Statistical Analysis of Eco-Toxicologic Data of Mammals from a Polluted Area

Several eco-toxicological studies have shown that insectivorous mammals, due to their feeding habits, easily accumulate high amounts of pollutants in relation to other mammal species. To assess the bio-accumulation levels of toxic metals and their in°uence on essential metals, we quantified the concentration of 19 elements (Ca, K, Fe, B, P, S, Na, Al, Zn, Ba, Rb, Sr, Cu, Mn, Hg, Cd, Mo, Cr and Pb) in bones of 105 greater white-toothed shrews (Crocidura russula) from a polluted (Ebro Delta) and a control (Medas Islands) area. Since chemical contents of a bio-indicator are mainly compositional data, conventional statistical analyses currently used in eco-toxicology can give misleading results. Therefore, to improve the interpretation of the data obtained, we used statistical techniques for compositional data analysis to define groups of metals and to evaluate the relationships between them, from an inter-population viewpoint. Hypothesis testing on the adequate balance-coordinates allow us to confirm intuition based hypothesis and some previous results. The main statistical goal was to test equal means of balance-coordinates for the two defined populations. After checking normality, one-way ANOVA or Mann-Whitney tests were carried out for the inter-group balances

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table has n rows and m columns and all probabilities are non-null. This kind of table can be seen as an element in the simplex of n · m parts. In this context, the marginals are identified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclidean elements of the Aitchison geometry of the simplex can also be translated into the table of probabilities: subspaces, orthogonal projections, distances. Two important questions are addressed: a) given a table of probabilities, which is the nearest independent table to the initial one? b) which is the largest orthogonal projection of a row onto a column? or, equivalently, which is the information in a row explained by a column, thus explaining the interaction? To answer these questions three orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independent two-way tables and fully dependent tables representing row-column interaction. An important result is that the nearest independent table is the product of the two (row and column)-wise geometric marginal tables. A corollary is that, in an independent table, the geometric marginals conform with the traditional (arithmetic) marginals. These decompositions can be compared with standard log-linear models. Key words: balance, compositional data, simplex, Aitchison geometry, composition, orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure, contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears when dealing with proportions. Proportions are by construction parts of a whole, which can be interpreted as compositions assuming they only carry relative information. The Aitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinear operation within that structure. Here we propose to use balances, which are specific elements of this structure, to analyse situations where the paradox might appear. With the proposed approach we obtain that the centre of the tables analysed is a natural way to compare them, which avoids by construction the possibility of a paradox. Key words: Aitchison geometry, geometric mean, orthogonal projection

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocks based on compositional statistics is introduced. It improves and generalizes the common joins-count statistics known from map analysis in geographic information systems. Assigning phases independently to objects in RD is modelled by a single-trial multinomial random function Z(x), where the probabilities of phases add to one and are explicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistencies of the tests based on the conventional joins{count statistics and their possibly contradictory interpretations are avoided. In practical applications we assume that the probabilities of phases do not depend on the location but are identical everywhere in the domain of de nition. Thus, the model involves the sum of r independent identical multinomial distributed 1-trial random variables which is an r-trial multinomial distributed random variable. The probabilities of the distribution of the r counts can be considered as a composition in the Q-part simplex SQ. They span the so called Hardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This is a generalisation of the well-known Hardy-Weinberg law of genetics. If the assignment of phases accounts for some kind of spatial dependence, then the r-trial probabilities do not remain on H. This suggests the use of the Aitchison distance between observed probabilities to H to test dependence. Moreover, when there is a spatial uctuation of the multinomial probabilities, the observed r-trial probabilities move on H. This shift can be used as to check for these uctuations. A practical procedure and an algorithm to perform the test have been developed. Some cases applied to simulated and real data are presented. Key words: Spatial distribution of crystals in rocks, spatial distribution of phases, joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinberg manifold, Aitchison geometry

