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We consider calculation of the mode of compositional data, the data related to each other through a linear constraint. Compositional data arises in various extensions of the fuzzy sets theory (type-2 interval-valued, intuitionistic, hesitant fuzzy sets), biomedicine (relative abundance, genome sequencing, activity recognition), and data analytics (various wealth indices, interval-valued observations, traffic congestion, etc.). Mode is a pre-aggregation function in the case of single variable, used as a classical estimator robust to outliers, but its multivariate extensions face the challenges of high computational complexity and potential oversmoothing. In this work we present several novel techniques for mode estimation on the unit k-simplex representing compositional, interval-valued, and general vector-valued data. We highlight the re-weighted k-nearest neighbours algorithm based on the Choquet integral with respect to a 2-additive fuzzy measure, compare its performance against other approaches based on spatial partitioning, and illustrate its applications to aggregation of real-world interval-valued data sets.

By-elections, or special elections, play an important role in many democracies – but whilst there are multiple forecasting models for national elections, there are no such models for multiparty by-elections. Multiparty by-elections present particular analytic problems related to the compositional character of the data and structural zeros where parties fail to stand. I model party vote shares using Dirichlet regression, a technique suited for compositional data analysis. After identifying predictor variables from a broader set of candidate variables, I estimate a Dirichlet regression model using data from all post-war by-elections in the UK (n=468). The cross-validated error of the model is comparable to the error of costly and infrequent by-election polls (MAE: 4.0 compared to 3.6 for polls). The steps taken in the analysis are in principle applicable to any system that uses by-elections to fill legislative vacancies.

Background Four models are commonly used to adjust for energy intake when estimating the causal effect of a dietary component on an outcome: 1) the “standard model” adjusts for total energy intake, 2) the “energy partition model” adjusts for remaining energy intake, 3) the “nutrient density model” rescales the exposure as a proportion of total energy, and 4) the “residual model” indirectly adjusts for total energy by using a residual. It remains underappreciated that each approach evaluates a different estimand and only partially accounts for confounding by common dietary causes. Objectives We aimed to clarify the implied causal estimand and interpretation of each model and evaluate their performance in reducing dietary confounding. Methods Semiparametric directed acyclic graphs and Monte Carlo simulations were used to identify the estimands and interpretations implied by each model and explore their performance in the absence or presence of dietary confounding. Results The “standard model” and the mathematically identical “residual model” estimate the average relative causal effect (i.e., a “substitution” effect) but provide biased estimates even in the absence of confounding. The “energy partition model” estimates the total causal effect but only provides unbiased estimates in the absence of confounding or when all other nutrients have equal effects on the outcome. The “nutrient density model” has an obscure interpretation but attempts to estimate the average relative causal effect rescaled as a proportion of total energy. Accurate estimates of both the total and average relative causal effects may instead be derived by simultaneously adjusting for all dietary components, an approach we term the “all-components model.” Conclusions Lack of awareness of the estimand differences and accuracy of the 4 modeling approaches may explain some of the apparent heterogeneity among existing nutritional studies. This raises serious questions regarding the validity of meta-analyses where different estimands have been inappropriately pooled.

The Mediterranean olive triptych –i.e. the conceptual integration of an ecosystem (the olive-grove), a product (olive-oil) and a nutrition/diet scheme (Mediterranean olive-based diet)– is a discernable cultural model in Europe. In this paper, we attempt to explore the potential and limitations of statistical analysis of compositional data –especially ternary plotting techniques– vs. typical representations of Google Trends-based Conservation Culturomics. In that perspective, typical representations of GT-data in published Culturomics literature, e.g. reference term/country/language/time, are considered as descriptors of variation of public interest (2D trend lines, 3D graphics and triangular projections). Ternary plots, i.e. a typical representation of compositional data, conventionally differ significantly from the previous representations, since the primary GT-data are weighted so that ternary sum equals to 1 (or 100%). We present the technique for such a calculation method. The comparison of these representation techniques allows for strongly diverging interpretations. Lower level interpretations show significant differences between (Mediterranean) countries and/or groups-of-countries (Mediterranean vs. non-Mediterranean) where higher ternary compilations do suggest that cultural pattern across Europe actually diverge. The overall conclusion of this research is that GT-based Culturomics should overcome earliest simplistic approaches, such as linear regressions; and, it has to progressively construct a new epistemology where the significance of accumulation of empirical evidence should be strictly connected to scientific paradigm shift.

