Revisiting the compositional data. Some fundamental questions and new prospects in Archaeometry and Archaeology

In this paper we examine the problem of compositional data from a different startingpoint. Chemical compositional data, as used in provenance studies on archaeologicalmaterials, will be approached from the measurement theory. The results will show, in avery intuitive way that chemical data can only be treated by using the approachdeveloped for compositional data. It will be shown that compositional data analysis is aparticular case in projective geometry, when the projective coordinates are in thepositive orthant, and they have the properties of logarithmic interval metrics. Moreover,it will be shown that this approach can be extended to a very large number ofapplications, including shape analysis. This will be exemplified with a case study inarchitecture of Early Christian churches dated back to the 5th-7th centuries AD

Vertebrates Limb Geometry in the Simplex space

A novel metric comparison of the appendicular skeleton (fore and hind limb) ofdifferent vertebrates using the Compositional Data Analysis (CDA) methodologicalapproach it’s presented.355 specimens belonging in various taxa of Dinosauria (Sauropodomorpha, Theropoda,Ornithischia and Aves) and Mammalia (Prothotheria, Metatheria and Eutheria) wereanalyzed with CDA.A special focus has been put on Sauropodomorpha dinosaurs and the Aitchinsondistance has been used as a measure of disparity in limb elements proportions to infersome aspects of functional morphology

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr)transformation to obtain the random vector y of dimension D. The factor model istheny = Λf + e (1)with the factors f of dimension k & D, the error term e, and the loadings matrix Λ.Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysismodel (1) can be written asCov(y) = ΛΛT + ψ (2)where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as theloadings matrix Λ are estimated from an estimation of Cov(y).Given observed clr transformed data Y as realizations of the random vectory. Outliers or deviations from the idealized model assumptions of factor analysiscan severely effect the parameter estimation. As a way out, robust estimation ofthe covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), seePison et al. (2003). Well known robust covariance estimators with good statisticalproperties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), relyon a full-rank data matrix Y which is not the case for clr transformed data (see,e.g., Aitchison, 1986).The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves thissingularity problem. The data matrix Y is transformed to a matrix Z by usingan orthonormal basis of lower dimension. Using the ilr transformed data, a robustcovariance matrix C(Z) can be estimated. The result can be back-transformed tothe clr space byC(Y ) = V C(Z)V Twhere the matrix V with orthonormal columns comes from the relation betweenthe clr and the ilr transformation. Now the parameters in the model (2) can beestimated (Basilevsky, 1994) and the results have a direct interpretation since thelinks to the original variables are still preserved.The above procedure will be applied to data from geochemistry. Our specialinterest is on comparing the results with those of Reimann et al. (2002) for the Kolaproject data

Immigració francesa i repressió a la Catalunya del segle XVI: alguns exemples del Comtat d'Empúries

Aquest estudi pretén ser una petita aportació al coneixement del fenomen immigratori francès a la comarca de l' Alt Empordà durant els segles XVI-XVII. L' objectiu principal és donar a conèixer alguns exemples de la magnitud i les característiques d’aquest flux migratori en l’àmbit concret del Comtat d’Empúries, per després, introduir el tema del control i de la repressió que les autoritats catalanes i emporitanes varen exercir sobre aquesta immigració francesa, en particular, durant les dècades centrals del segle XVI

Els professionals de la sanitat a la Catalunya de mitjan segle XIX

Dissertació sobre els professionals de la sanitat a la Catalunya de mitjan segle XIX

La freqüentació dels parcs naturals a Catalunya

This article offers a series of reflections and proposals concerning the visitors usage of Catalonia's Natural Parks. The basis of these affirmations is the analysis of the parks which exist at the present in Catalonia, as well as the study of the current legislation in Catalonia and in Spain. Although the article deals exclusively with protected natural areas, it must be remembered that people's recreational activities affect the entire natural environment. It is therefore necessary to extend planning to the impact of such activities in all natural areas. The author proposes as a possible solution a hierarchy of leisure zones in natural spaces, divided into three different levels: Municipal Parks, Regional Parks as well as Natural and National Parks

La història de Catalunya a Talteüll

L' any 1992, aprofitant les Olimpíades de Barcelona, és l'any en què a Talteüll hi tenen també lloc diferents esdeveniments com la inauguració del nou Museu de Prehistòria de Talteüll i la realilzació d'un cicle de conferències sobre la història de Catalunya

Arquitectura i paisatge a l'obra de Josep Danés

Crònica de l’exposició 'Josep Danés, l’arquitecte dels Pirineus', dedicada a mostrar les obres que durant les primeres dècades del segle XX va dur a terme aquest arquitecte a les comarques pirinenques i que es va dur a terme a Núria l'estiu de 2007

Els Atles comarcals de Catalunya: un producte innovador per a uns continguts tradicionals

