Zipf-Mandelbrot law

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	Zipf-Mandelbrot law - Wikipedia, the free encyclopedia
		Also known as the Pareto-Zipf law, it is a power-law distribution on ranked data, named after the Harvard linguistics professor George Kingsley Zipf (1902-1950) who suggested a simpler distribution called Zipf's law, and the mathematician Benoit Mandelbrot (born November 20, 1924), who subsequently generalized it.
		In probability theory and statistics, the Zipf-Mandelbrot law is a discrete probability distribution.
		For finite N and q = 0 the Zipf-Mandelbrot law becomes Zipf's law.
	en.wikipedia.org /wiki/Zipf-Mandelbrot_law (208 words)

	Zipf's Law, Benford's Law
		Mandelbrot's generalization of Zipf's law is still very simple: the additional complexity lies only in the introduction of the two new adjustable constants, a number added to the rank and a number added to the power 1.
		In Zipf's law the quantity under study is inversely proportional to the rank, that is, proportional to 1, 1/2, 1/3, 1/4, etc. Benoit Mandelbrot has shown that a more general power law (nearly the most general) is obtained by subjecting this sequence successively to two kinds of modification.
		With this in mind, it's natural that statistical data for a phenomenon that obeys one of the power laws (b) is biased towards the lower part of the range, whereas that for a phenomenon with saturation (d) tends to be biased towards the upper part of the range.
	www.cut-the-knot.org /do_you_know/zipfLaw.shtml (2320 words)

	Zipf's law - Psychology Central
		Zipf's law is thus an experimental law, not a theoretical one.
		Zipf's law is most easily observed by scatterplotting the data, with the axes being log(rank order) and log(frequency).
		The "law" was publicized by Harvard linguist George Kingsley Zipf (IPA [zɪf]).
	psychcentral.com /psypsych/Zipf's_law (1021 words)

	Talk:Zipf's law - Wikipedia, the free encyclopedia
		I think we may be fast approaching the point when merging this article with Zipf-Mandelbrot law would be appropriating, along the way doing some reorganizing of the article.
		While it is true that Zipf's law is empirical, I agree with AxelBoldt that it is useful to have an interpretation of it.
		This would agree more with the origin of Zipf's law, which is that the frequency of the i'th word in a written text is proportional to 1/i.
	www.wikipedia.org /wiki/Talk:Zipf%27s_law (1767 words)

	Hukum Zipf-Mandelbrot - Wikipédia
		Hukum Zipf-Mandelbrot (oge dipikanyaho salaku hukum Pareto-Zipf) nyaeta power-law distribution dina ranked data, dipake sanggeus Harvard linguistic professor George Kingsley Zipf (1902-1950) nu ngusulkeun dina teks regularity, sarta mathematician Benoit Mandelbrot (lahir November 20, 1924), no nga-generalisir.
		Distribution kecap dirangking ku frequency-na dina random corpus text ngarupakeun power-law distribution umum, dipikanyaho salaku Zipf's law.
		Lamun hiji plot rangking frequency kecap dikandung dina corpus nu gede tina data teks ka jumlah kajadian atawa frequencies sabenerna, meunangkeun power-law distribution, mibanda exponent raket ka hiji (tapi tempo Gelbukh jeung Sidoro 2001).
	su.wikipedia.org /wiki/Zipf-Mandelbrot_law (112 words)

	Hurwitz zeta function : Information and resources about Hurwitz zeta function : School Work Guru
		Although Hurwitz's zeta function is thought of by mathematicians as being relevant to the "purest" of mathematical disciplines, number theory, it also occurs in applied statistics; see Zipf's law and Zipf-Mandelbrot law.
		This means that the Hurwitz zeta-functions for q a rational number have analytic properties that are closely related to that class of L-functions.
	www.schoolworkguru.org /encyclopedia/h/hu/hurwitz_zeta_function.html (195 words)

	cskw:writings:computers:evomuszipf
		In particular, Zipfï¿½s law inspired and was extended by Benoit Mandelbrot to account for a wider range of natural phenomena [9].
		Zipf distributions are exhibited by words in human languages, computer languages, operating system calls, colors in images, city sizes, incomes, music, earthquake magnitudes, thickness of sediment depositions, extinctions of species, traffic jams, and visits of websites, among others.
		Zipf distributions across certain dimensions appear to be a necessary, but not sufficient condition for pleasant music.
	shaunwagner.com /writings/computers/evomuszipf.html (4197 words)

	Zipf-Mandelbrot law: Encyclopedia topic
		For finite and the Zipf-Mandelbrot law becomes Zipf's law (Zipf's law: originally the term zipfs law meant the observation of harvard linguist...
		Also known as the Pareto (Pareto: Italian sociologist and economist whose theories influenced the development of fascism in Italy (1848-1923)) -Zipf law, it is a power-law (power-law: a power law relationship between two scalar quantities x and y is any such that...
		as Zipf's law (Zipf's law: originally the term zipfs law meant the observation of harvard linguist...
	www.absoluteastronomy.com /reference/zipf-mandelbrot_law (457 words)

