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Record Statistics and Dynamics

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Encyclopedia of Complexity and Systems Science

Definition of the Subject

The term record statistics covers the statistical properties of records within an orderedseries of numerical data obtained from observations or measurements. A record within such series is simply a value larger (or smaller) than allpreceding values. The mathematical properties of records strongly depend on the properties of the series from which they are extracted. These propertieshave been investigated for many different cases, the simplest cases perhaps being series of independent random numbers drawn from the same (arbitrary)distribution, and series produced by a diffusion process with independent random increments.

The term record dynamicscovers the rather new idea that records may, in special situations, have measurabledynamical consequences. The approach applies to the aging dynamics of glasses and other systems with multiple metastable states. The basic idea is thatrecord sizes fluctuations of e. g. the energy are able...

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Notes

  1. 1.

    Apart from this constraint, the form of the distribution is immaterial.

Abbreviations

Aging:

The slow time evolution of a class of complex systems, which are brought into a far-from‐equilibrium state by the sudden change of an external parameter, e. g. the temperature.

Complex dynamics:

The collective or emergent time dependent properties of interacting multi‐component and multi agent systems.

Marginal stability :

A metastable state is marginally stable if it can be destroyed by slight perturbations.

Metastability:

The ability of a non‐equilibrium system to remain in, or close to, the same state for a certain characteristic time.

Record:

In a time ordered series of random numbers, a record is an entry larger than all preceding entries.

Scale invariant process:

A scale invariant process looks the same under re‐scaling of time and/or space variables.

Stationary process:

A stationary process is time homogeneous, i. e. it is invariant under time translations.

Bibliography

Primary Literature

  1. Anderson P, Jensen HJ, Oliveira LP, Sibani P (2004) Evolution in complex systems. Complexity 10:49–56

    MathSciNet  Google Scholar 

  2. Angelani L, Di Leonardo R, Parisi G, Ruocco G (2003) Topological description of the aging dynamics in simple glasses. Phys Rev Lett 87:055502

    ADS  Google Scholar 

  3. Bak P (1997) How Nature Works. The science of self‐organized criticality. Oxford University Press, Oxford

    Google Scholar 

  4. Bak P, Tang C, Wiesenfeld K (1987) Self‐organized criticality: An explanation of 1/f noise. Phys Rev Lett 59:381–384

    MathSciNet  ADS  Google Scholar 

  5. Boettcher S, Percus A (2001) Optimization with extremal dynamics. Phys Rev Lett 86:5211–5214

    ADS  Google Scholar 

  6. Bouchaud JP (1992) Weak ergodicity breaking and aging in disordered systems. J Phys I France 2:1705–1713

    Google Scholar 

  7. Bray AJ, Moore MA (1987) Chaotic nature of the spin-glass phase. Phys Rev Lett 58:57–60

    ADS  Google Scholar 

  8. Buisson L, Bellon L, Ciliberto S (2003) Intermittency in aging. J Phys Condens Matter 15:S1163

    ADS  Google Scholar 

  9. Christensen K, di Collobiano SA, Hall M, Jensen HJ (2002) Tangled Nature: A Model of Evolutionary Ecology. J Theor Biol 216:73–84

    MathSciNet  Google Scholar 

  10. Cipelletti L, Manley S, Ball RC, Weitz DA. Universal aging features in the restructuring of fractal colloidal gels. Phys Rev Lett 84:2275–2278

    Google Scholar 

  11. Civale L, Marwick AD, McElfresh MW, Worthington TK, Malozemoff AP, Holtzberg FH, Thompson JR, Kirk MA (1990) Defect independence of the irreversibility line in proton‐irradiated y-ba-cu-o crystals. Phys Rev Lett 65(9):1164–1167

    ADS  Google Scholar 

  12. Coppersmith SN, Littlewood PB (1987) Pulse‐duration memory effect and deformable charge‐density waves. Phys Rev B 36:311–317

    ADS  Google Scholar 

  13. Cugliandolo LF, Kurchan J, Peliti L (1997) Energy flow, partial equilibration, and effective temperature in systems with slow dynamics. Phys Rev E 55:3898–3914

    ADS  Google Scholar 

  14. Davidsen J, Grassberger P, Paczuski M (2007) Networks of recurrent events, a theory of records, and an application to finding causal signatures in seismicity. cond-mat/0701190

    Google Scholar 

  15. Fisher DS, Huse DA (1986) Ordered phase of short-range Ising spin‐glasses. Phys Rev Lett 56:1601–1604

    ADS  Google Scholar 

  16. Glick N (1978) Breaking records and breaking boards. Am Math Mon 85:2–26

    MathSciNet  MATH  Google Scholar 

  17. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading

    MATH  Google Scholar 

  18. Hall M, Christensen K, di Collabiano SA, Jensen HJ (2002) Time dependent extinction rate and species abundance in the Tangled Nature model of biological evolution. Phys Rev E 66:011904

    ADS  Google Scholar 

  19. Hammann J, Bouchaud J-P, Dupuis V, Vincent E (2001) Separation of time and length scales in spin glasses: Temperature as a microscope. Phys Rev B 65:024439

    Google Scholar 

  20. Hoffmann KH, Sibani P (1988) Diffusion in hierarchies. Phys Rev A 38:4261–4270

    MathSciNet  ADS  Google Scholar 

  21. Hérisson D, Ocio M (2002) Fluctuation‐dissipation ratio of a spin glass in the aging regime. Phys Rev Lett 88:257202

    Google Scholar 

  22. Jensen HJ (1998) Self‐Organized Complex Systems. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  23. Jonason K, Vincent E, Hammann J, Bouchaud JP, Nordblad P (1998) Memory and Chaos Effects in Spin Glasses. Phys Rev Lett 81:3243–3246

    ADS  Google Scholar 

  24. Jönsson PE, Takayama H, Katori AH, Ito A (2005) Dynamical breakdown of the ising spin-glass order under a magnetic field. Phys Rev B 71:180412(R)

    Google Scholar 

  25. Katzgraber HG, Young AP (2005) Probing the Almeida‐Thouless line away from the mean-field model. Phys Rev B 72:184416

    ADS  Google Scholar 

  26. Keller C, Kupfer H, Meier-Hirmer R, Wiech U, Selvamanickam V, Salama K (1990) Irreversible behaviour of oriented grained \( { yba2cu3ox } \). part 2: relaxation phenomena. Cryogenics 30:410–416

    Google Scholar 

  27. Keller C, Kupfer H, Meier-Hirmer R, Wiech U, Selvamanickam V, Salama K (1990) Irreversible behaviour of oriented grained YBa2Cu3Ox. part 1: transport and shielding currents. Cryogenics 30:401–409

    Google Scholar 

  28. Krug J (2007) Records in a changing world. cond-mat/0702136

    Google Scholar 

  29. Lundgren L, Nordblad P, Sandlund L (1986) Memory behaviour of the spin glass relaxation. Europhys Lett 1:529–534

    ADS  Google Scholar 

  30. Mossa S, Ruocco G, Sciortino F, Tartaglia PP (2002) Quenches and crunches: does the system explore in ageing the same part of the configuration space explored in equilibrium? Phil Mag B 82:695–705

    ADS  Google Scholar 

  31. Nicodemi M, Jensen HJ (2001) Aging and memory phenomena in magnetic and transport properties of vortex matter: a brief review. J Phys A 34:8425

    MathSciNet  ADS  MATH  Google Scholar 

  32. Oliveira LP, Jensen HJ, Nicodemi M, Sibani P (2005) Record dynamics and the observed temperature plateau in the magnetic creep rate of type ii superconductors. Phys Rev B 71:104526

    ADS  Google Scholar 

  33. Parisi G (1979) Infinite number of order parameters for spin‐glasses. Phys Rev Lett 43:1754–1756

    ADS  Google Scholar 

  34. Parisi G, Marinari E, Ruiz-Lorenzo JJ (1998) On the phase structure of the 3D Edwards-Anderson spin-glass. Phys Rev B 58:14852

    ADS  Google Scholar 

  35. Redner S, Petersen MR (2007) Role of global warming on the statistics of record‐breaking temperatures. Phys Rev E 74:061114

    ADS  Google Scholar 

  36. Rodriguez GF, Kenning GG, Orbach R (2003) Full Aging in Spin Glasses. Phys Rev Lett 91:037203

    ADS  Google Scholar 

  37. Rudin W (1966) Real and complex analysis. McGraw Hill, New York

    MATH  Google Scholar 

  38. Schön JC, Putz H, Jansen M (1996) Studying the energy hypersurface of continuous systems–the threshold algorithm. J Phys: Condens Matter 8:143–156

    Google Scholar 

  39. Sibani P (2006) Aging and intermittency in a p-spin model. Phys Rev E 74:031115

    ADS  Google Scholar 

  40. Sibani P (2006) Mesoscopic fluctuations and intermittency in aging dynamics. Europhys Lett 73:69–75

    ADS  Google Scholar 

  41. Sibani P, Andersen CM (2001) Aging and self‐organized criticality in driven dissipative systems. Phys Rev E 64:021103