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materials represent a composition of mineralogies or solute species. Minerals are composed of structured relationships between cations and anions which, through atomic and molecular forces, keep the elements bound in specific configurations. The chemical compositions of minerals have specific relationships that are governed by these molecular controls. In the case of olivine, there is a well-defined relationship between Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition and other significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linear relationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe), which is typically described but poorly illustrated in the simplex. The present contribution corresponds to ongoing research, which attempts to relate stoichiometry and geochemical data using compositional geometry. We describe here the approach by which stoichiometric relationships based on mineralogical constraints can be accounted for in the space of simplicial coordinates using olivines as an example. Further examples for other mineral types (plagioclases and more complex minerals such as clays) are needed. Issues that remain to be dealt with include the reduction of a bulk chemical composition of a rock comprised of several minerals from which appropriate balances can be used to describe the composition in a realistic mineralogical framework. The overall objective of our research is to answer the question: In the cases where the mineralogy is unknown, are there suitable proxies that can be substituted? Kew words: Aitchison geometry, balances, mineral composition, oxides

La biblioteca escolar como recurso educativo

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Elaboraci??n de aplicaciones educativas con Neobook

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Aplicaciones did??cticas de las TIC a la ense??anza de las Ciencias Experimentales

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Xera.

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Actividades para la ense??anza de ingl??s a trav??s de contenidos en secundaria : (Curso PALE de Secundaria 2007, C.P.R. de Oviedo)

El Programa PALE (programa de apoyo al aprendizaje de lenguas extranjeras), cofinanciado por el Ministerio de Educaci??n y Ciencia y las Comunidades Aut??nomas, pretende dar respuesta, desde el Sistema Educativo, a las necesidades derivadas de la mejora de la ense??anza y el aprendizaje de lenguas extranjeras en una sociedad como la actual, donde las lenguas se consideran conocimientos b??sicos que precisa la ciudadan??a europea para su formaci??n, para mejorar sus posibilidades de empleo, para la promoci??n del intercambio cultural y para la realizaci??n personal. Esta publicaci??n es el fruto del grupo de trabajo constituido en la tercera fase del curso PALE 2007 para Secundaria del C.P.R. de Oviedo, tras la formaci??n recibida en Asturias y en el extranjero. Se presentan una serie actividades para llevar a cabo en el aula a partir de los contenidos en Secundaria en las ??reas de: Arte, Biolog??a, Ciudadan??a, Ciencias Sociales, Matem??ticas, M??sica, Educaci??n F??sica, F??sica y Qu??mica, y Tecnolog??a. Las unidades trabajadas son respectivamente: Observation; Vertebrate animals; Human rights; 3-d shapes; Sound and its properties; Outdoor activities; Work and energy; Electricity; Technical materials. El libro est?? acompa??ado por 1 CD-ROM que muestra los contenidos en versi??n PDF y PowerPoint.

VII Jornadas de Intercambio de Experiencias Educativas : Avilés, 10, 11 y 12 de noviembre de 2008.

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VIII Jornadas de Intercambio de Experiencias Educativas : Avilés, 16, 17 y 18 de Noviembre de 2009.

Comunicaciones presentadas en las VIII Jornadas de Intercambio de Experiencias Educativas, celebradas en el Centro del Profesorado y de Recursos de Avilés en noviembre de 2009, acompañadas en cada caso de las correspondientes presentaciones y aplicaciones empleadas en la exposición y de fragmentos videográficos relativos a cada intervención. En la línea de ediciones anteriores de las Jornadas, continúan su apuesta por dar a conocer experiencias educativas de centro y de aula. La selección de experiencias se ha llevado a cabo utilizando el mismo protocolo que en años anteriores. A partir de la valoración de las memorias presentadas por la totalidad de Seminarios y Grupos de Trabajo desarrollados en este C.P.R. durante el curso escolar 2008-2009, se ha efectuado la correspondiente selección teniendo en cuenta criterios de calidad y proyección en las actividades de aula. Se han incluido en la presente edición experiencias procedente de ámbitos geográficos próximos, en función de la valía y oportunidad de la temática abordada, pudiendo diferenciarse en conjunto tres grandes temáticas: el tratamiento de la diversidad desde la dimensión de las altas capacidades, las bibliotecas escolares en distintos tipos de centros y el tratamiento de las Tecnologías de la Información y la Comunicación desde la doble perspectiva de un modelo de integración de las TIC en un centro educativo y la elaboración de aplicaciones para la pizarra digital interactiva.