	Paul Vogt, - 2004 - Minimum cost and the emergence of the Zipf-Mandelbrot law
		The results indicate that a tendency to communicate in general terms, which is less costly, can contribute to the emergence of the Zipf-Mandelbrot law.
		This paper illustrates how the Zipf-Mandelbrot law can emerge in language as a result of minimising the cost of categorising sensory images.
		The discrimination game is embedded in a variant of the language game model, called the selfish game, which in turn is embedded in the framework of iterated learning.
	edfu.lis.uiuc.edu /~amag/langev/paper/vogt04alife9.html (146 words)

	Sigma Xi: The Scientific Research Society: 2001 Forum Contributed Papers
		Zipf's law was extended by Benoit Mandelbrot to account for additional phenomena--these are phenomena that generate lines with slopes ranging between 0 (random phenomena) and negative infinity (monotonous phenomena).
		Zipf's law states that phenomena generated by self-adapting organisms (e.g., humans) follow the principle of least effort.
		In this light, Zipf's original law could be seen as describing phenomena that are ordered "just right" with respect to human sensory processes.
	www.sigmaxi.org /meetings/archive/forum.2001.prog.pap.shtml (5366 words)

	Zipf's law
		Paul E. Black, "Zipf's law", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
		This law applies to words in human or computer languages, operating system calls, colors in images, etc., and is the basis of many (if not, all!) compression approaches.
		A brief explanation of the law with links to dozens of papers.
	www.nist.gov /dads/HTML/zipfslaw.html (163 words)

	Document Server@UHasselt: Item 1942/802
		It is well-known that, in the latter case, the law of Zipf is valid (i.e.
		We furthermore show that - in case we want to approximate the found distribution by Zipfs law - we obtain exponents p, in this power law for which the sequence (P,),,, is strictly decreasing.
		We prove that in the case of m - word phrases (m22) this is not the case.
	hdl.handle.net /1942/802 (178 words)

	g3inh
		At the 100th anniversary of the birth of George Kingsley Zipf, one striking fact about the statistical regularity that bears his name, Zipf's law, is that it seems to appear everywhere.
		First, the status of Zipf(-Menzerath)’s Law and its criticisms are discussed, and the application of power law models, particularly in linguistics, is supported from a general point of view.
		In which fields are the data sets claiming to exhibit Zipf's law?
	www.ram-verlag.de /g5inh.htm (1018 words)

	Talk:Zipf-Mandelbrot law - Wikipedia, the free encyclopedia
		Is this the same thing as Zipf's law?
		Unless it is more general, probably the two articles should be merged.
	www.wikipedia.org /wiki/Talk:Zipf-Mandelbrot_law (56 words)

	1980s
		Ju K Orlov, RY Chitashvili (1983), "On the statistical interpretation of Zipf's law", Bulletin of the Academy of Sciences of the Georgian, 109(3):505-508.
		JE Fedorowicz (1982), "The theoretical foundation of Zipf's law and its application to the bibliographic data base environment", Journal of the American Society for Information Science, 33(5):284-292.
		JS Nicolis, I Tsuda (1989), "On the parallel between Zipf's Law and 1/f processes in chaotic systems possessing coexisting attractors: a possible mechanism for language formation in the cerebral cortex", Progress of Theoretical Physics, 82(2):254-274.
	www.nslij-genetics.org /wli/zipf/1980s.html (933 words)

	Untitled Document
		A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law.
		Two different approaches to the explanation of Zipf's law is very well summarized in G.Miller's introduction to the 1965 edition of Zipf's book: ``Faced with this massive statistical regularity, you have two alternatives.
		For this reason the general management policy is to emphasize the importance of the organization variable (mainly the human resources employed) based on the knowledge we already have of the laws and scientific relationships between the elements which form the system.
	www.isss.org /99abstPS.htm (14074 words)

	Teleconference "Information technologies in the humanity science"
		By applying a relationship between resolving powers of a complex system and its constituent parts, the expression for the Zipf law in the form, offered by Woronczak, is obtained.
		The unlimited resolving power (vocabulary words packing density) of the canonical form of Zipf law interplays with limitations, imposed by the particular language (sublanguage, idiolect).
		The obtained model of rank distribution is of interest, in particular, for linguadidactics.
	www.ksu.ru /eng/gum_konf/ot2t_en.htm (80 words)

	2002-7-1.txt
		Nature, Music, and the Zipf-Mandelbrot Law Bill Manaris, Charles McCormick, and Tarsem Purewal Computer Science Department College of Charleston Abstract We discuss the application of the Zipf-Mandelbrot law to musical pieces encoded in MIDI.
		Specifically, we have identified a set of metrics on which to apply this law.
		These metrics include pitch of musical events, duration of musical events, the combination of pitch and duration of musical events, and several others.
	stono.cs.cofc.edu /~mccauley/TReports/2002-7-1.txt (158 words)

	Imprint
		The second component is a coupling law responsible for the formation of "cognitive bridges" between operator and target, and may well be topological in nature (see Pitkanen articles in this issue).
		The accuracy of target specificity in coordinate remote viewing and diagnosis strongly suggests that entanglement occurs among all participants in a given intentional set-up, much like the simultaneous activation of various brain modules in object recognition.
		Based on the above discussion we conclude that mental intent has two components: one is energetic/informational, and consists of specialized electromagnetic frequencies and interference patterns which provide a continuous "dialogue" between mind, body and environment (including other minds).
	www.emergentmind.org /sidorov_I.htm (7409 words)

