Patricia Sastre-Vázquez

STATISTICAL LINGUISTIC LAWS IN ECOLOGICAL MODELS

This paper gives the theoretical setup so that an ecological model, as a particular mathematical model, can be considered a text written in a formal language (mathematics), and therefore, statistical linguistic laws can be applied to obtain information parameters in different semantic levels of the same model. The statistical laws will be useful to: a) compare semantic levels, submodels, and different models mutually; b) prove that information temperature parameter is an indirect measure of meaning: the significance or semantic component of information, opposed to significant, or comprehension, on the part of the observer (modeller) of the model text. We will apply these ideas in two practical examples.

Syntax and first entropic approximation of L(MT)

Any mathematical model underlying a system of the complex reality (for example, in ecology, socioeconomy, etc.) defines a text written in a given language which belongs to a literature. A text‐model based language, L(MT) is developed, which focuses on its syntax. Three generative grammars are built for its alphabet (lexic unities). Further, the linguistic entropy of this language is analyzed from the Vakar’s point of view. Finally, this theory is applied to a particular ecological model, as an example of a text written in L(MT).

UNCERTAINTY AND COMPLEMENTARITY PRINCIPLES IN ECOLOGICAL MODELS

Literature about models and modelling is very extensive, but the linguistic aspect of ecological models is not so popular. In this paper, the authors develop a linguistic theory of ecological models from the mathematical linguistic theory and its semantic background. From the equivalence relationship defined upon the language L(M), which describes an ecological model in mathematical terms, it will be possible to statistically determine the semantic component associated to each sentence. The authors also propose an uncertainty principle for the equations (called flow equations) that are used to model ecological processes. The following hypothesis will be considered: a) The first-order vocabulary associated to a variable, a transformed function, is a sememe; b) The flow equation is a complex sentence; c) There is a synonymy relationship among sentences that describe the same process; d) The synonymy relationship forms classes of equivalence. The following results will be reported: a) The cardinal of each class of equivalence is a dimension of the process complexity; b) Each sentence can be defined through a pair of numbers (r,m)ER, 0 < =r < =1, 0 < =m < =1, where r defines the coefficient of determination and m the emotional component of meaning (semantics) of the equation; c) The meaning m can be calculated approximately by statistical methods; d) An uncertainty principle (Delta r . Delta m < =0) and a semantic complementarity principle are proposed.Literature about models and modelling is very extensive, but the linguistic aspect of ecological models is not so popular. In this paper, the authors develop a linguistic theory of ecological models from the mathematical linguistic theory and its semantic background. From the equivalence relationship defined upon the language L(M), which describes an ecological model in mathematical terms, it will be possible to statistically determine the semantic component associated to each sentence. The authors also propose an uncertainty principle for the equations (called flow equations) that are used to model ecological processes. The following hypothesis will be considered: a) The first-order vocabulary associated to a variable, a transformed function, is a sememe; b) The flow equation is a complex sentence; c) There is a synonymy relationship among sentences that describe the same process; d) The synonymy relationship forms classes of equivalence. The following results will be reported: a) The cardinal of each cl...

Adaptation of linguistic laws to ecological models

It is known that a mathematical ecological model and, in general, a particular methodology of modelling, can be considered a literary text written in a formal mathematical language. In this context, stylometric mathematical laws such as Zipf’s (range‐frequency and number‐frequency) can be applied to obtain information parameters in different semantic levels within the same model. Adapts several of these laws and introduces new elements, lexic units, operating and separating units, to carry out several statistical analyses upon two models or texts. The estimated slopes in the regression equations obtained in the present work are compared with the results of previous papers where Mandelbrot’s law was applied and comparisons between them are shown.

A systems study of lotus's leaf area

Purpose – A systematic study of a lotuss leaf area is described through the genetic improvement of Lotus glaber, an induced tetraploid population known as, Leonel, was obtained. Initial assessment showed an increase in dry material in comparison with a diploid population. The aim was to evaluate whether the increased production of forage found in the tetraploid population Leonel was due to increased foliolae sizes.Design/methodology/approach – Three populations were studied L. glaber: diploid cytotype: seeds from a naturalised population of La Pampa Deprimida (Azul, Argentina); Tetraploid cytotype C1 seeds from the Leonel population, and Lotus corniculatus (Italia) seeds from Italy. Analysis of variance was carried out with a random design using a single factor, for the variables of area, length and width of the central foliolae. Linear and non‐linear model families were determined to estimate the area of the central foliolae. The selection criteria applied were: the best R2, good efficiency, the greates...