Las bibliotecas escolares : estado de la cuestión y estudio de la situación en las provincias de Jaén y Cádiz.

Mostrar la situación de las bibliotecas escolares en Jaén y Cádiz, haciendo un análisis de estas bibliotecas y de las tendencias más destacables que se presentan dentro de dicho campo de estudio. Se tratan aquí la fundamentación pedagógica de la biblioteca escolar, así como lo referente al personal, colección, edificio, medios audiovisuales y normas. Por otro lado se relaciona esto con un estudio histórico, geográfico y económico de las citadas provincias. Bibliotecas de centros escolares de EGB, BUP, COU y Formación Profesional. Encuesta enviada a todos los centros, tanto oficiales como privados, así como la consulta a diversos profesionales de la enseñanza: profesores, directores, pedagogos etc. Se realizan también visitas personales a los distintos centros, entre el 30 y el 40 por ciento del total. Cuestionarios compuestos de 17 cuestiones básicas y datos recogidos de las distintas visitas. Tablas descriptivas y comparación y análisis de datos de distintos grupos de enseñanza entre una y otra provincia. Los resultados de la investigación son similares tanto en la provincia de Jaén como en Cádiz; las diferencias son más de tipo cuantitativo que cualitativo; la realidad es una situación de ineficacia en cuanto a la labor social que estas bibliotecas escolares deben cumplir y por otro lado presentan unas características de absoluta inadecuación en cuanto a la misión de completar los planes de estudios y de servir de herramienta para profesores y alumnos. Son pocas las bibliotecas escolares existentes y las pocas que hay con inadecuadas instalaciones, escasos fondos bibliográficos y nulo personal exclusivamente dedicado a ellas y adecuadamente preparado. Señalar la cada vez más generalizada conciencia de que hay que acabar con esta situación. Desde el punto de vista pedagógico, es la escuela moderna el sistema que mejor justifica la existencia y promoción de la biblioteca escolar. Es preferible la existencia de un bibliotecario profesional; también es de vital importancia la configuración física de la biblioteca escolar. La situación estudiada en Jaén y Cádiz es perfectamente generalizada al resto de España. Es de vital urgencia y necesidad la formación de un equipo a nivel nacional, que elabore una normativa y plan general para el establecimiento de un sistema nacional de bibliotecas escolares.

La Ense??anza del modelado en Artes y Oficios : un dise??o escolar

Potenciar en los alumnos el conocimiento de la realidad por medio de la observaci??n del entorno. Hacer asimilables estas observaciones. Actuar sobre los materiales para poder acceder a formas completas de organizaci??n estructural en el espacio. Alumnos de la Escuela de Artes Aplicadas de Le??n. An??lisis de los elementos que rodean el ??rea de Modelado, aplicaci??n de esta teor??a al campo de las Artes Aplicadas estructurando un programa y una metodolog??a para primero, segundo y tercero de Artes Aplicadas. T??cnica de modelado. La programaci??n para los tres primeros cursos de Modelado en Artes Aplicadas con la seguridad que aporta un an??lisis de los elementos disponibles y de una metodolog??a apropiada. El intento de aunar la capacidad de innovaci??n, la aportaci??n de nuevas alternativas, la inventiva y originalidad. La sintetizaci??n de problemas y el planteamiento y aportaci??n de soluciones inesperadas, coherentes y v??lidas dentro de un campo un poco desorganizado como es el Modelado en Artes Aplicadas.