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

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

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

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

Reconeixement facial en obres d'art : avaluació del rendiment dels mètodes de l'estat de l'art actual

Aquest paper es divideix en 3 parts fonamentals, la primera relata el que pretén mostrar aquest estudi, que és aplicar els sistemes actuals de reconeixement facial en una base de dades d'obres d'art. Explica quins mètodes s'utilitzaran i perquè es interessant realitzar aquest estudi. La segona passa a mostrar el detall de les dades obtingudes en l'experiment, amb imatges i gràfics que facilitaran la comprensió. I en l'última part tenim la discussió dels resultats obtinguts en l'anàlisi i les seves posteriors conclusions.

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

Solving Large Location-Allocation problems by Clustering and Simulated Annealing

Globalization involves several facility location problems that need to be handled at large scale. Location Allocation (LA) is a combinatorial problem in which the distance among points in the data space matter. Precisely, taking advantage of the distance property of the domain we exploit the capability of clustering techniques to partition the data space in order to convert an initial large LA problem into several simpler LA problems. Particularly, our motivation problem involves a huge geographical area that can be partitioned under overall conditions. We present different types of clustering techniques and then we perform a cluster analysis over our dataset in order to partition it. After that, we solve the LA problem applying simulated annealing algorithm to the clustered and non-clustered data in order to work out how profitable is the clustering and which of the presented methods is the most suitable

Comparació de la tecnologia LiDAR vers els mètodes tradicionals d’inventari forestal, a la finca La Vall de Benifallet, al Baix Ebre

L’inventari forestal és una eina molt important per obtenir la informació necessària, sobre una massa arbrada, respecte a la seva situació actual i la seva possible evolució en el temps, a fi i efecte de poder prendre les decisions necessàries sobre la seva planificació i gestió. Amb aquest treball s’ha volgut avaluar la possible millora que es pot obtenir aplicant les noves tecnologies en la realització dels inventaris forestals, com la tecnologia LiDAR (Light Detection and Ranging). El mètode tradicional de realitzar un inventari forestal, consisteix en anar a camp i prendre dades d’unes mostres representatives, de les variables dasomètriques que caracteritzen una massa forestal. La tecnologia LiDAR és un sistema de teledetecció que calcula distàncies a partir de, la mesura del temps entre l’emissió d’un làser polsat i el seu retorn desprès de la seva reflexió en tocar terra. El resultat és un núvol de punts a diferents alçades, amb el qual s’aconsegueix un Model Digital del Terreny (MDT) i un Model Digital de Superfície (MDS). De la resta d’aquests dos models s’obté una imatge de l’estructura vertical de la vegetació, a partir de la qual es poden deduir dades bàsiques del bosc amb mesures per tot el territori. L’àrea d’estudi on es va dur a terme el present treball, és una finca del terme municipal de Benifallet, al Baix Ebre, província de Tarragona. L’estudi ha consistit en la comparació dels dos mètodes, tradicional i LiDAR, a l’hora d’obtenir les variables de densitat, alçada i fracció de cabuda coberta (FCC). El mètode tradicional consisteix en mesurar les variables en 24 parcel•les representatives i posteriorment, en extrapolar-les als estrats, que són les unitats en que es divideix la part de la finca on es realitza l’inventari. En el mètode utilitzant la tecnologia LiDAR, s’utilitzen dos tipus de resolucions (8 píxels i 24 píxels) a l’hora de treballar amb les dades

Dimensionat de la instal·lació de climatització d'un edifici de vivendes mitjançant el programa de simulació HvacCad : estudi comparatiu amb els mètodes tradicionals de càlcul

L’objecte d’aquest treball és fer una posta a punt d’un programa de simulació. En el nostre cas el programa s’anomena HvacCad. A partir d’aquest programa trobarem les càrregues tèrmiques d’un edifici de vivendes exemple tant per a l’ hivern com a l’estiu. Paral•lelament a aquests càlculs farem els mateixos però amb un full de càlcul convencional, anomenat Aguilar, així podrem comparar els resultats obtinguts. No realitzarem el càlcul de la instal•lació de climatització, només trobarem la potència màxima dels aparells

Mètodes de multiplicació escalar en corbes de gènere 2

En els últims anys la criptografia basada en el problema del logaritme discret ha despertat un gran interes. Un dels grups que s'utilitza per plantejar aquest problema és el conjunt de divisors de la varietat jacobiana d'una corba de gènere 2, i, l'operació bàsica és el producte escalar de divisions. En aquest treball estudiem mètodes per calcular aquest producte de forma eficient emprant tècniques de harving de divisors. Comparem també aquest mètode amb el de doblat de divisors, mostrant una comparativa entre ells.

Estudi i implementació de diferents eines/mètodes de comunicació entre SAP i altres aplicacions o sistemes externs, segons requeriments funcionals específics

Estudi de diferents mètodes de comunicació amb SAP i detall de la implementació.

Nanostructuració d'òxids mitjançant mètodes de solució química avançats i nanolitografia tova

Un dels reptes tecnològics més importants del segle XXI és el desenvolupament i organització de materials funcionals a escala nanomètrica ja que permet modificar-ne les propietats fonamentals i generar-ne de noves. En el cas dels òxids complexos aquesta tecnologia ha generat grans perspectives en diferents àrees d’estudi perquè presenten propietats molt interessants com la magnetoresistència colossal, superconductivitat o multiferroicitat. En particular, en l’òxid complex superconductor YBa2Cu3O7 (YBCO) s’ha demostrat que la formació de capes superconductores sobre plantilles nanoestructurades o bé la formació de nanocompostos en una matriu superconductora permet millorar de manera espectacular les seves propietats (corrent crític). Aquests resultats introduiran canvis paradigmàtics en la tecnologia de l’energia elèctrica (cables, motors, generadors) i en totes aquelles aplicacions que requereixin camps magnètics intensos. Ara bé, cal aconseguir-ho mitjançant tècniques de baix cost i que permetin un fàcil escalat. Durant els 4 mesos que s’ha disfrutat de l’ajut BP s’han preparat amb èxit noves capes primes superconductores nanoestructurades mitjançant la introducció d’una fase secundària nanomètrica complexa, Ba2YTaO6 (BYTO), dins la matriu d’YBCO pel mètode de baix cost de deposició de solucions químiques. Aquesta nova composició ha donat lloc a un augment significatiu de les propietats superconductores comparat amb la fase tradicional d’YBCO i per tant tenen gran potencial per fabricar futures cintes superconductores.