Skip to main content
SpringerLink
Log in

Applications to Life Science

  • Chapter
Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems

Part of the book series: Theoretical and Mathematical Physics ((TMP))

  • 2118 Accesses

Abstract

In this chapter, we discuss some applications of mathematics in the quantum theory and information science to the biosystems and life sciences.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Aarts, E., Korst, J.: Simulated Annealing and Boltzmann Machines. Wiley, New York (1989)

    MATH  Google Scholar 

  2. Abdel-Ghafar, A.N., Chotpitayasunondh, T., Gao, Z., Hayden, F.G., Nguyen, D.H., de Jong, M.D., Naghdaliyev, A., Peiris, J.S., Shindo, N., Soeroso, S., Uyeki, T.M.: Update on avian influenza A (H5N1) virus infection in humans. N. Engl. J. Med. 358(3), 261–273 (2008)

    Article  Google Scholar 

  3. Accardi, L., Khrennikov, A., Ohya, M.: Quantum Markov model for data from Shafir-Tversky experiments in cognitive psychology. Open Syst. Inf. Dyn. 16, 371–385 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ando, T., Yamato, I: Basics of molecular simulation and its application to biomolecules. In: Quantum Bio-Informatics II, pp. 228–241. World Scientific, Singapore (2009)

    Chapter  Google Scholar 

  5. Asano, M., Khrennikov, A., Ohya, M.: Quantum like model for decision making process in two players game. Found. Phys. (2010). doi:10.1007/s10701-010-9454-y

    Google Scholar 

  6. Avetisov, V.A., Bikulov, A.H., Kozyrev, S.V., Osipov, V.A.: p-adic models of ultra-metric diffusion constrained by hierarchical energy landscapes. J. Phys. A, Math. Gen. 35(2), 177 (2002)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  7. Avetisov, V.A., Bikulov, A.Kh.: Protein ultrametricity and spectral di usion in deeply frozen proteins. Biophys. Rev. Lett. 3(3), 387–396 (2008)

    Article  Google Scholar 

  8. Beratran, D.N., Betts, J.N., Onuchic, J.N.: Protein electron transfer rates are predicted to be set by the bridging secondary and tertiary structure. Science 252, 1285 (1991)

    Article  ADS  Google Scholar 

  9. Brekke, L., Freund, P.G.O.: p-adic numbers in physics. Phys. Rep. 233, 1–66 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  10. Busemeyer, J.R., Matthews, M., Wang, Z.: A quantum information processing explanation of disjunction effects. In: Sun, R., Myake, N. (eds.) The 29th Annual Conference of the Cognitive Science Society and the 5th International Conference of Cognitive Science, pp. 131–135. Erlbaum, Mahwah (2006)

    Google Scholar 

  11. Busemeyer, J.B., Wang, Z., Townsend, J.T.: Quantum dynamics of human decision making. J. Math. Psychol. 50, 220–241 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Busemeyer, J.R., Santuy, E., Lambert-Mogiliansky, A.: Comparison of Markov and quantum models of decision making. In: Bruza, P., Lawless, W., van Rijsbergen, K., Sofge, D.A., Coeke, B., Clark, S. (eds.) Quantum Interaction: Proceedings of the Second Quantum Interaction Symposium, pp. 68–74. College Publications, London (2008)

    Google Scholar 

  13. Caruso, F., Chin, A.W., Datta, A., Huelga, S.F., Plenio, M.B.: Highly efficient energy excitation transfer in light-harvesting complexes: The fundamental role of noise-assisted transport. J. Chem. Phys. 131, 105106 (2009)

    Article  ADS  Google Scholar 

  14. Caruso, F., Huelga, S.F., Plenio, M.B.: Noise-enhanced classical and quantum capacities in communication networks. arXiv:1003.5877 (2010)

  15. Cleland, A., Watson, H.G., Robertson, P., Ludlam, C.A., Brown, A.J.: Evolution of zidovudine resistance-associated genotypes in human immunodeficiency virus type 1-infected patients. J. Acquir. Immune Defic. Syndr. Hum. Retrovirol. 12(1), 6 (1996)