Marine shales, the most common lithology in the stratigraphic record, represent an archive of long-term changes in sediment production, weathering intensity, and seawater chemistry through Earth history whose potential has been underexploited to date. In this study, we compiled compositional data for 14,531 samples from 268 shale and mud units ranging in age from the early Cryogenian (840 Ma) to the Recent. We examined secular variation in the Al-normalized concentrations of ten elements (Mg, Na, K, Ba, Sr, Y, Th, Rb, Nb, and Zr) selected for (1) their presence in typical X-ray fluorescence (XRF) datasets (thus providing sufficient data), and (2) their lack of redox sensitivity (thus excluding elements whose primary control is aqueous redox conditions). Relationships among the study elements were quantified using principal component analysis (PCA) and cluster analysis (CA), revealing several significant groupings: (1) a subset of “detrital elements” (K, Rb, Th, Nb, Y, and Zr) whose concentrations are primarily controlled by subaerial weathering processes; (2) a subset of “hydrogenous elements” (Mg, Na, and Sr) whose concentrations are significantly influenced by seawater chemistry, and (3) Ba, which is subject to multiple controls. The dominant influence on the detrital elements appears to have been not chemical weathering intensity per se but the ratio of Al-poor silt to Al-rich clay in the particulate weathering flux. Although possibly modulated by factors such as climate and land plant evolution, silt:clay ratios appear most closely linked to tectonism, with higher values associated with major orogenic events. The concentrations of the hydrogenous elements in marine shales were likely related to their seawater inventories, which were modulated at long time scales by rates of submarine hydrothermal alteration. Ba in marine shales may have been significantly influenced by atmospheric pO2 and seawater sulfate levels via their control of barite saturation in seawater. In summary, our findings document significant relationships of marine shale composition to first-order geological controls, suggesting that long-term secular changes in sediment and seawater chemistry can be reconstructed from fine-grained siliciclastic sediments.

Evaluating the effect of nutritional components on health outcomes is hampered by technical difficulties that are closely related to the compositional nature of dietary data. Compositional data consist of parts of a whole and, on the basis of the assumption that any relevant information they provide is contained in the ratios between them, procedures based on log-ratio transformations have been proposed for their analysis. It has been previously suggested that nutrient compositions can be analyzed using isometric log-ratio transformations which allow the compositions to be represented by a system of orthogonal coordinates corresponding to the log-contrasts between the compositional parts. One particular expression of these contrasts is called balances, and the aim of this note is to provide a step-by-step description of how to construct orthonormal balances and show how they can be applied to dietary data by means of an example based on data coming from an Italian population-based study. Nutrient balances are new variables that can be included as covariates in regression models. After fitting a linear regression model using estimates of relative fat mass as a response variable, scores indicating the obesogenic potential of foods can be defined on the basis of their nutritional contents and the estimated effect of the balances on relative fat mass. This approach to evaluating the relationship between diet and health outcomes provides insights into the roles of specific nutrient ratios and foods within a comprehensive and integrated framework that complies with the essentially compositional nature of dietary data.

