A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

Discovering similarities in the time use patterns of the Spanish Autonomous Communities by Fuzzy techniques

In 2000 the European Statistical Office published the guidelines for developing theHarmonized European Time Use Surveys system. Under such a unified framework,the first Time Use Survey of national scope was conducted in Spain during 2002–03. The aim of these surveys is to understand human behavior and the lifestyle ofpeople. Time allocation data are of compositional nature in origin, that is, they aresubject to non-negativity and constant-sum constraints. Thus, standard multivariatetechniques cannot be directly applied to analyze them. The goal of this work is toidentify homogeneous Spanish Autonomous Communities with regard to the typicalactivity pattern of their respective populations. To this end, fuzzy clustering approachis followed. Rather than the hard partitioning of classical clustering, where objects areallocated to only a single group, fuzzy method identify overlapping groups of objectsby allowing them to belong to more than one group. Concretely, the probabilistic fuzzyc-means algorithm is conveniently adapted to deal with the Spanish Time Use Surveymicrodata. As a result, a map distinguishing Autonomous Communities with similaractivity pattern is drawn.Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance

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

Pautes de classificació i desclassificació de sòl en nuclis petits de l’Empordà en aplicació de la normativa territorial vigent

Estudi sobre la classificació i desclassificació de sòl en nuclis petits de l’Empordà en aplicació de la normativa territorial vigent

Recuperació de metalls en l’aigua residual de la indústria galvànica mitjançant l’electròlisi i l’energia solar

Proposta del procés d’electròlisi com a mètode de recuperació de metalls pesants presents en les aigües de rentat de la indústria galvànica i l’obtenció de l’energia necessària a través de l’energia solar fotovoltaica

Estudi de la mobilitat a Roses : anàlisi de la situació actual i propostes de millora

Estudi econòmic, de població, turístic i descriptiu de la zona de Roses, aprofundint en l’aspecte de la mobilitat (motorització, vehicle privat, aparcaments, autobús, bicicleta i seguretat vial). Es fan estudis de camp per estimar la contaminació i enquestes a les escoles per conèixer el medi de transport que utilitzen els alumnes. Finalment es fan una sèrie de propostes de millora

Monitoratge dels nivells d’aigua de les llacunes costaneres dels Aiguamolls de l’Empordà i control de les eclosions de mosquits

Proposta d’una sèrie de mesures de gestió als gestors del parc i empreses de serveis en relació a la creixent salinització i a les eclosions de mosquits, als Aiguamolls de l’Empordà per tal de posar en pràctica una eficaç metodologia de prevenció

Quantificació i estudi dels impactes potencial de les deixalles de pesca recreativa a Port Salvi

Les deixalles acumulades per la pràctica de la pesca recreativa, sobretot des de roca, produeixen impactes sobre les espècies de flora i fauna. En aquest estudi es fa una caracterització de les modalitats de pesca recreativa i els estris emprats, una quantificació de les pèrdues dels materials al mar i una avaluació dels impactes potencials. Els resultats obtinguts de la quantificació d’ormeigs trobats al fons marí de Port Salvi (Sant Feliu de Guixols), mostren que els estris predominants són ploms, hams, esmerillons, mosquetons i fils. Les plomades més abundants són les de surfacting i les de pesca a fons de roca. Els materials que més abunden en la composició d’ormeigs de pesca són en gran part metalls i plàstics, ambdós de lenta descomposició i alta persistència al medi

Avaluació i implantació d’un sistema de climatització amb energia solar a la Facultat de Ciències de la UdG

Estudi de viabilitat de climatització de la Facultat de Ciències de la UdG per energia solar. Estudi de costos i comparació de l’estalvi respecte al sistema actual

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

Application of discriminant function analysis and change-point problem in dating volcanic ashes

The application of Discriminant function analysis (DFA) is not a new idea in the studyof tephrochrology. In this paper, DFA is applied to compositional datasets of twodifferent types of tephras from Mountain Ruapehu in New Zealand and MountainRainier in USA. The canonical variables from the analysis are further investigated witha statistical methodology of change-point problems in order to gain a betterunderstanding of the change in compositional pattern over time. Finally, a special caseof segmented regression has been proposed to model both the time of change and thechange in pattern. This model can be used to estimate the age for the unknown tephrasusing Bayesian statistical calibration

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

Several eco-toxicological studies have shown that insectivorous mammals, due to theirfeeding 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°uenceon 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 greaterwhite-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 givemisleading results. Therefore, to improve the interpretation of the data obtained, weused statistical techniques for compositional data analysis to define groups of metalsand to evaluate the relationships between them, from an inter-population viewpoint.Hypothesis testing on the adequate balance-coordinates allow us to confirm intuitionbased hypothesis and some previous results. The main statistical goal was to test equalmeans 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

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