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Complexity Primer

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Networks of Echoes

Abstract

Complexity is one of those foundational concepts that is difficult to pin down without an operational definition. Even our intuition about complexity is not always reliable and because of that it is useful to consider how the concept originated and developed in the physical sciences before we apply it to the human sciences. In this chapter we try to provide enough explanation of the origins and development of complexity that the reader may develop an overview that is useful for interpreting the results obtained in the subsequent numerical calculations done on complex networks. However if the reader has experience with these ideas skipping this chapter would not be a hardship. If necessary one can always return to read sections as needed.

A man in daily muddy contact with field experiments could not be expected to have much faith in any direct assumption of independently distributed normal events…. George E. P. Box

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Bibliography

  1. R. Adrian, Anal. Math. Mus. 1, 93–109 (1809)

    Google Scholar 

  2. P. Allegrini, D. Menicucci, R. Bedini, L. Fronzoni, A. Gemignani, P. Grigolini, B.J. West, P. Paradisi, Phys. Rev. E 80, 061914 (2009)

    Article  ADS  Google Scholar 

  3. D. Ariely, Predictably Irrational (Harper, New York, 2008)

    Google Scholar 

  4. W.B. Arthur, On the evolution of complexity, in Complexity: Mataphors, Models, and Reality, ed. by G. Cowan, D. Pines, D. Meltzer. SFI Studies in the Sciences of Complexity, Proceedings, vol. XIX (Addison-Wesley, New York, 1994)

    Google Scholar 

  5. R. Badii, A. Politi, Complexity: Hierarchical Structures and Scaling in Physics (Cambridge University Press, Cambridge, 1997)

    Book  MATH  Google Scholar 

  6. K.D. Bailey, Social Entropy Theory (State University of New York (SUNY) Press, Albany, 1990)

    Google Scholar 

  7. F. Bailly, G. Longo, Mathematics and the Natural Sciences: The Physical Singularity of Life (Imperial College Press/World Scientific, Singapore, 2011)

    Google Scholar 

  8. D.A. Ball, Information Theory, 2nd edn. (Pitman, New York, 1956)

    Google Scholar 

  9. C.H. Bennett, Int. J. Theor. Phys. 21, 905 (1982); Sci. Am. 256, 108 (1987)

    Google Scholar 

  10. S. Bianco, M. Ignaccolo, M.S. Rider, M.J. Ross, P. Winsor, P. Grigolini, Phys. Rev. E 75, 061911 (2007)

    Article  ADS  Google Scholar 

  11. G.D. Birkoff, PNAS 17, 656–660 (1931)

    Article  ADS  Google Scholar 

  12. L. Boltzmann, Lectures on Gas Theory, (University of California Press, Berkeley, 1964); Original publication: ‘Vorlesungen über Gastheorie’, J.A. Barth, Leipzig, 1896.

    Google Scholar 

  13. L. Boltzmann, Lectures on Gas Theory (Dover, New York, 1995); first published in 1895, trans. by S.G. Brush

    Google Scholar 

  14. L. Brillouin, Science and Information Theory (Academic, New York, 1962)

    MATH  Google Scholar 

  15. X. Brokmann, J.P. Hermier, G. Messin, P. Desbiolles, J.P. Bouchaud, M. Dahan, Phys. Rev. Lett. 90, 120601 (2003)

    Article  ADS  Google Scholar 

  16. D.R. Brooks, E.O. Wiley, Evolution as Entropy (The University of Chicago Press, Chicago, 1986) (Entropy is used as a unifying concept in biology theory and its use in measuring a system’s degree of order through the evenness and redundancy parameters is reviewed)

    Google Scholar 

  17. R.C. Conant, W.R. Ashby, Int. J. Sys. Sci. 1, 89–97 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  18. J. Correll, J. Personal. Soc. Psych. 94, 48 (2008)

    Article  Google Scholar 

  19. J.P. Crutchfield, Nat. Phys. 8, 17–24 (2011)

    Article  Google Scholar 

  20. J.P. Crutchfield, K. Young, Phys. Rev. Lett. 63, 105–108 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  21. J.P. Crutchfield, J.D. Farmer, N.H. Packard, R.S. Shaw, Sci. Am. 255, 46–57 (1986)

    Article  ADS  Google Scholar 

  22. J.P. Crutchfield, D.P. Feldman, C.R. Shalizi, Santa Fe Institute working paper 99-06-040 (1999). http://www.santafe.edu/media/workingpapers/99-06-040.pdf.