5 Páginas.-- 8 Figuras.-- 3 Tablas, Essential oils (EOs) are natural products formed by plant volatile compounds. EOs are frequently used in the cosmetic and food industries as well as for domestic purposes, because of their physiochemical, biological and sensory properties. The functional groups (FG), corresponding to various chemical structures present in EOs, are responsible for their biological activities. Therefore, simple, rapid, and economical techniques suitable to characterize the EOs features by measuring their contents, are of great interest. Near-infrared spectroscopy (NIRS) highlights because of its rapidity, and being no-contaminant, as a potential solution. Multivariate cor- relation methods are commonly used to build NIRS calibrations. These methods were designed for the real space, that is for values comprised between - ¿ and +¿. However, EOs components are co-dependent data restricted to a simplex space. These are the so-called compositional data (CoDa), needing specific methods to be correlated with a set of spectral explicative variables. In this study, compositional visible and near-infrared (VISNIRS) models have been assessed to quantify the FG of the analyzed EOs. For this purpose, the FG were organized according to their greater frequency in 1) alcohol; 2) ether; 3) ester; 4) aldehydes; 5) ketones, and the hydro- carbon fraction representing the remainder EOs mass, to characterize them. The approach of this study, based on compositional models from VISNIRS spectra, has provided a satisfactory predictive performance for the quan- titative estimation of the main FG of the EOs. The proposed approach can be an alternative to traditional chemical methods to characterize EOs., The authors thank the Spanish Council for Scientific Research (CSIC) for funding the COOPB20466 project, entitled 'Evaluation of near-infrared (NIRS) and visible/NIRS spectroscopy techniques for essential oil composition analysis', within the scientific cooperation program for the development of CSIC ICOOP' 2019.

Publisher Copyright: © 2022 The Authors Weakly-supervised learning has recently emerged in the classification context where true labels are often scarce or unreliable. However, this learning setting has not yet been extensively analyzed for regression problems, which are typical in macroecology. We further define a novel computational setting of structurally noisy and incomplete target labels, which arises, for example, when the multi-output regression task defines a distribution such that outputs must sum up to unity. We propose an algorithmic approach to reduce noise in the target labels and improve predictions. We evaluate this setting with a case study in global vegetation modelling, which involves building a model to predict the distribution of vegetation cover from climatic conditions based on global remote sensing data. We compare the performance of the proposed approach to several incomplete target baselines. The results indicate that the error in the targets can be reduced by our proposed partial-imputation algorithm. We conclude that handling structural incompleteness in the target labels instead of using only complete observations for training helps to better capture global associations between vegetation and climate.

Research on magmatic Cl has proven useful for understanding melt evolution, degassing, and other igneous processes. Magmatic Cl behavior varies strongly with its solubility in melt, and Cl solubility and its partitioning between melts and fluids vary with the Cl content of the system, melt composition, pressure, and the abundance of oxidized magmatic sulfur. Given these relationships and given that they differ from other magmatic volatiles, Cl can provide unique insights on magma evolution. We present a new method of interpreting melt Cl concentrations that are normalized to their calculated Cl solubilities, and the most accurate results apply to solubilities computed at 200 MPa due to insufficient experimental data for other pressures. We apply the new method to compositional data for more than 3500 dacitic to rhyolitic melt inclusions and matrix glasses, representing 64 felsic igneous systems, to demonstrate how the behavior of Cl during magmatic, magmatic-hydrothermal, and degassing processes can be more accurately interpreted. Variations in Cl for most of the 64 systems agree with modeled Cl behavior indicative of melt evolution dominated by fractional crystallization of fluid(s)-saturated melts, and the majority of these systems were apparently saturated in fluid(s) well before melt inclusion entrapment. Comparison of Cl solubility-normalized Cl concentrations of these glasses with modeled results identifies magmas saturated in hydrosaline liquid ± vapor at pressures as high as 600 MPa. Modeling of pressure reductions from 600 down to 20 MPa distinguishes other magmas that exsolved hydrosaline liquid as magmas ascend to shallower depths. This new approach also supports computation of Cl concentrations of magmatic fluids at 200 MPa, for each of the >3500 glasses, and shows how the Cl contents of fluids vary with the (fluid/melt) mass ratio. For example, Cl contents of magmatic fluids range from 0.3 to nearly 70 wt.% at fluid/melt mass ratios of 2 × 10−3, and from 0.3 to a maximum of only 11 wt.% Cl for fluid/melt mass ratios of 4.2 × 10−2. Compositional trends in the glass data show either increasing Cl contents of residual melt, essentially no change of Cl in melt, or decreasing Cl contents of aliquots of residual melt with progressive melt evolution. This method identifies melts that have assimilated magmatic or externally sourced hydrosaline liquids. Plots of (measured Cl in melt/modeled solubility of Cl in melt; Cl[Me/Mo]) versus the Larsen melt differentiation index show minimal dispersion for the least-evolved dacitic melts and increasing dispersion with melt evolution to rhyolitic compositions. Increased dispersion may be a consequence and indication of equilibrium or non-equilibrium degassing and/or assimilation of hydrosaline liquid.

We re-examine the Renazzo-like (CR) chondrite metamorphic trend based on Cr2O3 contents of FeO-rich olivine, indicating that it is only appropriate to use such analyses to identify the endmembers of this group (i.e., those that have experienced either no detectable heating or significant heating). As such Miller Range (MIL) 090657 appears to have experienced very minimal (if any) thermal processing and is one of the most pristine CR chondrites analyzed to date, while Graves Nunataks 06100 is the most shock-heated CR chondrite studied. On the basis of bulk H-C-N isotopic compositions, MIL 090657 appears to be of petrological type 2.7. We also report the H-C-N isotopic compositions of extracted insoluble organic matter, in situ chemical compositional data, presolar grain abundances, and a petrologic description of MIL 090657. As a minimally altered CR chondrite of relatively high mass (133.1 g), MIL 090657 provides an invaluable opportunity to perform coordinated, often destructive, analyses on pristine CR chondrite material. By combining a number of petrographic characteristics (Cr2O3-content of ferroan olivine, Co/Ni ratios of Fe,Ni metal, ratios of Fe# in chondrule olivine and low-Ca pyroxene, and the presence of excess silica in chondrule plagioclase) with bulk isotopic compositions, we demonstrate their utility as indicators for determining the relative pristinity/heating of low petrographic (type 1–3) chondrites.

Studying the chemistry of surface waters and their resilience to compositional changes represents a global challenge to preserve them from human- and changing climate-induced modifications. River waters are sentinel parameters for all processes occurring in a river basin. This is particularly true for regional watersheds, which can include both natural- and anthropogenic-sourced solutes such as those present in the Tiber River basin, the biggest one in Central Italy. In this work, innovative applications of statistical methods are proposed, from the perspective of Compositional Data Analysis theory, in order to consider the geochemical riverine system as a whole and detect compositional changes throughout the catchment. Robust compositional biplots highlighted different sources of variability linked to geological (low variability) and anthropogenic origin (high variability) of the main compounds, thus identifying a hierarchy in the variance of the riverine geochemical processes. On a different scale, the innovative use of the robust Mahalanobis distance in an iterative way monitored spatial compositional shifts for single cases. The effectiveness of this method consists in minimising the influence of an individual anomalous point on the compositional centre and the covariance structure of the data highlighting when along the river a significant compositional shift occurs. The study provides powerful compositional tools for detecting potential contamination events or climate-induced modifications both at catchment and river scale.

34 Páginas.-- 3 Figuras.-- 4 Tablas, The work studies the effect of season, montanera length, and sampling location on the Iberian pig fat, using compositional data (CoDa) analysis and standard statistics. CoDa variation array and logratios involving C18:3: (C18:3/C17:1), (C18:3/C20:0), and (C18:3/18:0) as well as the ilr balances (coordinates), based on C18:3, C17:1, and C20:0, showed the highest variances. Discriminant Analysis (DA) led to similar (conventional/coordinates) correct assignations regarding seasons (69/70%), montanera length (71/70%) and sampling location (68/67%). Re-analyzing the subcomposition of only the major fatty acids (FAs), led to slightly poorer results; therefore, the removed FAs might play a role in segregation. Results are in line with those from other authors and could indicate a partial capacity of pigs to control their FA profiles. Overall, CoDa analysis provided useful information on data variability, the effects of factors and, after conversion into coordinates, allowed applying standard statistics while being respectful with the compositional sampling space., This work was supported by the Spanish Government (project AGL2010-15494/ALI, partially financed by European regional development funds, ERDF), and Junta de Andalucía (through financial support to group AGR-125 and AGR-283).

Tracing indicator minerals and geochemical pathfinders in glacial sediments back to their up-ice source is a common mineral exploration approach in prospective, formerly glaciated regions. In this study, we utilize surface and subsurface data from the Lac de Gras area of the Northwest Territories to develop a three-dimensional understanding of till compositional anomalies emanating from two known kimberlite pipes, DO-18 and DO-27. Specifically, this study examines the three-dimensional shape of dispersal trains as defined by geochemical pathfinder elements and kimberlite indicator minerals shed from a pair of kimberlite pipes within a till cover of variable thickness. From our ninety-four reverse circulation boreholes (n = 251 till samples), and other publicly-available geologic datasets, we have reconstructed bedrock topography, till thickness, and the subsurface geometry of two dispersal trains. Utilizing our three-dimensional dataset, we have documented the role of basal topography in creating dispersal patterns with contrasting geometries from two adjacent kimberlites, as well as in the preferential preservation of older till units. The combination of field observations of ice-flow indicators and till compositional data demonstrates that features produced by multiple ice flows are preserved in both the erosional and depositional records in this region. Three-dimensional dispersion patterns of kimberlite indicators reflect the effect of shifting ice-flow direction with respect to slope aspect of bedrock topography in governing compositional variability within glacial drift. Our findings suggest that surficial data do not capture the full extent of dispersion patterns even in areas of relatively thin and discontinuous till cover.

A particulate matter (PM) source apportionment study was carried out in one of the most polluted districts of Tuscany (Italy), close to an old waste incinerator plant. Due to the high PM10 levels, an extensive field campaign was supported by the Regional Government to identify the main PM sources and quantify their contributions. PM10 daily samples were collected for one year and analysed by different techniques to obtain a complete chemical characterisation (elements, ions and carbon fractions). Hourly fine (2.5 μm) and coarse (2.5-10 μm) aerosol samples were collected by a Streaker sampler for a shorter period and hourly elemental concentrations were obtained by PIXE. Positive Matrix Factorization (PMF) analysis of daily and hourly data allowed the identification of 10 main sources: six anthropogenic (Biomass Burning, Traffic, Secondary Nitrates, Secondary Sulphates, Incinerator, Heavy Oil combustion), two natural (Saharan Dust and Fresh Sea Salt) and two mixed sources (Local Dust and Aged Sea Salt). Biomass burning turned out to be the main source of PM, accounting for 30% of the PM10 mass as annual average, followed by Traffic (18%) and Secondary Nitrates (14%). Emissions from the Incinerator turned out to be only 2% of PM10 mass on average. PM10 composition and source apportionment have been assessed in a polluted area near a waste incinerator, by PMF analysis on daily and hourly compositional data sets.

Compositional data analysis is becoming increasing important in economic research, where the variables of interest may be structural indicators, such as the investment proportion of industries. In many applications, the measurements of these indicators are collected from countries/regions on a yearly/monthly basis, which falls into the paradigm of longitudinal data. Typically, data from the same individual may show potential association due to unobserved shared factors. To incorporate the dependence within the individual, we investigate the linear mixed-effects model for multivariate longitudinal compositional data. We develop and implement a maximum likelihood estimation procedure through the expectation maximization algorithm. We also investigate the statistical inferences of fixed effects coefficients and the selection of random effects via a proposed Bayesian information criterion. The proposed method shows desirable properties and performs well in finite samples, as comprehensive numerical studies indicate. We further illustrate the practical utility of the proposed method in a real data study based on China’s industrial structure, and show that it can improve the performance and enhance the interpretability of the regression on multivariate compositional data.

