Re-inventing Willis

Physics Reports

Volumn 502, Issue 1, 2011, Pages 1-35

  Simkin, M V ^a   Roychowdhury, V P ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79954620921     PISSN: 03701573     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physrep.2010.12.004     Document Type: Review

References (104)

1. Willis J.C., Yule G.U. Some statistics of evolution and geographical distribution in plants and animals, and their significance. Nature 1922, 109:177.
2. Willis J.C. Age and Area: A Study in Geographical Distribution and Origin of Species 1922, University press, Cambridge.
3. Yule G.U. A mathematical theory of evolution, based on the conclusions of Dr. J.C. Willis, F.R.S. Philosophical Transactions of the Royal Society of London B 1925, 213:21.
4. Günter R., Schapiro B., Wagner P. Physical complexity and Zipf's law. International Journal of Theoretical Physics 1992, 31:524.
5. Günter R., Levitin L., Schapiro B., Wagner P. Zipf's law and the effect of ranking on probability distributions. International Journal of Theoretical Physics 1996, 35:395.
6. Krapivsky P.L., Redner S. Organization of growing random networks. Physical Review E 2001, 63:066123.
7. Newman M.E.J. Power laws, Pareto distributions and Zipf's law. Contemporary Physics 2005, 46:323-351. arxiv://arxiv.org/abs/cond-mat/0412004.
8. Simon H.A. On a class of skew distribution functions. Biometrika 1955, 42:425.
9. Champernowne D.G. A model of income distribution. Economic Journal 1953, 63:318.
10. Levy M., Solomon S. Dynamical Explanation for the Emergence of Power Law in a Stock Market Model. International Journal of Modern Physics C 1996, 7:65.
11. Levy M., Solomon S. Power laws are logarithmic Boltzmann laws. International Journal of Modern Physics C 1996, 7:595. arxiv://www.arxiv.org/abs/adap-org/9607001.
12. J.B. Estoup, Gammes sténographique, 1916 (as cited in Ref. [43]). See also: http://torvald.aksis.uib.no/corpora/2002-2/0070.html.
13. Condon E.U. Statistics of vocabulary. Science 1928, 67:300.
14. Zipf G.K. The Psycho-biology of Language 1965, MIT Press, Cambridge, This is a re-issue of the book originally published in 1935.
15. Price D.de S. A general theory of bibliometric and other cumulative advantage process. Journal of American Society for Information Science 1976, 27:292.
16. Price D.de S. Networks of scientific papers. Science 1965, 149:510.
17. Silagadze Z.K. Citations and Zipf-Mandelbrot law. Complex Systems 1997, 11:487.
18. Redner S. How popular is your paper? An empirical study of citation distribution. European Physics Journal B 1998, 4:131. arxiv:cond-mat/9804163.
19. Barabasi A.-L., Albert R. Emergence of scaling in random networks. Science 1999, 286:509.
20. Dorogovtsev S.N., Mendes J.F.F. Evolution of networks. Advances in Physics 2002, 51:1079. See the section "accelerated growth of networks".
21. A.A. Markov, Extension of the law of large numbers to dependent variables in: A.A. Markov, Selected Works, Izdatel'stvo Akademii Nauk SSSR, Moscow, 1951 (in Russian). (The original paper was published in 1907 in an obscure journal.) The ball problem is discussed on pp. 351-354.
22. Chung F., Handjani S., Jungreis D. Generalizations of Polya's urn problem. Annals of Combinatorics 2003, 7:141-153.
23. Johnson N.L., Kotz S. Urn Models and their Application 1977, John Wiley, New York.
24. Simkin M.V., Cohen E.G.D. Magnetic properties of a Bose-Einstein condensate. Physical Review A 1999, 59:1528.
25. Yamada K. Thermal properties of the system of magnetic bosons - Bose-Einstein ferromagnetism. Progress of Theoretical Physics 1982, 67:443.
