B. Mandelbrot. An informational theory of the statistical structure of language. In W. Jackson, editor, Communication Theory. Butterworths, 1953. 20 Kb 40 Kb 2 am 6 am 10 am 2 pm 6 pm 10 pm 100 Kb 200 Kb 300 Kb node 1 --> node 2 2 am 6 am 10 am 2 pm 6 pm 10 pm 50 Kb 200 Kb 2 am 6 am 10 am 2 pm 6 pm 10 pm 200 Kb 400 Kb 600 Kb  Home/Search   Document Not in Database   Summary   Related Articles   Check

....before the modern e ort to understand power laws on the Web, and how much computer scientists had to reinvent. 4 Power Laws via Optimization Mandelbrot had developed other arguments for deriving power law distributions based on information theoretic considerations somewhat earlier than Simon [55]. His argument is very similar in spirit to other recent optimization based arguments for heavy tailed distributions [17, 27, 85] We sketch Mandelbrot s framework, which demonstrates a power law in the rankfrequency distribution of words. That is, the frequency p j of the jth most used word, ....

B. Mandelbrot. An informational theory of the statistical structure of languages. In Communication Theory, edited by W. Jackson, Betterworth, pages 486-502, 1953.

.... Auerbach [5] Lotka (circa 1926) found in examining the number of articles produced by chemists that the distribution followed a power law [42] Mandelbrot had developed other arguments for deriving power law distributions based on information theoretic considerations somewhat earlier than Simon [44]. His argument is very similar in spirit to other recent optimization based arguments for heavy tailed distributions [14, 69] We sketch Mandelbrot s framework. Consider some language consisting of n words. The cost of using the jth word of the language in a transmission is C j . For example, if ....

B. Mandelbrot. An informational theory of the statistical structure of languages. In Communication Theory, edited by W. Jackson, Betterworth, pp. 486-502, 1953.

.... Auerbach [5] Lotka (circa 1926) found in examining the number of articles produced by chemists that the distribution followed a power law [42] Mandelbrot had developed other arguments for deriving power law distributions based on information theoretic considerations somewhat earlier than Simon [44]. His argument is very similar in spirit to other recent optimization based arguments for heavy tailed distributions [14, 68] We sketch Mandelbrot s framework. Consider some language consisting of n words. The cost of using the jth word of the language in a transmission is C j . For example, if ....

B. Mandelbrot. An informational theory of the statistical structure of languages. In Communication Theory, edited by W. Jackson, Betterworth, pp. 486-502, 1953.

....words account for almost all of the data, and almost all words occur fewer than ten times. The frequency f of the nth most frequent word is usually given by Zipf s Law: f = k (n m) s . 1] where k, m and s are nearly constant for a given collection of documents [Zipf49] [Mand53]. As a result, the optimisation whereby lq text packs the first half dozen or so matches into the end of the fixed size record for that word, filling the space reserved for storing long words, is a significant saving. On the other hand, the delta encoding gives spectacular savings for those few ....

Mandelbrot, Benoit, "An informational theory of the statistical structure of language," in Communication Theory, ed. Willis Jackson, pp. 486--502, Butterworths, 1953.

.... 1) L ; 11) which can be written as: P i (L) C (r(L) B) P i (L 1) 12) with = log(M 1) log(M) B = M M 1 ; and C = 1 M M (M 1) M 1 (M 1) 13) The functional form P (r) C (r B) 14) is also called the generalized Zipf s law by Mandelbrot [3, 5]. Let us check how close the generalized Zipf s law for random texts can be to Zipf s law in English: since the number of alphabets is M = 26, we have = 1:01158 and C = 0:04. The exponent is extremely close to what is observed in English, an amazing fact considering how little we have assumed. ....

B. Mandelbrot, \An informational theory of the statistical structure of language," in Communication Theory, ed. Willis Jackson (Betterworths, 1953).

....it has been used in the study of systems such as chaotic dynamical systems [5] biological sequences [6,7] and economic systems [8,9] Zipf found, for texts written in natural languages, a universal power law behavior characterized by a power law exponent close to 1. Several theoretical models [10,11,12,13] have been proposed to explain Zipf s law. Some of them [11,13] show, theoretically and empirically, that Zipf s law is also satisfied in randomly generated symbolic sequences, with an exponent i close to one. These theoretical models and empirical results suggest that Zipf s law and the value of ....

B. Mandelbrot, An Informational Theory of the Statistical Structure of Language, in Communication Theory, W. Jackson, Ed., Butterworths Scientific Publications, London (1953).

....speech signal can be efficiently coded. The approach taken is to examine certain observed phenomena in speech, and suggest how their exploitation could have conferred an advantage as human language evolved. The starting point for this approach comes from work done many years ago by Mandelbrot [17]. He proposed that a general statistical structure, independent of meaning, underlies human languages, and that language is intentionally if not consciously produced in order to be decoded word by word in the easiest possible fashion . By examining how language is produced for humans to decode, ....

B Mandelbrot. An informational theory of the statistical structure of language. In Symposium on Applications of Communication Theory. Butterworth, 1952.

....Jamison in 1968 [10] used Shannon s method of guessing to get an estimate of 1.65 bpc and they pointed out a connection between entropy and partial knowledge of languages in linguistics. The use of information theoretic methods in the study of language has been studied extensively by Mandelbrot [18], Chomsky [4] Newman [20] Yaglom, Dobrushin and Yaglom [30] and Paisley [23] among many others. The texts [29] 27] 1] and the paper [7] contain extensive bibliographies on the subject. 3 Machines vs Humans How come humans, using just a few characters, can estimate entropy so much more ....

B. Mandelbrot. An informational theory of the statistical structure of language. In W. Jackson, editor, Communication Theory, pages 485--502. New York: Academic Press, 1953.

....and the case 1 (more precisely, between 1.5 and 2.0) fits better the real data [ANZ97] This case is very different, since the distribution is much more skewed, and H V ( O(1) There have been attempts to correct the inaccuracies of Zipf s Law. One attempt is the Mandelbrot distribution [Man52] which states that the frequency of the i th word is n = c i) for some constants c and . We do not use this distribution in this work because its asymptotical effect is negligible and it is much harder to deal with mathematically. It is interesting to notice that Zipf like distributions ....

B. Mandelbrot. An informational theory of the statistical structure of language. In Proc. Symposium on Applications of Communication Theory, pages 486--500, 1952.

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B. Mandelbrot, #An informational theory of the statistical structure of language", in Communication Theory, ed. W. Jackson #Academic Press, 1953#.

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B. Mandelbrot. An informational theory of the statistical structure of language. In W. Jackson, editor, Communication Theory. Butterworths, 1953. 20 Kb 40 Kb 2 am 6 am 10 am 2 pm 6 pm 10 pm 100 Kb 200 Kb 300 Kb node 1 --> node 2 2 am 6 am 10 am 2 pm 6 pm 10 pm 50 Kb 200 Kb 2 am 6 am 10 am 2 pm 6 pm 10 pm 200 Kb 400 Kb 600 Kb

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B. Mandelbrot. An informational theory of the statistical structure of language. In W. Jackson, editor, Symp. Applied Communications Theory, pages 486--500. Betterworth, 1953.

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Number 333. B Mandelbrot. 1952. An informational theory of the statistical structure of language. In Symposium on Applications of Communication Theory.

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