Please wait a minute...
Frontiers of Electrical and Electronic Engineering

ISSN 2095-2732

ISSN 2095-2740(Online)

CN 10-1028/TM

Front Elect Electr Eng Chin    0, Vol. Issue () : 181-189    https://doi.org/10.1007/s11460-010-0122-y
RESEARCH ARTICLE
Information in hierarchical modular system
Cheng-Yuan LIOU1(), Ming-Shing CHEN1, Daw-Chih LIOU2
1. Department of Computer Science and Information Engineering, Taiwan University, Taipei 10617, China; 2. Department of Electrical Engineering, Dong Hwa University, Hualien 97401, China
 Download: PDF(358 KB)   HTML
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
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     
Corresponding Author(s): LIOU Cheng-Yuan,Email:cyliou@csie.ntu.edu.tw   
Issue Date: 05 March 2011
 Cite this article:   
Cheng-Yuan LIOU,Ming-Shing CHEN,Daw-Chih LIOU. Information in hierarchical modular system[J]. Front Elect Electr Eng Chin, 0, (): 181-189.
 URL:  
https://academic.hep.com.cn/fee/EN/10.1007/s11460-010-0122-y
https://academic.hep.com.cn/fee/EN/Y0/V/I/181
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
doi: 10.1016/0165-1889(94)90069-8
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
doi: 10.1257/jep.14.1.133
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
doi: 10.1103/PhysRev.106.620
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
doi: 10.1109/TIT.1980.1056144
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
doi: 10.1109/29.45622
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
doi: 10.1109/TSP.2008.917878
15 Frieden B R. Science from Fisher Information: A Unification. Cambridge: Cambridge University Press, 2004
doi: 10.1017/CBO9780511616907
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
doi: 10.1121/1.381721
19 Frieden B R, Hughes R J. Spectral 1/f noise derived from extremized physical information. Physical Review E , 1994, 49(4): 2644-2649
doi: 10.1103/PhysRevE.49.2644
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed