Zipf's Law, Power Law

一般

• Eric W. Weisstein, Zipf's Law.
• Zipf's Law, Zipfian Probability Distribution in San Diego State University Lecture Notes.
• B. Mandelbrot, Fractals. (広中平祐監訳 "フラクタル幾何学")
• Wentian Li, References on Zipf's law.
• M. E. J. Newman, Power laws, Pareto distributions and Zipf's law, cond-mat/0412004, 2004.

自然言語

• Jamie Callan, Characteristics of Text.
• G. R. Turner, Relationship Between Vocabulary, Text Length and Zipf's Law.
• John Cowan, tanru and lujvo-making. (constructed human language)
• 北村博, Zipfの法則とtextの情報量, 情報処理学会研究報告, NL-052-002, 1985.
• Koichi Ejiri, Adolph E. Smith, Proposal of a New `Constraint Measure' for Text, in Reinhard Köhler, Burghard B. Rieger (Eds.) Contributions to Quantitative Linguistics, pp. 195-211, Kluwer Academic Publishers, 1993.
• Wentian Li, Random Texts Exhibit Zipf's-Law-Like Word Frequency Distribution.
• Alexander Gelbukh, Grigori Sidorov, Zipf and Heaps Laws’ Coefficients Depend on Language, in Proceedings of Conference on Intelligent Text Processing and Computational Linguistics (Notes in Computer Science 2004), 2001.
• Nobuhide Kitabayashi, Zipf's Law Obtained from a Fixed Point in a Transition in the Processes of Learning a Language, Biomedical Fuzzy and Human Sciences, Volume 6, Number 1, pp. 35-40, 2000.
• Ramon Ferrer i Cancho, Ricard V. Solé, Least effort and the origins of scaling in human language, Proc. Nat. Acad. Sci. USA. 100, pp. 788-791, 2003.

ネットワーク

• Web Traffic
  • Jakob Nielsen, Zipf Curves and Website Popularity.
  • Carlos R. Cunha, Azer Bestavros and Mark E.Crovella, Characteristics of WWW Client-based Traces.
  • Steven Glassman, A Caching Relay for the World Wide Web
  • M. Aida and N. Takahashi, Design of Address Cache Table for Data Networking Based on Complementary Use of Two Types of Zipf's Law, in Proceedinfs of APSITT '97, 1997.
  • Yinglian Xie, David O'Hallaron, Locality in Search Engine Queries and Its Implications for Caching, IEEE Infocom 2002, 2002.
• Network topology, routing
  • Andre Broido, Distribution of peering sessions carried by routers.
  • Michalis Faloutsos, Petros Faloutsos, and Christos Faloutsos, On Power-Law Relationships of the Internet Topology, in Proceedings of SIGCOMM'99, pp. 251-262, 1999.

社会, 経済

• Ann L. Chervenak, David A. Patterson and Randy H. Katz, Storage Systems for Movies-on-Demand Video Servers.
• M. H. R. Stanley, S. V. Buldyrev, S. Havlin, R. Montegna, M. A. Salinger, and H. E. Stanley, Zipf Plots and the Size Distribution of Firms.
• Ed Stephan, Time-Minimization and Other Laws in The Division of Territory in Society.
  (Distribution of size of cities in U.S.)
• M. Marsili, Y.-C. Zhang, Interacting Individuals Leading to Zipf's Law, Phys. Rev. Lett. 80, 2741, 1998.
• K. Okuyama, M. Takayasu, H. Takayasu, Zipf's law in income distribution of companies, Physica A 269, 1999.

Human behavior

• Robert Wray et. al., Power Law of Practice.
• 奥乃博, 画面エディタEmacsのユーザ特性について, 情報処理学会第25回プログラミングシンポジウム.

生物学

• physnews@aip.org, Non-coding DNA may be more like a compressed computer file than a natural language, in PHYSICS NEWS UPDATE.
• Partha Niyogi and Robert C. Berwick, A Note on Zipf's Law, Natural Languages, and Noncoding DNA regions .
• P. Schuster, W. Fontana, P. F. Stadler and I. Hofacker, From Sequences to Shapes and Back: A Case Study in RNA Secondary Structures ,

プログラミング

• Douglas W. Clark, C. Cordell Green, An empirical study of list structure in Lisp, Communications of the ACM, Vol. 20, Issue 2, pp. 78-87, 1977.
• J. M. Bennett, Zipf's Law, Structured Programming and Creativity.
• A. Laemmel and M. Shooman, Statistical (Natural) Language Theory and Computer Program Complexity. (in reference)
• Peter Kokol and Tatjana Kokol, Linguistic Laws and Computer Programs.

理論, モデル

• I. Kanter and D. A. Kessler, Markov Processes: Linguistics, Zipf's Law and Long-Range Correlations .
• Christer Samuelsson, Relating Turing's Formula and Zipf's Law.

エッセイ

• Cosma Rohilla Shalizi, Power Law Distributions, 1/f Noise, Long-Memory Time Series, 2004.

その他の法則

• Gutenberg-Richter law
  • 地震の大きさと頻度の関係． マグニチュード M の地震が起きる回数は 10^-bMに比例する． b は 1 に近い値をとる．
  • F. Tzschichholz and H.J. Herrmann, Simulations of pressure fluctuations and acoustic emission in hydraulic fracturing.
• Benford's Law
  • 自然や社会に関係する数量の first digit の出現頻度分布． 数字 D が1文字目に現れる頻度は log (1 + 1/D) に比例する．
  • The power of one, New Scientist, July 10, pp. 26-30, 1999.
  • T.P. Hill, The First-Digit Phenomenon, American Scientist, July-August 1998.
  • Theodore Hill's page.