    Google Scholar 

  16. Collini, E., Wong, C.Y., Wilk, K.E., Curmi, P.M.G., Brumer, P., Scholes, G.D.: Coherently wired light-harvesting in photosynthetic marinealgae at ambient temperature. Nature 463, 644–647 (2010)

    Article  ADS  Google Scholar 

  17. Conte, E., Khrennikov, A., Todarello, O., Federici, A., Zbilut, J.P.: Mental states follow quantum mechanics during perception and cognition of ambiguous figures. Open Syst. Inf. Dyn. 16, 1–17 (2009)

    Article  MathSciNet  Google Scholar 

  18. Crick, F.: The origin of the genetic code. J. Mol. Biol. 38, 367–379 (1968)

    Article  Google Scholar 

  19. Croson, R.: The disjunction effect and reasoning-based choice in games. Organ. Behav. Hum. Decis. Process. 80, 118–133 (1999)

    Article  Google Scholar 

  20. Derrickson, B.H., Tortora, G.J.: Principles of Anatomy and Physiology, 11th edn. Wiley, New York (2005)

    Google Scholar 

  21. Dragovich, B., Dragovich, A.: A p-adic model of DNA sequence and genetic code. arXiv:q-bio/0607018 (2006)

  22. Dragovich, B., Dragovich, A.: p-adic modelling of the genome and the genetic code. arXiv:0707.3043 (2007)

  23. Dragovich, B., Khrennikov, A.Yu., Kozyrev, S.V., Volovich, I.V.: On p-adic mathematical physics. p-Adic Numb. Ultrametric Anal. Appl. 1(1), 1–17 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  24. Dugan, V.G., Chen, R., Spiro, D.J., Sengamalay, N., Zaborsky, J., Ghedin, E., Nolting, J., Swayne, D.E., Runstadler, J.A., Happ, G.M., Senne, D.A., Wang, R., Slemons, R.D., Holmes, E.C., Taubenberger, J.K.: The evolutionary genetics and emergence of avian influenza viruses in wild birds. PLoS Pathog 4(5), e1000076 (2008)

    Article  Google Scholar 

  25. Engel, G.S., et al.: Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems. Nature 446, 782–786 (2007)

    Article  ADS  Google Scholar 

  26. Felsenstein, J.: PHYLIP phylogeny inference package. http://evolution.genetics.washington.edu/phylip/doc/main.html

  27. Felsenstein, J.: Neighbor–Neighbor-joining and UPGMA methods. http://evolution.genetics.washington.edu/phylip/doc/neighbor.html

  28. Fichtner, K.-H., Freudenberg, W.: Characterization of states of infinite Boson systems I. On the construction of states. Commun. Math. Phys. 137, 315–357 (1991)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. Fichtner, K.-H., Freudenberg, W., Liebscher, V.: On exchange mechanisms for bosons. Random Oper. Stoch. Equ. 12(4), 331–348 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  30. Fichtner, K.-H., Fichtner, L.: Bosons and a quantum model of the brain. Jenaer Schriften zur Mathematik und Informatik Math/Inf/08/05, FSU Jena, Faculty of Mathematics and Informatics, Jena (2005), 27 pp.

    Google Scholar 

  31. Fichtner, K.-H., Freudenberg, W., Ohya, M.: Recognition and teleportation. In: Quantum Information, vol. V, pp. 1–17 (2006)

    Google Scholar 

  32. Fichtner, K.-H., Fichtner, L., Freudenberg, W., Ohya, M.: On a mathematical model of brain activities. In: Quantum Theory, Reconsideration of Foundations, vol. 4. AIP Conference Proceedings, vol. 962, pp. 85–90, Melville, New York. Am. Inst. Phys., New York (2007)

    Google Scholar 

  33. Fichtner, K.-H., Fichtner, L.: Quantum Markov chains and the process of recognition. Jenaer Schriften zur Mathematik und Informatik Math/Inf/02/07, FSU Jena, Faculty of Mathematics and Informatics, Jena (2007), 24 pp.