Lotus glaber Mill: comparison of some morphological-physiological characters between an induced autotetraploid population and diploid cultivars.

Lotus glaber Mill, a diploid forage legume (2n=2x=12), has successfully adapted to the ecological characteristics of the Flooding Pampas region of the Province of Buenos Aires, Argentina. This species is highly valued, basically due to its ability to adapt to soils that do not allow other forage legumes to prosper, as well as for its high nutritional value. A genetic improvement programme of the species resulted in an induced autotetraploid population known as “Leonel” (2n=4x= 24). Generally speaking, induced autotetraploid forms are larger and also more vigorous and productive than their diploid counterparts. Although fewer seeds are produced, they are heavier. This article compares certain morphological-physiological characters of the “Leonel” population and diploid cultivars. The characteristics evaluated were length (CFL), width (CFW), area (CFA), length/width ratio (L/W) of the central foliolae of the first expanded leaf from the stem apex and the vigour of the plants (V) from May to December. The following variables were also studied: days to flowering (BFP), air biomass, expressed as green material (GM) and dry material (DM), weight of a thousand seeds (WS), number of seeds per pod (NS), number of empty seeds per pod (ES) and the number of full seeds per pod (FS). Variance analysis was carried out with a completely random design using two factors, cytotype and month, for the following variables: CFL, CFW, CFA, L/W and V. For the remaining variables, variance analysis was carried out with a completely random design using one factor: cytotype. The Duncan’s Test, using a level of confidence of 5%, was used to compare the mean values. In addition, analysis of the L/W ratio allowed the form of the foliolae to be determined.

INFORMATION STORAGE SYSTEM

This paper examines an Information Storage System (ISS), in which a vocabulary and set of experimental data are defined, on the basis of which both linear and linearized (meaning that they are treated in linear fashion) mathematical models are generated. The studies obtained lead to establish certain objective criteria that let us select the best characters to observe and establish a methodology, which allows us to select the mathematical functions that best represent a given system. The studies provide the theoretical basis for obtaining computational algorithms that allow the computational implementation of model selection.

Model information transmission system

Purpose – The purpose of this paper is to study a theory of systems and their models on the basis of studying the information channels between their elements, meaning that it is a continuation of those studies already carried out on the theory of systems and their models applied to environmental systems.Design/methodology/approach – The model information transmission system (MITS) can be defined as the theoretical structure that makes it possible to describe the way information is stored and transmitted in a modelling process, and which will be completed in future studies. The basis for a taxonomy of languages is also presented.Findings – The theoretical structure described will lead to the study of a theory of information from the point of view of the analysis of text systems and models, but analysed within the theoretical structure presented, which includes the study of an information source and an information channel.Originality/value – These theoretical findings will improve the information channels u...

INTERPRETATION OF THE GENERALIZED ZIPF-MANDELBROT LAW PARAMETERS

This article provides an interpretation of the parameters of the generalized Zipf-Mandelbrot law, which the authors have called the generalized range-frequency law which has been developed in 2009. Said law models the distribution of frequencies of words in school textbooks obtained using a Pearson system. The significance of the parameters gathered was obtained by analyzing certain variables. The fact that the statistical law can be applied to texts written using natural language means that it may be applicable to ecological models, these being considered as a particular case of mathematical models written as texts in a formal language, as developed in 1999. After establishing certain hypotheses regarding the significance of the parameters of the generalized law obtained for natural language, this study was designed to analyze whether this law is applicable to models considered as texts written in formal language. If this were so, the law would be a very useful tool for comparing models.

MODELLING OF STATISTICAL LAWS FOR TEXTS USING A PEARSON SYSTEM

In this article, we have obtained a generalization of statistical laws for texts for application to natural languages, in order to determine whether this general law is applicable to model texts in accordance with the definition given in Villacampa et al. (1999a). The studies were carried out in the context of a system whose components generated model texts, through which we confirmed that the laws of Zipf and Mandelbrot are appropriate for explaining the texts. On the basis of a Pearson System, we also obtained a unique function for the distribution of frequencies, with said distribution being a generalization of the above-mentioned laws. For the problem analyzed in this article, the text or text system constitutes a model of the cognitive development of individuals. We can thus infer the cognitive characteristics of different individuals by studying text systems.