  23. C.F. Gauss, Theoria motus corporum coelestrium (Hamburg, 1809) Theory of Motion of Heavenly Bodies moving about the Sun in Conic Sections, Dover Publications, Mineola, 1963 (Academic, New York, 1963)

    Google Scholar 

  24. M. Gell-Mann, S. Lloyd, Complexity 2, 44–52 (1996)

    Article  MathSciNet  Google Scholar 

  25. N. Georgescu-Roegen, The Entropy Law and the Economic Process (Harvard University Press, Cambridge/Massachusetts, 1971)

    Book  Google Scholar 

  26. J.W. Gibbs, Elementary Principles in Statistical Mechanics (Ox Bow, Woodbridge, Conn. 1981); first published in 1901

    Google Scholar 

  27. D.L. Gilden, T. Thornton, M.W. Mallon, Science 267, 1837 (1995)

    Article  ADS  Google Scholar 

  28. P. Grigolini, D. Leddon, N. Scafetta, Phys. Rev. E 65, 046203 (2002)

    Article  ADS  Google Scholar 

  29. P. Grigolini, G. Aquino, M. Bologna, M. Lukovič, B.J. West, Physica A 388, 4192–4204 (2009)

    Article  ADS  Google Scholar 

  30. M. Haase, C.G. Hübner, E. Reuther, A. Herrmann, K. Müllen, Th. Basché, J. Phys. Chem. B 108, 10445 (2004)

    Article  Google Scholar 

  31. M. Ignaccolo, P. Allegrini, P. Grigolini, P. Hamilton, B. West, Physica A 336, 623 (2004)

    Article  ADS  Google Scholar 

  32. M. Ignaccolo, M. Latka, W. Jernajczyk, P. Grigolini, B.J. West, Phys. Rev. E Phys. Rev. E 81, 031909 (2010)

    Google Scholar 

  33. A.I. Khinchin, Mathematical Foundaitons of Statistical Mechanics, trans. by G. Gamow (Dover, New York, 1949)

    Google Scholar 

  34. D.C. Krakauer, CHAOS 21, 037110 (2011)

    Article  ADS  Google Scholar 

  35. R. Landauer, Physica A 194, 551 (1993)

    Article  ADS  Google Scholar 

  36. R. Landaurer, Science 272, 1914 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  37. R. Landaruer, Phys. Lett. A 217, 188 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  38. P. Landsberg, On Self-Organization. Springer Series in Synergetics, vol. 61 (Springer, Berlin, 1994)