Factor analysis models use the covariance of measured variables to identify and apportion sources. These models, particularly positive matrix factorization (PMF), have been extensively used for analyzing particle number concentrations (PNCs) datasets. However, the variation of observed PNCs and particle size distribution are driven by both the source emission rates and atmospheric dispersion as well as chemical and physical transformation processes. This variation in the observation data caused by meteorologically induced dilution reduces the ability to obtain accurate source apportionment results. To reduce the influence of dilution on quantitative source estimates, a methodology for improving the accuracy of source apportionment results by incorporating a measure of dispersion, the ventilation coefficient, into the PMF analysis (called dispersion normalized PMF, DN-PMF) was applied to a PNC dataset measured from a field campaign that includes the Spring Festival event and the start of the COVID-19 lockdown in Tianjin, China. The data also included gaseous pollutants and hourly PM2.5 compositional data. Eight factors were resolved and interpreted as municipal incinerator, traffic nucleation, secondary inorganic aerosol (SIA), traffic emissions, photonucleation, coal combustion, residential heating and festival emissions. The DN-PMF enhanced the diel patterns of photonucleation and the two traffic factors by enlarging the differences between daytime peak values and nighttime concentrations. The municipal incinerator plant, traffic emissions, and coal combustion have cleaner and more clearly defined directionalities after dispersion normalization. Thus, dispersion normalized PMF is capable of enhancing the source emission patterns. After the COVID-19 lockdown began, PNC of traffic nucleation and traffic emissions decreased by 41% and 44%, respectively, while photonucleation produced more particles likely due to the reduction in the condensation sink. The significant changes in source emissions indicate a substantially reduced traffic volume after the implement of lockdown measures., Graphical abstract Unlabelled Image, Highlights • A dispersion normalized PMF was applied to PNCs dataset. • DN-PMF enhanced the diel emission pattern and directionality of sources. • Traffic emissions decreased by more than 40% after the COVID-19 outbreak.

Geochemical studies that focus on environmental applications tend to approach the chemical elements as individual entities and may therefore offer only partial and sometimes biased interpretations of their distributions and behaviour. A potential alternative approach is to consider a compositional data analysis, where every element is part of a whole. In this study, an integrated methodology, which included compositional data analysis, multifractal data transformations and interpolation, as well as enrichment factor analysis, was applied to a geochemical dataset for the Campania region, in the south of Italy, focusing in particular on the behaviour, footprints and sources of a smaller pool of elements: Al, Na, K and P. The initial dataset included 3669 topsoil samples, collected at an average sampling density of 1 site per 2.3 km(2), and analyzed (after an aqua regia extraction) by a combination of ICP-AES and ICP-MS for 53 elements. Frequency based methods (Clr biplot, Enrichment Factor computation) and frequency spatial-method (fractal and multifractal plots) allowed identifying the relationships between the elements and their possible source patterns in Campania soils in relation to a natural occurring concentrations in geogenic material (rocks, soils and sediments) or human input. Results showed how the interpretation of concentration and behaviour of Al, Na, K and P was enhanced thanks to the application of data log-ratio transformation in univariate and multivariate analysis compared to the use of raw or log-normal data. Multivariate analyses with compositional biplot allowed the identification of four element associations and their potential association with the underling geology and/or human activities. When focusing on the smaller pool of elements (Al, P, K and Na), these relationships with the unique geology of the region, were largely confirmed by multifractal interpolated maps. However, when the local background was used for the calculation of the enrichment factor, the resulting interpolated maps allowed to identify smaller areas where the greater concentrations of P could not be possibly associated to a mineralisation (e.g., ultrapotassic rocks) but were more likely to be associated to anthropogenic input such as agriculture activities with potentially extensive use of phosphate fertilizers. The integrated approach of this study allowed a more robust qualitative and quantitative evaluation of elemental concentration, providing in particular new and vital information on the distribution and patterns of P in soils of the Campania region, but also a viable, more robust, methodological approach to regional environmental geochemistry studies.

