Y. Villacampa

MATHEMATICAL MODELS OF COMPLEX STRUCTURAL SYSTEMS. A LINGUISTIC VISION

The concept of structure is essential in the definition of a system, not only as the basis or backbone of relationships, but also as organization. But where it acquires its most relevant aspect is in ecological or socio-economic systems, where the number of relationships among objects is very high. At the same time, the structure itself is synchronic and develops, in time, a diachronic behavior. It is from the point of view of modern linguistic theories that the authors have developed a concept of structure that is based on the following assumptions: (1) The attributes may or may not be measurable. (T) Each measurable attribute defines an associative field or vocabulary. (3) The whole of all the vocabularies forms the lexicon. (4) With these elements we can define a language of L(m) models. In this paper, the authors will study the synchronic aspect of structure in complex structural models from the point of view of L(m).

A new methodology for modelling highly structured systems

Abstract Highly structured systems (HSS) combine relations among predictive variables to build models that exhibit great complexity. Most of the environmental processes or systems are based on HSS. Based on the generality of this topic, a new methodology for modelling HSS is presented in this paper. The proposed methodology is based on the generation of a regular language which allows the researcher to build some equations with particular language elements. As a consequence of the complexity of the model, most of the functions defining the equations are not linear, which provide much more information than the usual linear equations. Computer software is also presented here.

Generative and recognoscitive grammars of ecological models

Abstract All models have in common that they encode experience and always involve signs, signals, syntax, semantics and an ability to decode and derive meaning from what is encoded. Ecological models can be considered as complex structures and a new way of approaching to these models is through developing a formal language. In this paper, the authors develop the syntax’s of a formal language of complex structures, called here L(M), based on general assumptions from the theory of linguistic mathematics. The syntax and semantics proposed are not a new methodology but a new linguistic interpretation of traditional methodologies. We develop this interpretation over a reproductive submodel of a more general one.

A computer program for a Monte Carlo analysis of sensitivity in equations of environmental modelling obtained from experimental data

In the construction of mathematical models from experimental data, it is possible to determine equations that mode1 relations using several methodologies [Un nuevo algoritmo para la modelizacion de sistemas altamente estructurados (2000); Env. Model. Software 15 (2000) 461; Guide to Statistics 1,2 (1999); Regression models (1999); Ecosystems and Sustainable Development II (1999)]. These methodologies build equations that are in line with the experimental data and they analyse a dimension of adjustment and a dimension of error or distance between the experimental data and the data that is produced by the model. There are studies of sensitivity of the sample of data, as found by Bolado and Alonso [Proceedings SAMO 2001]. The authors consider that it is useful to obtain new parameters that relate the sensitivity of the equations to the variations that are produced by the experimental data. This will allow the selection of the model according to new criteria.On the one hand, the authors present a theoretical study of sensitivity of the models according to different points of view. On the other hand, they discuss a computing algorithm that allows the analysis of sensitivity (and stability) of the mathematical equations, which are built from any methodology. An interface has been incorporated into this algorithm to allow a graphic visualisation of the effects that are produced when modifications of the model are carried out.

A computational algorithm for the multiple generation of nonlinear mathematical models and stability study

This paper presents an algorithm that generates families of mathematical models with nonlinear parameters, and includes the study of linear models, based on the experimental data of the intervening variables. The implementation of this algorithm has been named polymodel and is based on the application of the Gauss-Newton algorithm for obtaining the parameters of nonlinear models [Verdu F. Un Algoritmo para la construccion multiple de modelos matematicos no lineales y el estudio de su estabilidad. Doctoral Tesis. Universidad de Alicante, 2004]. One of its characteristics is a search among different nonlinear models within the parameters; unlike the methods found in the scientific literature [Camacho Rosales J. Estadistica con SPSS para windows. Ed. Ra-Ma, 2002; Mathsoft Inc. Splus-4. Guide to Statistics. Seattle, 1997], the user does not intervene in their generation. A pruning criteria has also been introduced that is based on the stability analysis of models generated from perturbations, applying studies carried out by the authors and published in [Verdu F, Villacampa Y. A computer program for a Monte Carlo analysis of sensitivity in equations of environmental modelling obtained from experimental data. Advances in Engineering Software, 2002]. Object-oriented Pascal has been used in Delphi 6.

Using the Presence of Seagrass Posidonia oceanica to Model the Equilibrium Profile Parameter A of Sandy Beaches in Spain

ABSTRACT Aragonés, L.; López, I.; Villacampa, Y., and Navarro-González, F.J., 2017. Using the presence of seagrass Posidonia oceanica to model the equilibrium profile parameter A of sandy beaches in Spain. The study of equilibrium profile is a fundamental concept in beach morphodynamics and necessary in the design of nourishment. For this reason, it is important to introduce new modelling methodologies that are capable of analysing its behaviour. The aim of the research was to generate mathematical models for obtaining parameter A of the potential function, which describes the equilibrium beach profile on the coast of Valencia and Alicante, using only those variables that are easy to obtain. The presence of Posidonia oceanica in the study area was also taken into account, and on the basis of that, the energy reduction coefficient (Kv) was included as an independent variable in the models. To select the optimal model, the volume error, root mean-square error, mean error, and relative error percentage have been used. Finally, the sensitivity of the models against small perturbations in the independent variables was studied and the models were validated with experimental data obtained from a set of beaches with similar characteristics located outside the study area.

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...

Gravel beaches nourishment: Modelling the equilibrium beach profile

The erosion of the worlds coasts and the shortage of sand to mitigate beach erosion are leading to the increasingly common use of gravel for coastal protection and beach nourishment. Therefore, in order to determine the amount of gravel required for such actions, it is important to know perfectly the equilibrium profile of gravel beaches. However, at present, this profile is obtained from formulas obtained mainly after channel tests, and therefore most of them do not adapt to the real profiles formed by gravel beaches in nature. In this article, 31 variables related to sedimentology, waves, morphology and marine vegetation present on the beaches are studied to determine which are the most influential in the profile. From the study carried out, it is obtained that these variables are the steepness and probability of occurrence of the wave perpendicular to the coast, the profile starting slope (between MWL and -2m), the energy reduction coefficient due to Posidonia oceanica as well as the width of the meadow. Using these variables, different numerical models were generated to predict accurately the gravel beach profile, which will lead to a saving in the volume of material used in the order of 1300m3/ml of beach with respect to current formulations, and a greater certainty that the beach nourishment carried out will have the desired effect.

Modelling of Escherichia coli concentrations in bathing water at microtidal coasts

Monitoring of the quality of bathing water in line with the European Commission bathing water directive (Directive 2006/7/EC) is a significant economic expense for those countries with great lengths of coastline. In this study a numerical model based on finite elements is generated whose objective is partially substituting the microbiological analysis of the quality of coastal bathing waters. According to a study of the concentration of Escherichia coli in 299 Spanish Mediterranean beaches, it was established that the most important variables that influence the concentration are: monthly sunshine hours, mean monthly precipitation, number of goat cattle heads, population density, presence of Posidonia oceanica, UV, urbanization level, type of sediment, wastewater treatment ratio, salinity, distance to the nearest discharge, and wave height perpendicular to the coast. Using these variables, a model with an absolute error of 10.6±1.5CFU/100ml is achieved. With this model, if there are no significant changes in the beach environment and the variables remain more or less stable, the concentration of E. coli in bathing water can be determined, performing only specific microbiological analyses to verify the water quality.

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.