Frontiers of Electrical and Electronic Engineering >
0 181 - 189
Information in hierarchical modular system
Received date: 22 Jun 2010
Accepted date: 20 Sep 2010
Published date: 05 Mar 2011
Copyright
This paper presents a study on the hierarchical modular system (HMS). It shows how to generate the HMS by using the principle of extreme physical information. It also discusses the equal temperament music scale that has many shared properties with the HMS.
Cheng-Yuan LIOU , Ming-Shing CHEN , Daw-Chih LIOU . Information in hierarchical modular system[J]. Frontiers of Electrical and Electronic Engineering, 0 , 6(1) : 181 -189 . DOI: 10.1007/s11460-010-0122-y
1 |
Caianiello E R. Some remarks on organization and structure. Biological Cybernetics, 1977, 26(3): 151-158
|
2 |
Caianiello E R, Scarpetta G, Simoncelli G. A systemic study of monetary systems. International Journal of General Systems, 1982, 8(2): 81-92
|
3 |
Caianiello E R, Marinaro M, Scarpetta G, Simoncelli G. Structure and modularity in self-organizing complex systems. In: Caianiello E R, Aizerman M A, eds. Topics in the General Theory of Structure. D. Reidel Publishing Company, 1987, 5-57
|
4 |
Frieden B R. Estimation of distribution laws, and physical laws, by a principle of extremized physical information. Physica A, 1993, 198(1-2): 262-338
|
5 |
Lavis D A, Streater R F. Physics from Fisher information. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 2002, 33(2): 327-343
|
6 |
Brissaud J B. The meanings of entropy. Entropy, 2005, 7(1): 68-96
|
7 |
Hentsch J C. La circulation des coupures qui constituent une monnaie. Journal de la Societe de Statistique de Paris, 1973, 114(4): 279-293
|
8 |
Van Hove L. Optimal denominations for coins and bank notes: In defense of the principle of least effort. Journal of Money, Credit and Banking, 2001, 33(4): 1015-1021
|
9 |
Banknotes and coins circulation of EUR. http://www.ecb.int/stats/euro/circulation/html/index.en.html
|
10 |
USA: Major Cities. http://www.citypopulation.de/USA-Cities.html
|
11 |
Jaynes E T. Information theory and statistical mechanics. Physical Review, 1957, 106(4): 620-630
|
12 |
Shore J E, Johnson R W. Axiomatic derivation of the principle of maximum entropy and the principle of minimum cross-entropy. IEEE Transactions on Information Theory, 1980, IT-26(1): 26-37
|
13 |
Liou C Y, Musicus B R. Separable cross-entropy approach to power spectrum estimation. IEEE Transactions on Acoustics, Speech and Signal Processing, 1990, 38(1): 105-113
|
14 |
Liou C Y, Musicus B R. Cross entropy approximation of structured Gaussian covariance matrices. IEEE Transactions on Signal Processing, 2008, 56(7): 3362-3367
|
15 |
Frieden B R. Science from Fisher Information: A Unification. Cambridge: Cambridge University Press, 2004
|
16 |
Isacoff S M. Temperament: The Idea That Solved Music’s Greatest Riddle. New York: Random House, Inc., 2001
|
17 |
Kohonen T. Self-Organizing Maps. Berlin: Springer, 2001
|
18 |
Voss R F, Clarke J. 1/f noise in music: Music from 1/f noise. Journal of the Acoustical Society of America, 1978, 63(1): 258-263
|
19 |
Frieden B R, Hughes R J. Spectral 1/f noise derived from extremized physical information. Physical Review E, 1994, 49(4): 2644-2649
|
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