CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is afundamental issue in palaeoclimatic and paleooceanographic investigations. TheModern Analogue Technique, a widely adopted method based on direct comparison offossil assemblages with modern coretop samples, was revised with the aim ofconforming it to compositional data analysis. The new CODAMAT method wasdeveloped by adopting the Aitchison metric as distance measure. Modern coretopdatasets are characterised by a large amount of zeros. The zero replacement was carriedout by adopting a Bayesian approach to the zero replacement, based on a posteriorestimation of the parameter of the multinomial distribution. The number of modernanalogues from which reconstructing the SST was determined by means of a multipleapproach by considering the Proxies correlation matrix, Standardized Residual Sum ofSquares and Mean Squared Distance. This new CODAMAT method was applied to theplanktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea.Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix,Standardized Residual Sum of Squares

Multi-isotopic and compositional exploration of factors controlling nitrate pollution

In Catalonia, according to the nitrate directive (91/676/EU), nine areas have been declared as vulnerable to nitrate pollution from agricultural sources (Decret 283/1998 and Decret 479/2004). Five of these areas have been studied coupling hydro chemical data with a multi-isotopic approach (Vitòria et al. 2005, Otero et al. 2007, Puig et al. 2007), in an ongoing research project looking for an integrated application of classical hydrochemistry data, with a comprehensive isotopic characterisation (δ15N and δ18O of dissolved nitrate, δ34S and δ18O of dissolved sulphate, δ13C of dissolved inorganic carbon, and δD and δ18O of water). Within this general frame, the contribution presented explores compositional ways of: (i) distinguish agrochemicals and manure N pollution, (ii) quantify natural attenuation of nitrate (denitrification), and identify possible controlling factors.To achieve this two-fold goal, the following techniques have been used. Separate biplots of each suite of data show that each studied region has a distinct δ34S and pH signatures, but they are homogeneous with regard to NO3- related variables. Also, the geochemical variables were projected onto the compositional directions associated with the possible denitrification reactions in each region. The resulting balances can be plot together with some isotopes, to assess their likelihood of occurrence

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materialsrepresent a composition of mineralogies or solute species. Minerals are composed of structuredrelationships between cations and anions which, through atomic and molecular forces, keep the elementsbound in specific configurations. The chemical compositions of minerals have specific relationships thatare governed by these molecular controls. In the case of olivine, there is a well-defined relationshipbetween Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition andother significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linearrelationship 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 andgeochemical data using compositional geometry. We describe here the approach by which stoichiometricrelationships based on mineralogical constraints can be accounted for in the space of simplicialcoordinates using olivines as an example. Further examples for other mineral types (plagioclases andmore complex minerals such as clays) are needed. Issues that remain to be dealt with include thereduction of a bulk chemical composition of a rock comprised of several minerals from which appropriatebalances can be used to describe the composition in a realistic mineralogical framework. The overallobjective of our research is to answer the question: In the cases where the mineralogy is unknown, arethere suitable proxies that can be substituted?Kew words: Aitchison geometry, balances, mineral composition, oxides

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering ofcompositional data in situations where observations are constituted by trajectories ofcompositional data, that is, by sequences of composition measurements along a domain.Observed trajectories are known as “functional data” and several methods have beenproposed for their analysis.In particular, methods for clustering functional data, known as Functional ClusterAnalysis (FCA), have been applied by practitioners and scientists in many fields. To ourknowledge, FCA techniques have not been extended to cope with the problem ofclustering compositional data trajectories. In order to extend FCA techniques to theanalysis of compositional data, FCA clustering techniques have to be adapted by using asuitable compositional algebra.The present work centres on the following question: given a sample of compositionaldata trajectories, how can we formulate a segmentation procedure giving homogeneousclasses? To address this problem we follow the steps described below.First of all we adapt the well-known spline smoothing techniques in order to cope withthe smoothing of compositional data trajectories. In fact, an observed curve can bethought of as the sum of a smooth part plus some noise due to measurement errors.Spline smoothing techniques are used to isolate the smooth part of the trajectory:clustering algorithms are then applied to these smooth curves.The second step consists in building suitable metrics for measuring the dissimilaritybetween trajectories: we propose a metric that accounts for difference in both shape andlevel, and a metric accounting for differences in shape only.A simulation study is performed in order to evaluate the proposed methodologies, usingboth hierarchical and partitional clustering algorithm. The quality of the obtained resultsis assessed by means of several indices

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By anessential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur inmany compositional situations, such as household budget patterns, time budgets,palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful insuch situations. From consideration of such examples it seems sensible to build up amodel in two stages, the first determining where the zeros will occur and the secondhow the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

La empresa farmacéutica de Japón en búsqueda de alianzas para la globalización

En este trabajo se investigarán cuatro estudios de caso de empresas farmacéuticas japonesas cuya estrategia es la adquisición o alianzas para poder internacionalizarse.

