ベキ分布の作り方

Algorithms / Models

• • Preferential attachment [1], [7], [8]

    • • Appletによるシミュレーション （Java2の実行環境が必要）

  • M-sided die [2]

  • Finite-state grammars [2]

  • Random texts [3]

  • Fragmentation process [4]

  • Self-Organized criticality (SOC) [5]

  • Highly optimized tolerance (HOT) [6]

  • Network optimization [9]

  • Random observation of exponential growth [10]

  • Fitness threshold [11]

  • Hierarchical organization [12]

  • Connecting nearest neighbor [13]

  • Coupled duplication-divergence (CDD) [13]  

References

• 1. H. A. Simon, On a class of skew distribution functions, Biometrika, 42, pp. 425-440, 1955.

  2. Partha Niyogi, Robert C. Berwick, A Note on Zipf's Law, Natural Languages, and Noncoding DNA regions, cmp-lg/9503012, 1995.

  3. Wentian Li, Random Texts Exhibit Zipf's-Law-Like Word Frequency Distribution, IEEE Transactions on Information Theory, Vol. 38, No. 6, pp. 1842-1845, 1992.

  4. Aram Z. Mekjian, Distribution of cluster sizes from evaporation to total multifragmentation, Phys. Rev. C, Vol. 41, No. 5, p. 2103-2117, 1990.

  5. Per Bak, Chao Tang, Kurt Wiesenfeld, Self-organized criticality - An explanation of 1/f noise, Physical Review Letters, Vol. 59, pp. 381-384, 1987.

  6. Jean M. Carlson, Jogn C. Doyle, Highly Optimized Tolerance: A mechanism for power laws in designed systems, Phys. Rev. E, Vol. 60, pp. 1412-1428, 1999.

  7. Albert-László Barabási, Réka Albert, Emergence of scaling in random networks, Science, No. 286, pp. 509-512, 1999.

  8. S. N. Dorogovtsev, J. F. F. Mendes, Language as an evolving word web, in Proceedings of The Royal Society of London, Series B, Biological Sciences, Vol. 268, No. 1485, pp. 2603-2606, 2001.

  9. Ramon Ferrer i Cancho, Ricard V. Solé, Optimization in complex networks, cond-mat/0111222, 2001.

  10. William J. Reed, Barry D. Hughes, From gene families and genera to incomes and internet file sizes: why power-laws are so common in nature, Phys. Rev. E 66, 067103, 2002.

  11. G. Caldarelli, A. Capocci, P. De Los Rios, M. A. Muoz, Scale-free networks from varying vertex intrinsic fitness, Phys. Rev. Lett. 89, 258702, 2002.

  12. Erzsébet Ravasz, Albert-László Barabási, Hierarchical organization in complex networks, Phys. Rev. E 67, 026112, 2003.

  13. Alexei Vázquez, Growing network with local rules: Preferential attachment, clustering hierarchy, and degree correlations, Phys. Rev. E 67, 056104, 2003.

  14. Michael Mitzenmacher, A Brief History of Generative Models for Power Law and Lognormal Distributions, Internet Mathematics, vol 1, No. 2, pp. 226-251, 2004.