	Evolutionary Music Bibliography
		Zipf-Mandelbrot Law (Manris et al, 2003) Derived Zipf-based metrics for a neural net fitness function that learned to recognize different musical styles.
	www.it.rit.edu /%7Ejab/EvoMusic/EvoMusBib.html (1995 words)

	The Hills Are Alive With The Semantics of Music MetaFilter
		See also Citations and the Zipf-Mandelbrot's law (pdf) which gives a nice overview of the occurrence of this kind of structure in a range of natural phenomena.
		He didn't know beforehand that notes would follow the Zipf Law.
		Besides, using notes, the law was remarkably upheld.
	www.metafilter.com /mefi/33861 (2411 words)

	References
		Beyond the Zipf-Mandelbrot law in quantitative linguistics, by M. Montemurro, http://xxx.lanl.gov/abs/cond-mat/0104066.
		Interacting individuals Leading to Zipf's Law, by M. Marsili and Y. Zhang, http://xxx.lanl.gov/abs/cond-mat/98011289.
	staff.science.nus.edu /~parwani/c1/node91.html (83 words)

	default.aspx?modulo=wikipedia&arg=Zipf's_law
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	www.kisanji.org /default.aspx?modulo=wikipedia&arg=Zipf's_law (518 words)

	Selected Publications
		Bill Manaris, Dallas Vaughan, Christopher Wagner, Juan Romero, and Robert B. Davis, “Evolutionary Music and the Zipf—Mandelbrot Law: Progress towards Developing Fitness Functions for Pleasant Music,” EvoMUSART2003 — 1st European Workshop on Evolutionary Music and Art, Essex, UK, Lecture Notes in Computer Science, Applications of Evolutionary Computing, LNCS 2611, Springer-Verlag, Apr.
		Bill Manaris, Tarsem Purewal, and Charles McCormick, “Progress Towards Recognizing and Classifying Beautiful Music with Computers—MIDI-Encoded Music and the Zipf-Mandelbrot Law,”
		"Zipf’s Law, Music Classification and Aesthetics." Computer Music Journal (to appear).
	www.cs.cofc.edu /%7Emanaris/publications/index.html (918 words)

	its only the end of the world again
		Searching for Beauty in Music - MIDI-Encoded Music and the Zipf Mandelbrot Law (with Bill Manaris and Charles McCormick), College of Charleston Chapter of the Association for Computing Machinery.
		" Progress Towards Recognizing and Classifying Beautiful Music with Computers--MIDI-Encoded Music and the Zipf Mandelbrot Law." (PDF format) Proceedings of the 2002 IEEE Southeastern Conference.
		" Can Beautiful Music be Recognized by Computers?--Nature, Music and the Zipf-Mandelbrot Law." Technical Report CoC/CS #2002-7-1, March 2002.
	stono.cofc.edu /%7Epurewalt (479 words)

	articles
		Boroda, M. and Polikarpov, A. "The Zipf-Mandelbrot Law and Units of Different Text Levels," Musikometrika 1 (1988)/37, 127-158.
		"Menzerath's Law in Musical Texts," Musikometrika 3 (1991)/46, 1-13.
	www.humanities.mcmaster.ca /~renwick/data/articles (11355 words)

	Semmy Purewal's Homepage
		(with Bill Manaris and Charles McCormick) "Progress Towards Recognizing and Classifying Beautiful Music with Computers--MIDI-Encoded Music and the Zipf Mandelbrot Law." Proceedings of the IEEE Southeastern Conference 2002, 52-57.
		The Journal of Combinatorial Mathematics and Combinatorial Computing 46 (2003).
		CSCI 1301 - Introduction to Computing and Programming (Summer 2004)
	www.cs.uga.edu /%7Epurewal (511 words)

	DBLP: Bill Z. Manaris
		Bill Z. Manaris, Dallas Vaughan, Christopher Wagner, Juan Romero, Robert B. Davis: Evolutionary Music and the Zipf-Mandelbrot Law: Developing Fitness Functions for Pleasant Music.
		Bill Z. Manaris, Penousal Machado, Clayton McCauley, Juan Romero, Dwight Krehbiel: Developing Fitness Functions for Pleasant Music: Zipf's Law and Interactive Evolution Systems.
		Ask others: ACM DL - ACM Guide - CiteSeer - CSB - Google - HomePageSearch
	www.vldb.org /dblp/db/indices/a-tree/m/Manaris:Bill_Z=.html (427 words)

	1999 Asilomar session organization
		Frederick Wolf, Eli Berniker, and Mitch Bloom, Organizational Temperature and Entropy: Some Thoughts on the Second Law
		The Thermodynamics of Organizing: Information and Noise in Terms of the Second Law
		James N Rose Integrity, Entropy, Emergy, Gaussian Bubbles
	www.isss.org /sessions.htm (3728 words)

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