Política Exterior y Parlamento Europeo

Desde el Acta Única Europea de 1987, las sucesivas reformas de la Unión Europea se han realizado con el doble lema de mejorar tanto la eficacia de las políticas de la Unión como la transparencia y posibilidades de control democrático en el proceso decisorio europeo. La consolidación del doble lema eficacia-democracia ha evidenciado la necesidad de la UE de satisfacer las dos vertientes de la legitimidad clásicas de las democracias liberales: por un lado, la legitimidad asentada en los resultados (output legitimacy), es decir, que las instituciones funcionen eficientemente y sean capaces de llevar a cabo políticas eficaces y conformes a los valores que imperan en una sociedad; y por el otro, la legitimidad del proceso (input legitimacy) o, lo que es lo mismo, que las políticas se desarrollen siguiendo los procesos institucionales establecidos y que permitan el grado de participación y control público considerado adecuado en una comunidad política. El ámbito de la política exterior no ha estado exento de este debate sobre la necesidad de combinar eficacia y democracia, sobre todo a medida que dicho ámbito se ha ido ampliando funcionalmente con el desarrollo la Política Exterior y de Seguridad Común (PESC), su dimensión de defensa (PESD), los aspectos exteriores de las políticas de Justicia y Asuntos de Interior (JAI), o la Política Europea de Vecindad, que pasa transversalmente por todos los "pilares" de la UE. Los capítulos del presente libro pretenden examinar cómo ha progresado en los años recientes la política exterior europea en las dos dimensiones de la legitimidad señaladas (eficacia y control democrático), en cuatro áreas temáticas de la política exterior europea: promoción de la democracia y los derechos humanos, dimensión exterior de las políticas de Justicia y Asuntos de Interior, Política Europea de Vecindad y, por último, el papel de la UE en la gobernanza global.

An alternative method for dating unknown tephras based on a segmented regression model

In CoDaWork’05, we presented an application of discriminant function analysis (DFA) to 4 differentcompositional datasets and modelled the first canonical variable using a segmented regression modelsolely based on an observation about the scatter plots. In this paper, multiple linear regressions areapplied to different datasets to confirm the validity of our proposed model. In addition to dating theunknown tephras by calibration as discussed previously, another method of mapping the unknown tephrasinto samples of the reference set or missing samples in between consecutive reference samples isproposed. The application of these methodologies is demonstrated with both simulated and real datasets.This new proposed methodology provides an alternative, more acceptable approach for geologists as theirfocus is on mapping the unknown tephra with relevant eruptive events rather than estimating the age ofunknown tephra.Kew words: Tephrochronology; Segmented regression

Spain in Europe 2004-2008

In March of 2004, the Observatory of European Foreign Policy published a special monograph about Spain in Europe (1996-2004) in digital format. The objective of the monograph was to analyse Spain’s foreign policy agenda and strategy during the period of José María Aznar’s presidency. As the title suggests, one of the initial suppositions of the analysis is the Europeanization of Spanish foreign activities. Is that how it was? Did Aznar’s Spain see the world and relate to it through Brussels? The publication was well received, considering the number of visits received and above all the institutions which asked to link the publication to their web pages. Among these, the EUobserver published the introduction to the piece in English titled Aznar: thinking locally, acting in Europe (described by the EUobserver as a paper of utmost importance). The fact that the elections were held three days after the tragic events of the 11th of March dramatically increased interest in Spain and the implications for Europe. This publication is the second of its type, in this case analysing the period of the Zapatero government (2004-2008). Once again the starting premise (the Europeanization of the agenda and the methods employed) has been considered by the analysts. And once again the articles collected in this publication serve to “triangulate” the analysis. Spain and Europe are two vertices (more or less distant, in essence and in form) which the authors handle in their analysis of the case (third vertex).