    Google Scholar 

  34. Fichtner, K.-H., Fichtner, L., Freudenberg, W. Ohya, M.: On a quantum model of the recognition process. In: QP-PQ: Quantum Prob. White Noise Anal. Quantum Bio-Informatics, vol. 21, pp. 64–84. World Scientific, Singapore (2008)

    Google Scholar 

  35. Fichtner, K.-H., Freudenberg, W.: The compound Fock space and its application to brain models. In: Accardi, L., Freudenberg, W., Ohya, M. (eds.) Quantum Bio-Informatics II. QP–PQ: Quantum Probability and White Noise Analysis, vol. XXIV, pp. 55–67. Singapore, World Scientific (2009)

    Chapter  Google Scholar 

  36. Fichtner, L., Gäbler, M.: Characterisation of beam splitters. In: Accardi, L., Freudenberg, W., Ohya, M. (eds.) Quantum Bio-Informatics II. QP–PQ: Quantum Probability and White Noise Analysis, vol. XXIV, pp. 68–80. World Scientific, Singapore (2009)

    Chapter  Google Scholar 

  37. Fichtner, K.-H., Fichtner, L., Freudenberg, W., Ohya, M.: Quantum models of the recognition process—on a convergence theorem. Open Syst. Inf. Dyn. 17(2), 161–187 (2010)

    Article  MATH  Google Scholar 

  38. Finkelshtein, A.V., Ptitsyn, O.B.: Physics of Proteins. Academic Press, San Diego (2002)

    Google Scholar 

  39. Fouchier, R.A.M., Munster, V., Wallensten, A., Bestebroer, T.M., Herfst, S., Smith, D., Rimmelzwaan, G.F., Olsen, B., Osterhaus, A.D.M.E.: Characterization of a novel influenza a virus hemagglutinin subtype (H16) obtained from black-headed gulls. J. Virol. 79(5), 2814–2822 (2005)

    Article  Google Scholar 

  40. Frappat, L., Sciarrino, A., Sorba, P.: Crystalizing the genetic code. J. Biol. Phys. 27, 1–38 (2001). arXiv:physics/0003037

    Article  Google Scholar 

  41. Frenkel, L.M., Wang, Y., Learn, G.H., McKernan, J.L., Ellis, G.M., Mohan, K.M., Holte, S.E., De Vange, S.M., Pawluk, D.M., Melvin, A.J., Lewis, P.F., Heath, L.M., Beck, I.A., Mahalanabis, M., Naugler, W.E., Tobin, N.H., Mullins, J.I.: Multiple viral genetic analyses detect low-level human immunodeficiency virus type 1 replication during effective highly active antiretroviral therapy. J. Virol. 77(10), 5721 (2003)

    Article  Google Scholar 

  42. Frenkel, V., Etherington, A., Greene, M., Quijiano, J., Xie, J., Hunter, F., Dromi, S., Li, K.C.P.: Delivery of liposomal doxorubicin(Doxil) in a breast cancer tumor model: investigation of potential enhancement by pulsed high intensity focused ultrasound exposure. Acad. Radiol. 13, 469–479 (2006)

    Article  Google Scholar 

  43. George, D.G., Barker, W.C., Hunt, L.T.: The protein identification resource (PIR). Nucleic Acids Res. 14(1), 11–15 (1986)

    Article  Google Scholar 

  44. Glezen, W.P.: Emerging infections: pandemic influenza. Epidemiol. Rev. 18, 64–76 (1996)

    Google Scholar 

  45. Gnutzman, S., Smilansky, U.: Quantum graphs: applications to quantum chaos and universal spectral statistics. Adv. Phys. 55, 527–625 (2006)

    Article  ADS  Google Scholar 

  46. Hara, T., Iriyama, S., Makino, K., Terada, H., Ohya, M.: Mathematical description of drug movement into tumor with EPR effect and estimation of its configuration for DDS. Colloids Surf. B, Biointerfaces 75, 42–46 (2009)