    Google Scholar 

  39. A. Lasota, M.C. Mackey, Chaos, Fractals and Noise (Springer, New York, 1994)

    Book  MATH  Google Scholar 

  40. H. Liepmann, Drei Aufätze aus dem Apraziegebiet (Karger, Berlin, 1908)

    Google Scholar 

  41. B.B. Mandelbrot, Fractals, Form, Chance and Dimension (W.H. Freeman, San Francisco, 1977)

    MATH  Google Scholar 

  42. G. Margolin, E. Barkai, Phys. Rev. Lett. 94, 080601 (2005)

    Article  ADS  Google Scholar 

  43. J.C. Maxwell, Theory of Heat (Dover, New York, 2001); first published in 1888

    Google Scholar 

  44. J.L. McCauley, Physica A 387, 5518–5522 (2008)

    Article  ADS  Google Scholar 

  45. E.W. Montroll, M.F. Shlesinger, PNAS 79, 337 (1982)

    Article  MathSciNet  Google Scholar 

  46. J.S. Nicolis, I. Tsuda, Bull. Math. Biol. 47, 343–365 (1985)

    MATH  MathSciNet  Google Scholar 

  47. C. Nicolls, G. Nicolis, Proc. Natl. Acad. Sci. U.S.A. 83, 536 (1986)

    Article  ADS  Google Scholar 

  48. J.S. Nicolis, Chaos and Information Processing: A Heuristic Outlline (World Scientific, Singapore, 1991)

    Book  Google Scholar 

  49. M. Nirmal, B.O. Dabbousi, M.G. Bawendi, J.J. Macklin, J.K. Trautman, R.D. Harris, L.E. Brus, Nature 383, 802 (1996); M. Kuno, D.P. Fromim, S.R. Hohmson, A. Gallagher, D.J. Nesbitt, Phys. Rev. B 67, 125304 (2003); K.R. Shimizu, R.G. Neuhauser, C.A. Leatherdale, S.A. Empedocles, W.K. Woo, M.G. Bawendi, Phys. Rev. B 63, 205316 (2001)

    Google Scholar 

  50. N. Scafetta, B.J. West, Phys. Rev. Lett. 90, 248701 (2003)

    Article  ADS  Google Scholar 

  51. N. Scafetta, P. Hamilton, P. Grigolini, Fractals 9, 193 (2001)

    Article  Google Scholar 

  52. E. Schrödinger, What Is Life? (Cambridge University Press, New York, 1995); first published in 1944 (This provides the first comprehensive lay discussion of the scientific problems associated with characterizing complexity in biology (life) using classical statistical physics and where the concept of negentropy was introduced)

    Google Scholar 

  53. D.L. Scholten, www.goodregulatorproject.org/images/A_Primer_For_Conant_And_Ashby_s_Good-Regulator_Theorem.pdf

  54. C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (University of Illinois, Urbana, 1949)

    MATH  Google Scholar 

  55. R. Shaw, Z. Naturforsch 36A, 80–112 (1981)

    ADS  Google Scholar 

  56. R. Shaw, The Dripping Faucet as a Model Chaotic System (Ariel, Santa Cruz, 1984)

    Google Scholar 

  57. M.F. Shlesinger, B.J. West, Phys. Rev. Lett. 67, 2106 (1991)

    Article  ADS  Google Scholar 

  58. L. Szilard, Z. Phys. 53, 840 (1929)

    Article  ADS  MATH  Google Scholar 

  59. A.A. Tsonis, J.B. Elsner, Nature 358, 217 (1992)

    Article  ADS  Google Scholar 

  60. G.E. Uhlenbeck, L.S. Ornstein, Phys. Rev. 36, 823 (1930)

    Article  ADS  MATH  Google Scholar 

  61. D.J. Wales, Nature 350, 485 (1991)

    Article  ADS  Google Scholar 

  62. M.C. Wang, G.E. Uhlenbeck, Rev. Mod. Phys. 17, 323 (1945)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  63. B.J. West, Fractal Physiology and Chaos in Medicine, 2nd edn. (World Scientific, Singapore, 2012); first published in 1990

    Google Scholar 

  64. B.J. West, Where Medicine Went Wrong: Rediscovering the Path to Complexity World Scientific, Singapore (2006)

    Google Scholar 

  65. B.J. West, H.J. Mackey, D. Chen, in Patterns, Information and Chaos in Neuronal Systems. Studies of Nonlinear Phenomena in Life Science, vol.2 (World Scientific, Singapore, 1993)

    Google Scholar 

  66. B.J. West, M. Bologna, P. Grigolini, Physics of Fractal Operators (Springer, Berlin, 2003)

    Book  Google Scholar 

  67. B.J. West, E. Geneston, P. Grigolini, Phys. Rep. 468, 1–99 (2008)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  68. N. Wiener, Cybernetics (MIT, Cambridge, 1948)

    Google Scholar 

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West, B.J., Turalska, M., Grigolini, P. (2014). Complexity Primer. In: Networks of Echoes. Computational Social Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-04879-6_2

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