26. Ijiri Y., Simon H.A. Skew Distributions and the Size of Business Firms 1977, North-Holland, Amsterdam.
27. Moran P.A.P. Random processes in genetics. Proceedings of the Cambridge Philosophical Society 1958, 54:60-72.
28. Karlin S., McGregor J. The number of mutant forms maintained in a population. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4 1967, 415-438. University of California Press, Berkeley.
29. Fermi E. On the origin of the cosmic radiation. Physical Review 1949, 75:1169.
30. Wilson K.G. Physical Review B 1971, 4:3174. (for simpler explanation see Chap. 9.4 of N.D. Goldenfeld Lectures on Phase Transitions and the Renormalization Group Addison-Wesley, 1992).
31. Thouless D.J. Percolation and Localization. Ill-condensed Matter 1979, North Holland, Amsterdam.
32. Reynolds P.J., Klein W., Stanley H E A real-space renormalization group for site and bond percolation. Journal of Physics C 1977, 10:L167-172.
33. Stinchcombe R.B. Introduction to scaling concepts. Scaling Phenomena in Disordered Systems 1985, Plenum, New York. R. Pynn, A. Skjeltorp (Eds.).
34. Stinchcombe R.B. Introduction to scaling concepts. Order and Chaos in Nonlinear Physical Systems 1988, Plenum, New York. S. Lundquist, N.H. March, M.P. Tosi (Eds.).
35. Naranan S. Bradfords's law of bibliography of science: an interpretation. Nature 1970, 227:631.
36. Huberman B.A., Adamic L. Growth dynamics of the World-Wide Web. Nature 1999, 401:131.
37. Naranan S. Power law relations in science bibliography - a self-consistent interpretation. Journal of Documentation 1971, 27:83.
38. Stevens S.S. Neural events and the psychophysical law. Science 1970, 170:1043-1055.
39. MacKay D.M. Psychophysics of perceived intensity: a theoretical basis for Fechner's and Stevens' laws. Science 1963, 139:1213-1216.
40. Mandelbrot B. An informational theory of the statistical structure of languages. Communication Theory 1953, Academic Press, New York. W. Jackson (Ed.).
41. Miller G.A Some effects of intermittent silence. American Journal of Psychology 1957, 70:311-314.
42. C.E. Shannon, A Mathematical Theory of Communication Reprinted with corrections from The Bell System Technical Journal, Vol. 27, pp. 379-423, 623-656, 1948. Available online at: http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf.
43. Fabrikant A., Koutsoupias E., Papadimitriou C.H. Heuristically Optimized Trade-Offs: A New Paradigm for Power Laws in the Internet. Lecture Notes in Computer Science 2002, vol. 2380. Springer, Berlin.
44. Mitzenmacher M. A brief history of generative models for power law and lognormal distributions. Internet Mathematics 2004, 1:226-251.
45. Mandelbrot B. Information theory and Psycholinguistic: a theory of word frequencies. Readings in Mathematical Social Science 1966, Science Research Associates, Chicago. P.F. Lazarsfeld, N.W. Henry (Eds.).
46. Li W. Random texts exhibit Zipf's-law-like word frequency distribution. IEEE Transactions on Information Theory 1992, 38:1842.
47. Carlson J.M., Doyle J. Highly optimized tolerance: a mechanism for power laws in designed systems. Physical Review E 1999, 60:1412.
48. Albert R., Jeong H., Barabasi A.-L. Diameter of the world-wide web. Nature 1999, 401:130.
49. Bornholdt S., Ebel H. World Wide Web scaling exponent from Simon's 1955 model. Physical Review E 2001, 64:035104.
50. Hill B.M. Zipf's law and prior distributions for the composition of a population. Journal of American Statistical Association 1970, 65:1220.
