American Journal of Systems and Software
ISSN (Print): 2372-708X ISSN (Online): 2372-7071 Website: http://www.sciepub.com/journal/ajss Editor-in-chief: Josué-Antonio Nescolarde-Selva
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American Journal of Systems and Software. 2016, 4(2), 32-39
DOI: 10.12691/ajss-4-2-1
Open AccessArticle

Diversity for Texts Builds in Language L(MT) II: Indexes Based in Abundances

José Luis Usó-Doménech1, Josué-Antonio Nescolarde-Selva1, 2, , Miguel Lloret-Climent1 and Meng Fan2

1Department of Applied Mathematics, University of Alicante, Alicante, Spain

2School of Mathematics and Statistics, Northeast Normal University, Changchun, China

Pub. Date: March 29, 2016

Cite this paper:
José Luis Usó-Doménech, Josué-Antonio Nescolarde-Selva, Miguel Lloret-Climent and Meng Fan. Diversity for Texts Builds in Language L(MT) II: Indexes Based in Abundances. American Journal of Systems and Software. 2016; 4(2):32-39. doi: 10.12691/ajss-4-2-1

Abstract

One saw previously that indications of diversity IT and the one of Shannon permits to characterize globally by only one number one fundamental aspects of the text structure. However a more precise knowledge of this structure requires specific abundance distributions and the use, to represent this one, of a suitable mathematical model. Among the numerous models that would be either susceptible to be proposed, the only one that present a real convenient interest are simplest. One will limit itself to study applied three of it to the language L(MT): the log-linear, the log-normal and Mac Arthur's models very used for the calculation of the diversity of the species of ecosystems, and used, we believe that for the first time, in the calculation of the diversity of a text written in a certain language, in our case L(MT). One will show advantages and inconveniences of each of these model types, methods permitting to adjust them to text data and in short tests that permit to decide if this adjustment is acceptable.

Keywords:
abundances complex systems distribution language law of Zipf model probability text

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References:

[1]  Forrester. J.W. 1961. Industrial Dynamics. MIT Press, Cambridge, MA.
 
[2]  Usó-Domènech, J. L., Mateu, J and J.A. Lopez. 1997. Mathematical and Statistical formulation of an ecological model with applications. Ecological Modelling. 101, 27-40.
 
[3]  Nescolarde-Selva, J.; Usó-Doménech, J. L.; Lloret-Climent, M. 2014. Introduction to coding theory for flow equations of complex systems models. American Journal of Systems and Software. 2(6). pp. 146-150.
 
[4]  Nescolarde-Selva, J., Usó-Doménech, J.L., Lloret- Climent, M. and González-Franco, L. 2015. Chebanov law and Vakar formula in mathematical models of complex systems. Ecological Complexity. 21. pp. 27-33.
 
[5]  Sastre-Vazquez, P., Usó-Domènech, J.L. and Mateu, J. 2000. Adaptation of linguistics laws to ecological models. Kybernetes. 29 (9/10). 1306-1323.
 
[6]  Usó-Domènech, J.L., Sastre-Vazquez, P. and Mateu, J. 2001. Syntax and First Entropic Approximation of L(MT): A Language for Ecological Modelling. Kybernetes. 30(9/10). 1304-1318.
 
[7]  Usó-Domènech, J.L. and Sastre-Vazquez, P. 2002. Semantics of L(MT): A Language for Ecological Modelling. Kybernetes. 31 (3/4), 561-576.
 
[8]  Usó-Domènech, J.L., Vives Maciá, F. and Mateu. J.. 2006a. Regular grammars of L(MT): a language for ecological systems modelling (I) –part I. Kybernetes. 35 nº6, 837-850.
 
[9]  Usó-Domènech, J.L., Vives Maciá, F. and Mateu. J. 2006b. Regular grammars of L(MT): a language for ecological systems modelling (II) –part II. Kybernetes. 35 (9/10), 1137-1150.
 
[10]  Usó-Doménech, J. L., Nescolarde-Selva, J., Lloret-Climent, M. 2014. Saint Mathew Law and Bonini Paradox in Textual Theory of Complex Models. American Journal of Systems and Software.2 (4), pp. 89-93.
 
[11]  Usó-Doménech, J. L., Nescolarde-Selva, J. 2014. Dissipation Functions of Flow Equations in Models of Complex Systems. American Journal of Systems and Software. 2 (4), pp. 101-107.
 
[12]  Usó-Doménech, J. L., Nescolarde-Selva, J., Lloret-Climent, M. and González-Franco, L. 2014. Diversity for Texts Builds in Language L(MT): Indexes Based in Theory of Information. American Journal of Systems and Software. 2(5). pp. 113-120.
 
[13]  Zipf, G.K. 1949. Human Behavior and the Principle of Least Effort. Cambridge, Mass.
 
[14]  Utida. T. 1943. Relation entre les populations expérimentales de Callosobrunchus chinensis Linné (Coléoptères) et son parasite (Hyménopttères). III. Influence de la densité de population de l'hôte sur la proliferation du parasite. Seitaigaku Kenkyuu, 9, 40-54.
 
[15]  Motomura, L. 1947. Further notes on the law of geometrical progression of the population density in animal association. Seiri Seitai. 1, 55-60.
 
[16]  Preston, F.W. (1948. The commoness and rarity of species. Ecology, 29, 254-283.
 
[17]  Preston, F.W. 1962). The canonical dsitribution of commonness and rarity. Ecology, 43, 185-215 and 410-432.
 
[18]  Mac Arthur, R.H. 1957. On the relative abundance of bird species. Proc. Nat. Acad. Sci. 43, 293-295.
 
[19]  Mac Arthur, R.H. 1960. On the relative abundance of species. Amer. Nat., 94, 25-36.
 
[20]  Mac Arthur, R.H. (1969. Patterns of communities in the tropics. Biol. J. Linn. Soc., 1, 19-30.
 
[21]  Hairston, N.G. 1959. Species abundance and community organization. Ecology. 40, 404-416.
 
[22]  King, S.E. (1964). Relative abundance of species and Mac Arthur model. Ecology. 45, 716-727.
 
[23]  David, F. N. 1947. A χ2 smooth test for goodness of fit. Biometrika. 34, 299-304.