    Article  Google Scholar 

  47. Hara, T., Sato, K., Ohya, M.: MTRAP: Pairwise sequence alignment algorithm by a new measure based on transition probability between two consecutive pairs of residues. BMC Bioinform. 11, 235 (2010)

    Article  Google Scholar 

  48. Hari, R., Lounasmaa, O.V.: Neuromagnetism: tracking the dynamics of the brain. Phys. World 13, 33–38 (2000)

    Google Scholar 

  49. Harris, J.M., Zalipsky, S.: Poly (ethylene glycol) Chemistry and Biological Application. ACS Symposium Series, vol. 680. Am. Chem. Soc., Washington (1997)

    Google Scholar 

  50. Hayes, B.: The invention of the genetic code. Am. Sci. 86(1), 8–14 (1998)

    Google Scholar 

  51. Hofstader, D.R.: Dilemmas for superrational thinkers, leading up to a luring lottery. Sci. Am. 6 (1983)

    Google Scholar 

  52. Hofstader, D.R.: Metamagical Themes: Questing for the Essence of Mind and Pattern. Basic Books, New York (1985)

    Google Scholar 

  53. Hornos, J.E.M., Hornos, Y.M.M.: Algebraic model for the evolution of the genetic code. Phys. Rev. Lett. 71, 4401–4404 (1993)

    Article  ADS  Google Scholar 

  54. Ibrahim, N.K., Desai, N., Legha, S., Shiong, P.S., Theriault, R.L., Rivera, E., Esmaeli, B., Ring, S.E., Bedikian, A., Hortobagyi, G.N., Ellerhorst, J.A.: Phase I and pharmacokinetic study of ABI-007, a cremophor-free protein-stabilized, nanoparticle formulation of paclitaxel. Clin. Cancer Res. 8, 1038–1044 (2002)

    Google Scholar 

  55. Ibrahim, N.K., Samuels, B., Page, R., Doval, D., Patel, K.M., Rao, S.C., Naie, M.K., Bhar, P., Desai, N., Hortobagyi, G.N.: Multicenter phase II trial of ABI-007, an albumin-bound paclitaxel, in woman with metastatic breast cancer. J. Clin. Oncol. 23, 6019–6025 (2005)

    Article  Google Scholar 

  56. Imamichi, H., Crandall, K.A., Natarajan, V., Jiang, M.K., Dewar, R.L., Berg, S., Gaddam, A., Bosche, M., Metcalf, J.A., Davey, R.T. Jr., Lane, H.C.: Human immunodeficiency virus type 1 quasi species that rebound after discontinuation of highly active antiretroviral therapy are similar to the viral quasi species present before initiation of therapy. J. Infect. Dis. 183(1), 36 (2001)

    Article  Google Scholar 

  57. Iriyama, S., Ohya, M., Volovich, I.V.: Generalized quantum Turing machine and its application to the SAT chaos algorithm. In: QP-PQ: Quantum Prob. White Noise Anal., Quantum Information and Computing, vol. 19, pp 204–225. World Scientific, Singapore (2006)

    Google Scholar 

  58. Iriyama, S., Ohya, M., Sato, K., Volovich, I.V.: Photosynthetic antenna and entropy decreasing. TUS preprint (2010)

    Google Scholar 

  59. Iriyama, S., Ohya, M., Yamato, I.: Quantum algorithm of protain folding. TUS preprint (2010)

    Google Scholar 

  60. Ishizakia, A., Fleming, G.F.: Theoretical examination of quantum coherence in a photosynthetic system at physiological temperature. Proc. Natl. Acad. Sci. USA 106, 17255–17260 (2009)

    Article  ADS  Google Scholar 

  61. Jukes, T.H.: Evolution of the amino acid code: inferences from mitochondrial codes. J. Mol. Evol. 19, 219–225 (1983)

    Article  Google Scholar 

  62. Khrennikov, A.: Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models. Kluwer Academic, Dordrecht (1997)

    MATH  Google Scholar 

  63. Khrennikov, A.: Contextual viewpoint to quantum statistics. J. Math. Phys. 44(6), 2471–2478 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  64. Khrennikov, A.: Information Dynamics in Cognitive, Psychological, Social and Anomalous Phenomena. Kluwer Academic, Dordrecht (2004)

    MATH  Google Scholar 

  65. Khrennikov, A.: On quantum-like probabilistic structure of mental information. Open Syst. Inf. Dyn. 11(3), 267–275 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  66. Khrennikov, A.: Quantum-like brain: Interference of minds. BioSystems 84, 225–241 (2006)

    Article  Google Scholar 

  67. Khrennikov, A.: p-Adic mathematical physics. In: Proceedings of the 2nd International Conference on p-Adic Mathematical Physics. AIP Conference Proceedings, vol. 826 (2006)

    Google Scholar 

  68. Khrennikov, A.Yu., Kozyrev, S.V.: Genetic code on the diadic plane. Phys. A, Stat. Mech. Appl. 381, 265–272 (2007)

    Article  Google Scholar 

  69. Khrennikov, A.: Contextual Approach to Quantum Formalism. Fundamental Theories of Physics. Springer, Berlin (2009)

    Book  MATH  Google Scholar 

  70. Khrennikov, A., Haven, E.: Quantum mechanics and violations of the sure-thing principle: the use of probability interference and other concepts. J. Math. Psychol. 53, 378–388 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  71. Khrennikov, A.: Ubiquitous Quantum Structure: From Psychology to Finance. Springer, Berlin (2010)

    MATH  Google Scholar 

  72. Kloeden, P.E., Platen, E.: Numerical Solution of Stochastic Differential Equations. Springer, Berlin (1992)

    MATH  Google Scholar 

  73. Knight, R.D., Freeland, S.J., Landweber, L.F.: Rewiring the keyboard: evolvability of the genetic code. Nat. Rev. Genet. 2, 49–58 (2001)

    Article  Google Scholar 

  74. Kobrak, M.N., Bittner, E.R.: Quantum molecular dynamics study of polaron recombination in conjugated polymers. Phys. Rev. B 62, 11473 (2000)

    Article  ADS  Google Scholar 

  75. Krauss, S., Obert, C.A., Franks, J., Walker, D., Jones, K., Seiler, P., Niles, L., Pryor, S.P., Obenauer, J.C., Naeve, C.W., Widjaja, L., Webby, R.J., Webster, R.G.: Influenza in migratory birds and evidence of limited intercontinental virus exchange. PLoS Pathog 3(11), 1684–1693 (2007)

    Article  Google Scholar 

  76. Maeda, H.: SMANCS and polymer-conjugated macromolecular drugs: advantages in cancer chemotherapy. Adv. Drug Deliv. Rev. 6, 181–202 (1991)

    Article  Google Scholar 

  77. Maeda, H.: The tumor blood vessel as an ideal target for macromolecular anti cancer agents. J. Control. Release 19, 315–324 (1992)

    Article  Google Scholar 

  78. Maeda, H., Wu, J., Sawa, T., Matsumura, Y., Hori, K.: Tumor vascular permeability and the EPR effect in macromolecular therapeutics: a review. J. Control. Release 65, 271–284 (2000)

    Article  Google Scholar 

  79. Maeda, H., Sawa, T., Konno, T.: Mechanism of tumor-targeted delivery of macromolecular drugs, including the EPR effect in solid tumor and clinicaloverview of the prototype polymeric drug SMANCS. J. Control. Release 74, 47–61 (2001)

    Article  Google Scholar 

  80. Maeda, N., Mchedlishvili, G.: Blood flow structure related to red cell flow: a determinant of blood fluidity in narrow microvessels. Jpn. J. Physiol. 51, 19–30 (2001)

    Article  Google Scholar 

  81. Miyazaki, S., Ohshima, Y., Ohya, M.: A new method of alignment of amino acid sequences. Viva Orig. 17, 139–151 (1989)

    Google Scholar 

  82. Miyazaki, S., Ogata, K., Ohya, M.: On multiple alignment of genome sequences. IEICE Trans. Commun. E75-B(6), 453–457 (1992)