España en Europa 2004-2008

En marzo de 2004 el Observatorio de Política Exterior Europea publicó, en versión digital, un monográfico especial sobre España en Europa (1996-2004). Su objetivo era analizar la agenda y la estrategia de España durante el período de José María Aznar en materia de relaciones internacionales. Como bien indicaba el título de aquella publicación, uno de los supuestos de partida del análisis era la europeización de la actividad internacional de España. ¿Era así?, ¿la España de Aznar veía el mundo y se aproximaba a él a través de Bruselas? Aquella publicación tuvo una buena acogida, a la vista de las visitas recibidas y sobre todo de las instituciones que nos pidieron vincular dicha publicación a sus páginas web y, entre ellas, hay que destacar que EUObserver publicó como comentario su artículo introductorio, en versión inglesa, Aznar: thinking locally, acting in Europe (calificado por EUObserver como lectura de máxima relevancia). El hecho de que las elecciones de 2004 se celebraran tres días después de los trágicos acontecimientos del 11-M hizo que el interés por España y por su proyección europea e internacional aumentara de manera destacada. La presente publicación constituye un segundo ejercicio de dicho tipo, en este caso para analizar el período del gobierno Zapatero (2004-2008). Una vez más, el supuesto de partida (la europeización de la agenda y del método) está en la mente de los analistas. Y una vez más los artículos recogidos en esta publicación hacen el ejercicio de “triangular” el análisis. España y Europa son dos vértices (más o menos alejados, en el fondo y en la forma) que los autores manejan en sus análisis de caso (tercer vértice)

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

The chemical variability at the surface of Mars: implications for exogenic processes

The chemical composition of sediments and rocks, as well as their distribution at theMartian surface, represent a long term archive of processes, which have formed theplanetary surface. A survey of chemical compositions by means of Compositional DataAnalysis represents a valuable tool to extract direct evidence for weathering processesand allows to quantify weathering and sedimentation rates. clr-biplot techniques areapplied for visualization of chemical relationships across the surface (“chemical maps”).The variability among individual suites of data is further analyzed by means of clr-PCA,in order to extract chemical alteration vectors between fresh rocks and their crusts andfor an assessment of different source reservoirs accessible to soil formation. Bothtechniques are applied to elucidate the influence of remote weathering by combinedanalysis of several soil forming branches. Vector analysis in the Simplex provides theopportunity to study atmosphere surface interactions, including the role andcomposition of volcanic gases

Statistical evidences of cyclic changes in volcanic gas chemistry composition by inverse modelling

The identification of compositional changes in fumarolic gases of active and quiescent volcanoes is one of the mostimportant targets in monitoring programs. From a general point of view, many systematic (often cyclic) and randomprocesses control the chemistry of gas discharges, making difficult to produce a convincing mathematical-statisticalmodelling.Changes in the chemical composition of volcanic gases sampled at Vulcano Island (Aeolian Arc, Sicily, Italy) fromeight different fumaroles located in the northern sector of the summit crater (La Fossa) have been analysed byconsidering their dependence from time in the period 2000-2007. Each intermediate chemical composition has beenconsidered as potentially derived from the contribution of the two temporal extremes represented by the 2000 and 2007samples, respectively, by using inverse modelling methodologies for compositional data. Data pertaining to fumarolesF5 and F27, located on the rim and in the inner part of La Fossa crater, respectively, have been used to achieve theproposed aim. The statistical approach has allowed us to highlight the presence of random and not random fluctuations,features useful to understand how the volcanic system works, opening new perspectives in sampling strategies and inthe evaluation of the natural risk related to a quiescent volcano

Elemental analysis of New Zealand Nephrite Jade (pounamu) for forensic purposes

Pounamu (NZ jade), or nephrite, is a protected mineral in its natural form following thetransfer of ownership back to Ngai Tahu under the Ngai Tahu (Pounamu Vesting) Act 1997.Any theft of nephrite is prosecutable under the Crimes Act 1961. Scientific evidence isessential in cases where origin is disputed. A robust method for discrimination of thismaterial through the use of elemental analysis and compositional data analysis is required.Initial studies have characterised the variability within a given nephrite source. This hasincluded investigation of both in situ outcrops and alluvial material. Methods for thediscrimination of two geographically close nephrite sources are being developed.Key Words: forensic, jade, nephrite, laser ablation, inductively coupled plasma massspectrometry, multivariate analysis, elemental analysis, compositional data analysis

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing modelsbetween end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework.We present here a possible solution based on factor analysis of compositions illustrated with a case study.We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables thatlay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hiddencomponents, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members.We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained totalvariance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphicalrepresentation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysisof diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, exceptfertilisers due to the heterogeneity of their composition.This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations areintrinsic to the relative nature of compositional data