51. Hill B.M. The rank-frequency form of Zipf's law. Journal of American Statistical Association 1974, 69:1017.
52. Bianconi G., Barabási A.-L. Bose-Einstein condensation in complex networks. Physical Review Letters 2001, 86:5632.
53. Feller W. An Introduction to Probability Theory and its Applications, vol. 1 1957, John Wiley, New York.
54. Harris T.E. The Theory of Branching Processes 1963, Springer, Berlin.
55. Athreya K.B., Nay P.E. Branching Process 1972, Springer-Verlag, Berlin.
56. Bru B., Jongmans F., Seneta E. I.J. Bienaymé family information and proof of the criticality theorem. International Statistical Review/Revue Internationale de Statistique 1992, 60:177-183.
57. Cournot A.A. De l'origine et des limites de la correspondence entre l'algèbre et la géométrie 1847, Hachette, Paris, (Chapter 36) (This book is digitized by Google, so one can read it in Google Books).
58. Heyde C.C., Seneta E. The simple branching process, a turning point test and a fundamental inequality: a historical note on I. J. Bienaymé. Biometrika 1972, 59:680-683.
59. Kendall D.G. The genealogy of genealogy: branching processes before (and after) 1873. Bulletin of the London Mathematical Society 1975, 7:225-253.
60. Watson H.W., Galton F. On the probability of the extinction of families. Journal of the Anthropological Institute 1875, 4:138. Available online at: http://galton.org/essays/1870-1879/galton-1874-jaigi-family-extinction.pdf.
61. Guttorp P. Three papers on the history of branching processes translated from Danish by Peter Guttorp. International Statistical Review 1995, 63:233-245.
62. Albertsen K. Slaegternes uddoen (The Extinction of Families). Nord. Mat. Tidsskr. 1976, 24:5-13. English translation published by Guttorp [58].
63. Steffensen J.F. Om Sandssynligheden for at Afkommet uddor (On the Probability that the Offspring Dies Out). Mat. Tidsskr: B 1930, 19-23. English translation published by Guttorp [58].
64. Albertsen K., Kristensen E. En hidtil utrykt losning pa Erlangs problem om slaegternes uddoen af Carl Marius Christensen. (A Previously Unpublished Solution to Erlang's Problem of Extinction of Families by Carl Marius Christensen). Nord. Mat. Tidsskr. 1976, 24:14-18. English translation published by Guttorp [58].
65. Fisher R.A. On the dominance ratio. Proceedings of the Royal Society of Edinburgh 1922, 42:321-341.
66. Fisher R.A. Genetical Theory of Natural Selection 1958, Dover, New York, first edition of the book was published in 1929.
67. Simkin M.V., Roychowdhury V.P. A mathematical theory of citing. Journal of American Society for Information Science and Technology 2007, 58:1661. arxiv://arxiv.org/abs/physics/0504094.
68. Semenoff N. Chemical Kinetics and Chain Reactions 1935, Clarendon, Oxford.
69. D. Hawkins, S. Ulam, Theory of Multiplicative Processes, Los Alamos report (LA-171, November 14, 1944). Reprinted in Ulam, S. M. Analogies Between Analogies, University of California Press, Berkeley, 1990. Available online at: http://content.cdlib.org/view?docId%3Dft9g50091s%26chunk.id%3Dd0e630.
70. Good I.J. The number of individuals in a cascade process. Proceedings of the Cambridge Philosophical Society 1949, 45:360.
71. Otter R. The multiplicative process. The Annals of Mathematical Statistics 1949, 20:206.
72. Zworykin V.K., Morton G.A., Malter L. The secondary emission multiplier-a new electronic device. Proceedings of the IRE 1936, 24:351.
73. Shockley W., Pierce J.R. A theory of noise for electron multipliers. Proceedings of the IRE 1938, 26:321.
74. Steffensen J.F. Deux problèmes du Calcul des Probabilités. Annales de l'institut Henri Poincaré 1933, 3:319. Available online at: http://www.numdam.org/item?id=AIHP_1933__3_3_319_0.