    Google Scholar 

  83. Montroll, E.W.: Quantum theory on a network. I. A solvable model whose wavefunctions are elementary functions. J. Math. Phys. 11, 635 (1970)

    Article  ADS  Google Scholar 

  84. Morens, D.M., Taubenberger, J.K., Fauci, A.S.: The persistent legacy of the 1918 influenza virus. N. Engl. J. Med. 361(3), 225–229 (2009)

    Article  Google Scholar 

  85. Nakamura, A., et al.: Somatosensory homunculus as drawn by meg. NeuroImage 7(4), 377–386 (1998)

    Article  Google Scholar 

  86. Needleman, S.B., Wunsch, C.D.: A general method applicable to search for similarities in the amino acid sequence of two proteins. J. Mol. Biol. 88, 233–258 (1986)

    Google Scholar 

  87. Nelson, M.I., Holmes, E.C.: The evolution of epidemic influenza. Nat. Rev. Genet. 8, 196–205 (2007)

    Article  Google Scholar 

  88. Nelson, M.I., Viboud, C., Simonsen, L., Bennett, R.T., Griesemer, S.B., George, K.S., Taylor, J., Spiro, D.J., Sengamalay, N.A., Ghedin, E., Taubenberger, J.K., Holmes, E.C.: Multiple reassortment events in the evolutionary history of H1N1 influenza a virus since 1918. PLoS Pathog 4(2), 1–12 (2008)

    Article  Google Scholar 

  89. Ogata, K., Ohya, M.: Multiple alignment for amino acid sequences by dynamic program. Electron. Commun. Jpn. Part 3 81(4), 12–20 (1998)

    Google Scholar 

  90. Ohya, M.: Information theoretical treatments of genes. Trans. IEICE E72(5), 556 (1989)

    Google Scholar 

  91. Ohya, M.: Information dynamics and its application to optical communication processes. In: Springer Lecture Note in Physics, vol. 378, pp. 81–92. Springer, Berlin (1991)

    Google Scholar 

  92. Ohya, M., Uesaka, Y.: Amino acid sequences and DP matching. Int. J. Inf. Sci. 63, 139–151 (1992)

    MATH  Google Scholar 

  93. Ohya, M.: Complexities and their applications to characterization of chaos. Int. J. Theor. Phys. 37(1), 495–505 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  94. Ohya, M., Sato, K.: Use of information theory to study genome sequences. Rep. Math. Phys. 46(3), 419–428 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  95. Ohya, M., Sato, K.: Analysis of the disease course of HIV-1 by entropic chaos degree. Amino Acids 20, 155–162 (2001)

    Article  Google Scholar 

  96. Ohya, M., Volovich, I.V.: Quantum computing and chaotic amplification. J. Opt. B 5(6), 639–642 (2003)

    MathSciNet  ADS  Google Scholar 

  97. Ohya, M., Volovich, I.V.: On quantum entropy and its bound. In: Infinite Dimensional Analysis and Quantum Probability, vol. 6, pp. 301–310 (2003)

    Google Scholar 

  98. Ohya, M., Volovich, I.V.: New quantum algorithm for studying NP-complete problems. Rep. Math. Phys. 52(1), 25–33 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  99. Ohya, M.: Information dynamics and its application to recognition process. In: A Garden of Quanta: Essays in Honor of Hiroshi Ezawa, pp. 445–462. World Scientific, Singapore (2003)

    Chapter  Google Scholar 

  100. Ohya, M.: Adaptive dynamics and its applications to chaos and NPC problem. In: QP-PQ: Quantum Probability and White Noise Analysis, Quantum Bio-Informatics, vol. 21, pp. 181–216 (2007)

    Google Scholar 

  101. Olsen, B., Munster, V.J., Wallensten, A., Waldenström, J., Osterhaus, A.D.M.E., Fouchier, R.A.M.: Global patterns of influenza a virus in wild birds. Science 312(5772), 384–388 (2006)

