims, Se-Ran Jun, Guohong A. Wu, and Sung-Hou 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 106 8 2009 2677 2682
36. William J. Murphy, Thomas H. Pringle, Tess A. Crider, Mark S. Springer, and Webb Miller Using genomic data to unravel the root of the placental mammal phylogeny Genome Research 17 2007 413 421 (Pubitemid 46556445)
37. Hao Zhao, and Guillaume Bourque Recovering genome rearrangements in the mammalian phylogeny Genome Research 19 2009 934 942
38. Arjun B. Prasad, and Marc W. Allard Confirming the phylogeny of mammals by use of large comparative sequence data sets Molecular Biology and Evolution 25 9 2008 1795 1808
39. Ingo Ebersberger, Petra Galgoczy, Stefan Taudien, Simone Taenzer, Matthias Platzer, and Arndt von Haeseler Mapping human genetic ancestry Molecular Biology and Evolution 24 10 2007 2266 2276 (Pubitemid 47574726)
40. Casey W. Dunn Broad phylogenomic sampling improves resolution of the animal tree of life Nature 452 2008 745 750
41. J.A. Tenreiro Machado, António C. Costa, and Maria Dulce Quelhas Fractional dynamics in DNA Communications in Nonlinear Science and Numerical Simulations 16 8 2011 2963 2969
42. Alan V. Oppenheim, Alan S. Willsky, and S.Hamid Nawab Signals and Systems 2nd ed. 1996 Prentice Hall