75. Woodward P.M. A statistical theory of cascade multiplication. Mathematical Proceedings of the Cambridge Philosophical Society 1948, 44:404.
76. Flory P.J. Molecular size distribution in three-dimensional polymers. I Gelation. Journal of the American Chemical Society 1941, 63:3083-3090.
77. Flory P.J. Molecular size distribution in three-dimensional polymers. II Trifunctional branching units. Journal of the American Chemical Society 1941, 63:3091-3096.
78. Stockmayer W.H. Theory of molecular size distribution and gel formation in branched-chain polymers. Journal of Chemical Physics 1943, 11:45-55.
79. Broadbent S.R., Hammersley J.M. Percolation processes. Proceedings of the Cambridge Philosophical Society 1957, 53:629.
80. Stauffer D. Introduction to Percolation Theory 1985, Taylor & Francis, London.
81. Solomon S., Weisbuch G., de Arcangelisc L., Jan N., Stauffer D. Social percolation models. Physica A 2000, 277:239.
82. Dietz K. Epidemics and rumours: a survey. Journal of the Royal Statistical Society. Series A 1967, 130:505.
83. Erdos P., Renyi A. On the evolution of random graphs. Publications of the Mathematical Institute of the Hungarian Academy of Science 1960, 5:17-61.
84. Durrett R. Random Graph Dynamics 2006, Cambridge University Press.
85. Milgram S. The Individual in a Social World: Essays and Experiments 1977, Addison Wesley, Reading.
86. Karp R.M. The transitive closure of a random digraph. Random Structures and Algorithms 1990, 1:73-94.
87. Spouge J.L. Polymers and random graphs: asymptotic equivalence to branching processes. Journal of Statistical Physics 1985, 38:573-587.
88. Smoluchowski M.v. Drei Vorträge über Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen. Zeitschrift für Physik 1916, 17:585.
89. McLeod J.B. On an infinite set of non-linear differential equations. Quarterly Journal of Mathematics Oxford 1962, 13(2):119-128.
90. Ben-Naim E., Krapivsky P.L. Kinetic theory of random graphs: from paths to cycles. Physical Review E 2005, 71:026129.
91. Klett J.D. A class of solutions to steady-state, source-enhanced, kinetic coagulation equation. Journal of the Atmospheric Sciences 1975, 32:380-389.
92. Quon J.E., Mockros L.F. International Journal of Air and Water Pollution 1965, 9:279.
93. Pushkin D.O., Aref H. Bank mergers as scale-free coagulation. Physica A 2004, 336:571-584.
94. Kim B.J., Trusina A., Minnhagen P., Sneppen K. Self organized scale-free networks from merging and regeneration. European Physics Journal B 2005, 43:369-372.
95. Kimura M., Crow J.F. The number of alleles that can be maintained in a finite population. Genetics 1964, 49:725.
96. Wright S. Evolution in Mendelian populations. Genetics 1931, 16:97-159.
97. Simkin M.V., Roychowdhury V.P. An explanation of the distribution of inter-seizure intervals. EPL 2010, 91:58005.
98. Hull J.C. Options, Futures, and Other Derivatives 1997, Prentice Hall, Upper Saddle River.
99. Uhlenbeck G.E., Ornstein L.S. On the theory of the Brownian motion. Physical Review 1930, 36:823.
100. Bak P. How Nature Works: The Science of Self-Organized Criticality 1999, Copernicus, New York.
101. Alstrøm P. Mean-field exponents for self-organized critical phenomena. Physical Review A 1988, 38:4905-4906.
102. Lauritsen K.B., Zapperi S., Stanley H.E. Self-organized branching processes: avalanche models with dissipation. Physical Review E 1996, 54:2483-2488.
103. Stigler S.M. Statistics on the Table: The History of Statistical Concepts and Methods 1999, Harvard University Press, Cambridge, Mass.
104. Andreski S. Social Sciences as Sorcery 1972, Andre Deutsch, London.