    Article  ADS  Google Scholar 

  102. Osawa, S., Jukes, T.H., Watanabe, K., Muto, A.: Recent evidence for evolution of the genetic code. Microbiol. Rev. 56(1), 229–264 (1992)

    Google Scholar 

  103. Pattnaik, B., Pateriya, A.K., Khandia, R., Tosh, C., Nagarajan, S., Gounalan, S., Murugkar, H.V., Shankar, B.P., Shrivastava, N., Behera, P., Bhagat, S., Peiris, J.S.M., Pradhan, H.K.: Phylogenetic analysis revealed genetic similarity of the H5N1 avian influenza viruses isolated from HPAI outbreaks in chickens in Maharashtra, India with those isolated from swan in Italy and Iran in 2006. Curr. Sci. 96(1), 77–81 (2006)

    Google Scholar 

  104. Pauling, L.J.: The diamagnetic anisotropy of aromatic molecules. Chem. Phys. 4, 673 (1936)

    ADS  Google Scholar 

  105. Philips, J.W., et al.: Imaging neural activity using MEG and EEG. IEEE Eng. Med. Biol. 16, 34–42 (1997)

    Article  Google Scholar 

  106. Robinson, D.F., Foulds, L.R.: Comparison of phylogenetic trees. Math. Biosci. 53, 131–147 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  107. Rose, P.G., Blessing, J.A., Lele, S., Abulafia, O.: Evaluation of pegylated liposomal doxorubicin (Doxil) as second-line chemotherapy of squamous cell carcinomaof the cervix: a phase II study of the Gynecologic Oncology Group. Gynecol. Oncol. 102, 210–213 (2006)

    Article  Google Scholar 

  108. Rumer, Yu.B.: On systematization of codons in the genetic code. Dokl. Acad. Nauk USSR 167(6), 1393–1394 (1966)

    Google Scholar 

  109. Saitou, N., Nei, M.: The neighbor-joining method: a new method for reconstructing phylogenetic trees. Mol. Biol. Evol. 4, 406–425 (1987)

    Google Scholar 

  110. Sato, K., Miyazaki, S., Ohya, M.: Analysis of HIV by entropy evolution rate. Amino Acids 14, 343–352 (1998)

    Article  Google Scholar 

  111. Sato, K., Tanabe, T., Ohya, M.: How can we classify Influenza A viruses and understand their severity? Open. Syst. Inf. Dyn. 17(3), 297–310 (2010)

    Article  MATH  Google Scholar 

  112. Scheraga, H.A., Khalili, M., Liwo, A.: Protein-folding dynamics: overview of molecular simulation techniques. Ann. Rev. Phys. Chem. 58, 57–83 (2007)

    Article  ADS  Google Scholar 

  113. Schlick, T.: Molecular Modeling and Simulation. Springer, New York (2002)

    MATH  Google Scholar 

  114. Sellers, P.H.: On the theory and computation of evolutionary distances. SIAM J. Appl. Math. 26(4), 787–793 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  115. Shafir, E., Tversky, A.: Thinking through uncertainty: nonconsequential reasoning and choice. Cogn. Psychol. 24, 449–474 (1992)

    Article  Google Scholar 

  116. Shafir, E., Tversky, A.: The disjunction effect in choice under uncertainty. Psychol. Sci. 3, 305–309 (1992)

    Article  Google Scholar 

  117. Shankarappa, R., Margolick, J.B., Gange, S.J., Rodrigo, A.G., Upchurch, D., Farzadegan, H., Gupta, P., Rinaldo, C.R., Learn, G.H., He, X., Huang, X.L., Mullins, J.I.: Consistent viral evolutionary changes associated with the progression of human immunodeficiency virus Type 1 infection. J. Virol. 73(12), 10489 (1999)

    Google Scholar 

  118. Shanta, M., Zimmer, M.D., Donald, S., Burke, M.D.: Historical perspective—emergence of influenza A (H1N1) viruses. N. Engl. J. Med. 361(3), 279–285 (2009)