    ADS  Google Scholar 

  42. Sibani P, Brandt M, Alstrøm P (1998) Evolution and extinction dynamics in rugged fitness landscapes. Int J Modern Phys B 12:361–391

    Google Scholar 

  43. Sibani P, Dall J (2003) Log‐Poisson statistics and pure aging in glassy systems. Europhys Lett 64:8–14

    ADS  Google Scholar 

  44. Sibani P, Jensen HJ (2005) Intermittency, aging and extremal fluctuations. Europhys Lett 69:563–569

    ADS  Google Scholar 

  45. Sibani P, Littlewood PB (1993) Slow Dynamics from Noise Adaptation. Phys Rev Lett 71:1482–1485

    ADS  Google Scholar 

  46. Sibani P, Pedersen A (1999) Evolution dynamics in terraced NK landscapes. Europhys Lett 48:346–352

    ADS  Google Scholar 

  47. Sibani P, Rodriguez GF, Kenning GG (2006) Intermittent quakes and record dynamics in the thermoremanent magnetization of a spin-glass. Phys Rev B 74:224407

    ADS  Google Scholar 

  48. Sibani P, Schmidt M, Alstrøm P (1995) Fitness optimization and decay of the extinction rate through biological evolution. Phys Rev Lett 75:2055–2058

    Google Scholar 

  49. Sibani P, Schriver P (1994) Phase‐structure and low‐temperature dynamics of short range Ising spin glasses. Phys Rev B 49:6667–6671

    ADS  Google Scholar 

  50. Sibani P, Schön C, Salamon P, Andersson J-O (1993) Emergent hierarchical structures in complex system dynamics. Europhys Lett 22:479–485

    Google Scholar 

  51. Stillinger FH, Weber TA (1983) Dynamics of structural transitions in liquids. Phys Rev A 28:2408–2416

    ADS  Google Scholar 

  52. Stillinger FH, Weber TA (1984) Packing Structures and Transitions in Liquids and Solids. Science 225:983–989

    ADS  Google Scholar 

  53. Struik LCE (1978) Physical aging in amorphous polymers and other materials. Elsevier, New York

    Google Scholar 

  54. Swift MR, Bokil H, Travasso RDM, Bray AJ (2000) Glassy behavior in a ferromagnetic p-spin model. Phys Rev B 62:11494–11498

    ADS  Google Scholar 

  55. Takayama H, Hukushima K (2002) Numerical Study on Aging Dynamics in 3D Ising Spin-Glass Model. III. Cumulative Memory and ‘Chaos’ Effects in the Temperature Shift Protocol. J Phys Soc JPN 71:3003–3010

    ADS  Google Scholar 

  56. Tang C, Wiesenfeld K, Bak P, Coppersmith S, Littlewood P (1987) Phase Organization. Phys Rev Lett 58:1161–1164

    MathSciNet  ADS  Google Scholar 

  57. Van Kampen NG (1992) Stochastic Processes in Physics and Chemistry. North Holland, Amsterdam

    Google Scholar 

  58. Vincent E (1991) Slow dynamics in spin glasses and other complex systems. In: Ryan DH (ed) Recent progress in random magnets. McGill University, Montreal, pp 209–246

    Google Scholar 

  59. Vincent E, Hammann J, Ocio M, Bouchaud J-P, Cugliandolo LF (1996) Slow dynamics and aging in spin‐glasses. SPEC-SACLAY-96/048

    Google Scholar 

Books and Reviews

  1. Tinkham M (1998) Introduction to Superconductivity. Krieger, Melbourne

    Google Scholar 

  2. Drossel B (2001) Biological evolution and statistical physics. Adv Phys 50:209–295

    ADS  Google Scholar 

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Acknowledgments

The authors are indebted to P. Anderson, J. Dall, L. Oliveira and S. Boettcher. P. Sibani did part of thiswork while visiting the Cherry L. Emerson Center for Scientific Computation at Emory University.

Author information

Authors and Affiliations

  1. Institut for Fysik og Kemi, SDU, Odense, Denmark

    Paolo Sibani

  2. Department of Mathematics, Imperial College London, London, UK

    Henrik, Jeldtoft Jensen

Authors
  1. Paolo Sibani
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  2. Henrik, Jeldtoft Jensen
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Editor information

Editors and Affiliations

  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Sibani, P., Jensen, H. (2009). Record Statistics and Dynamics. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_448

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