Information in hierarchical modular system

Cheng-Yuan LIOU, Ming-Shing CHEN, Daw-Chih LIOU

PDF(358 KB)
PDF(358 KB)
Front. Electr. Electron. Eng. ›› DOI: 10.1007/s11460-010-0122-y
RESEARCH ARTICLE
RESEARCH ARTICLE

Information in hierarchical modular system

Author information +
History +

Abstract

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.

Keywords

hierarchical modular system (HMS) / extreme physical information (EPI) / equal temperament / denomination / city population

Cite this article

Download citation ▾
Cheng-Yuan LIOU, Ming-Shing CHEN, Daw-Chih LIOU. Information in hierarchical modular system. Front Elect Electr Eng Chin, https://doi.org/10.1007/s11460-010-0122-y

References

[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[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
CrossRef Google scholar
[15]
Frieden B R. Science from Fisher Information: A Unification. Cambridge: Cambridge University Press, 2004
CrossRef Google scholar
[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
CrossRef Google scholar
[19]
Frieden B R, Hughes R J. Spectral 1/f noise derived from extremized physical information. Physical Review E, 1994, 49(4): 2644-2649
CrossRef Google scholar

RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
PDF(358 KB)

Accesses

Citations

Detail

Sections
Recommended

/