    Article  Google Scholar 

  119. Singer, W.: Consciousness and the structure of neuronal representations. Philos. Trans. R. Soc. Lond. B 353, 1829–1840 (1998)

    Article  Google Scholar 

  120. Singer, W.: Der Beobachter im Gehirn. Essays zur Hirnforschung. Suhrkamp, Frankfurt am Main (2002)

    Google Scholar 

  121. Smith, G.J.D., Bahl, J., Vijaykrishna, D., Zhang, J., Poon, L.L.M., Chen, H., Webster, R.G., Peiris, J.S.M., Guan, Y.: Dating the emergence of pandemic influenza viruses. Proc. Natl. Acad. Sci. USA 106(28), 11709–11712 (2009)

    Article  ADS  Google Scholar 

  122. Sokal, R.R., Sneath, P.H.A.: Numerical Taxonomy. Freeman, New York (1973)

    MATH  Google Scholar 

  123. Stapp, H.P.: Mind, Matter and Quantum Mechanics, 2nd edn. Springer, Berlin (2003)

    Google Scholar 

  124. Sterr, A., et al.: Perceptual correlates of changes in cortical representation of fingers in blind multifinger braille readers. J. Neurosci. 18(11), 4417 (1998)

    Google Scholar 

  125. Swanson, R.: A unifying concept for the amino acid code. Bull. Math. Biol. 46(2), 187–203 (1984)

    MATH  MathSciNet  Google Scholar 

  126. Taubenberger, J.K., Morens, D.M.: 1918 influenza: the mother of all pandemics. Emerg. Infect. Dis. 12(1), 15–22 (2006)

    Google Scholar 

  127. Trifonov, E.N.: The triplet code from first principles. J. Biomol. Struct. Dyn. 22(1), 1–11 (2004)

    MathSciNet  Google Scholar 

  128. Tumpey, T.M., Belser, J.A.: Resurrected pandemic influenza viruses. Annu. Rev. Microbiol. 63, 79–98 (2009)

    Article  Google Scholar 

  129. Uchiyama, K., Nagayasu, A., Yamagiwa, Y., Nishida, T., Harashima, H., Kiwada, H.: Effects of the size and fluidity of liposomes on their accumulation in tumors: a presumption of their interaction with tumors. Int. J. Pharm. 121(2), 195–203 (1995)

    Article  Google Scholar 

  130. Vladimirov, V.S., Volovich, I.V., Zelenov, E.I.: p-Adic Analysis and Mathematical Physics. World Scientific, Singapore (1994)

    Google Scholar 

  131. Volovich, I.V.: p-adic string. Class. Quantum Gravity 4, L83–L87 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  132. Watson, J.D., Baker, T.A., Bell, S.P., Gann, A., Levine, M., Losick, R.: Molecular Biology of the Gene. CSHL Press, Benjamin (2004)

    Google Scholar 

  133. Wikipedia: Amino acid. http://en.wikipedia.org/wiki/Amino_acid (2007)

  134. Wolfs, T.F., Zwart, G., Bakker, M., Valk, M., Kuiken, C.L., Goudsmit, J.: Naturally occurring mutations within HIV-1 V3 genomic RNA lead to antigenic variation dependent on a single amino acid substitution. Virology 185(1), 195 (1991)

    Article  Google Scholar 

  135. Wong, J.T.F.: A co-evolution theory of the genetic code. Proc. Natl. Acad. Sci. USA 72, 1909–1912 (1975)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Information Sciences, Tokyo University of Science, Yamazaki 2641, 278-8510, Noda, Japan

    Masanori Ohya

  2. Mathematical Physics, Steklov Mathematical Institute, Gubkin St 8, 119991, Moscow, Russia

    Igor Volovich

Authors
  1. Masanori Ohya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Igor Volovich
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Masanori Ohya .

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Ohya, M., Volovich, I. (2011). Applications to Life Science. In: Mathematical Foundations of Quantum Information and Computation and Its Applications to Nano- and Bio-systems. Theoretical and Mathematical Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0171-7_21

Download citation

Publish with us

Policies and ethics

Search

Navigation