La present comunicació pretén ressenyar l’aportació dels Atles comarcals de Catalunya al coneixement del nostre territori com una obra no només de caire acadèmic sinó també divulgatiu i aplicat. En primer lloc, es constata la filiació de l’obra al llegat de la geografia clàssica catalana i a les aportacions tradicionals —monografies i les obres generals― que han disseccionat el país des de l’òptica comarcal. En segon lloc, es detalla el seu procés de concepció i elaboració. Finalment, es destaquen les innovacions que el nou format CD-Rom i les possibilitats d’interacció cartogràfica amb servidors externs suposen en el sentit d’innovació respecte de les aportacions anteriors

Benet Sanxes Galindo, pintor i poeta del segle XVI a Catalunya

Estudi de l’obra de Benet Sanxes Galindo, conegut en castellà com Benito Sánchez Galindo. Poeta i pintor del s. XVI, ha estat poc conegut i estudiat. L’autor aprofita per fer un repàs de les obres que l’han tractat. L’article s’emmarca en un número monogràfic amb el títol “Miscel•lània d’homenatge a Modest Prats”

Una Nova dimensió de la xarxa de les ciutats a Catalunya: Les àrees de cohesió

L’article parteix de la hipòtesi de l’existència d'un nou concepte de ciutat. Aquesta ha passat de ser d'una naturalesa nodal o focal a ser-ho de funcionament, de concepte i percepció difusos. L'objectiu principal és determinar l’amplitud d'aquesta ciutat, utilitzant com a paràmetre principal la mobilitat laboral obligada. Es parla de ciutat real, d’àrees de cohesió a Catalunya, i de ciutats reals estructuradores del territori català

Inference of distributional parameters from compositional samples containing nondetects

Low concentrations of elements in geochemical analyses have the peculiarity of beingcompositional data and, for a given level of significance, are likely to be beyond thecapabilities of laboratories to distinguish between minute concentrations and completeabsence, thus preventing laboratories from reporting extremely low concentrations of theanalyte. Instead, what is reported is the detection limit, which is the minimumconcentration that conclusively differentiates between presence and absence of theelement. A spatially distributed exhaustive sample is employed in this study to generateunbiased sub-samples, which are further censored to observe the effect that differentdetection limits and sample sizes have on the inference of population distributionsstarting from geochemical analyses having specimens below detection limit (nondetects).The isometric logratio transformation is used to convert the compositional data in thesimplex to samples in real space, thus allowing the practitioner to properly borrow fromthe large source of statistical techniques valid only in real space. The bootstrap method isused to numerically investigate the reliability of inferring several distributionalparameters employing different forms of imputation for the censored data. The casestudy illustrates that, in general, best results are obtained when imputations are madeusing the distribution best fitting the readings above detection limit and exposes theproblems of other more widely used practices. When the sample is spatially correlated, itis necessary to combine the bootstrap with stochastic simulation

Mosques, sants i política a la Catalunya moderna. L’episodi del setge de 1653

Repàs de les posteriors referències en documents d’arxiu al miracle de les mosques als setges de Girona

Discrete and continuous compositions

This paper examines a dataset which is modeled well by thePoisson-Log Normal process and by this process mixed with LogNormal data, which are both turned into compositions. Thisgenerates compositional data that has zeros without any need forconditional models or assuming that there is missing or censoreddata that needs adjustment. It also enables us to model dependenceon covariates and within the composition

CODAPACK3D. A new version of Compositional Data Package

The statistical analysis of compositional data should be treated using logratios of parts,which are difficult to use correctly in standard statistical packages. For this reason afreeware package, named CoDaPack was created. This software implements most of thebasic statistical methods suitable for compositional data.In this paper we describe the new version of the package that now is calledCoDaPack3D. It is developed in Visual Basic for applications (associated with Excel©),Visual Basic and Open GL, and it is oriented towards users with a minimum knowledgeof computers with the aim at being simple and easy to use.This new version includes new graphical output in 2D and 3D. These outputs could bezoomed and, in 3D, rotated. Also a customization menu is included and outputs couldbe saved in jpeg format. Also this new version includes an interactive help and alldialog windows have been improved in order to facilitate its use.To use CoDaPack one has to access Excel© and introduce the data in a standardspreadsheet. These should be organized as a matrix where Excel© rows correspond tothe observations and columns to the parts. The user executes macros that returnnumerical or graphical results. There are two kinds of numerical results: new variablesand descriptive statistics, and both appear on the same sheet. Graphical output appearsin independent windows. In the present version there are 8 menus, with a total of 38submenus which, after some dialogue, directly call the corresponding macro. Thedialogues ask the user to input variables and further parameters needed, as well aswhere to put these results. The web site http://ima.udg.es/CoDaPack contains thisfreeware package and only Microsoft Excel© under Microsoft Windows© is required torun the software.Kew words: Compositional data Analysis, Software