Determining the viscosity of heavy crude oil is important in the field of petroleum science, and reservoir simulators are routinely used to achieve this goal. In this study, a new empirical model for predicting heavy-oil viscosity is presented. The model was developed using the compositional data of 28 heavy crude oil samples from the Middle East. Viscosity measurements from 196 data points in the 20–80 °C temperature range were used during model development, and another 47 viscosity measurements were used to validate the model. The compositional and viscosity measurements were also used to evaluate the accuracy of previously published methods for predicting heavy-oil viscosities. These methods include corresponding-states models, residual viscosity models, and equations-of-state-based models. The study reveals that none of the previously published methods adequately predict the viscosities of heavy crude oils. On the other hand, it shows that the new empirical model is able to predict the viscosities of heavy oils with an average relative error of 3.8%. The proposed model is much simpler and easier to use than existing methods.

The Olympic Dam Cu-U-Au-Ag deposit is dominantly composed of mineralised hematite-breccias and occurs entirely within the Roxby Downs Granite. Multivariate statistical analysis of a large whole-rock, 15 m-interval geochemical dataset (10,565 samples) was undertaken to identify geochemical signatures characteristic of iron-oxide copper gold (IOCG)-style mineralization and constrain the conspicuous lithogeochemical zonation observed at Olympic Dam. Statistical analyses include principal component analysis on centred logratio (clr)-transformed data coupled with hierarchical clustering. Certain groups of elements that can be interpreted in terms of an evolving hydrothermal system relative to host lithologies are derived from data analysis: granitophile (U-W-Sn-Mo); siderophile (Ni-Co); chalcophile (Ag-Bi) and related elements (As-Sb and Au-Te). The distributions of elements within each group are investigated through three vertical cross-sections and are compared with known lithological and Cu-(Fe)-sulphide zonation. Throughout the Olympic Dam Breccia Complex, the IOCG signature is defined by multi-element combinations of the commodity metals Cu, U, Au, and Ag, coupled with a range of trace elements. Overall, the IOCG signature overlaps well with Fe-metasomatism despite mismatch which is likely due to discrete styles of mineralisation found only on the margins of the deposit and also to the presence of mineralised domains within Fe-poor zones. The IOCG signature is composed of two geochemical associations, which exhibit distinct spatial distributions. The first group, Cu-U3O8-Se-S, shows concentric zonation whereas the second group, Au-W-Mo-Sb-As, forms a vertical ∼1800 m deep corridor in the southeastern lobe of the deposit. The specific Au-W-Mo-As-Sb signature could potentially be generic within IOCG systems across the Olympic Cu-Au province and if so, would provide a proxy model for near-mine exploration.

Different correlation detection methods have been specifically designed for the microbiome data analysis considering the compositional data structure and different sequencing depths. Along with the speedy development of omics studies, there is an increasing interest in discovering the biological associations between microbes and host metabolites. This raises the need of finding proper statistical methods that facilitate the correlation analysis across different omics studies. Here, we comprehensively evaluated six different correlation methods, i.e., Pearson correlation, Spearman correlation, Sparse Correlations for Compositional data (SparCC), Correlation inference for Compositional data through Lasso (CCLasso), Mutual Information Coefficient (MIC), and Cosine similarity methods, for the correlations detection between microbes and metabolites. Three simulated and two real-world data sets (from public databases and our lab) were used to examine the performance of each method regarding its specificity, sensitivity, similarity, accuracy, and stability with different sparsity. Our results indicate that although each method has its own pros and cons in different scenarios, Spearman correlation and MIC outperform the others with their overall performances. A strategic guidance was also proposed for the correlation analysis between microbe and metabolite.

22 Páginas; 5 Figuras; 3 Tablas, Food nutritional labeling is compulsory in the European Union since 13 December 2016. The olive oil fatty acid composition shows high variation depending mainly on the variety. Thus, olive oil nutritional labeling is problematic for the industry. Besides, the analysis of all batches of olive oil using the official methods is expensive. Therefore, the olive oil industry is seriously concerned about solutions for nutritional labeling. In this study, a new rapid technique to measure the nutrients for the olive oil nutritional labeling, is assessed. A novel partial least squares (PLS) calibration model using log-ratio coordinates has been formulated and successfully tested for predicting the percentages of monounsaturated, saturated, and polyunsaturated fatty acids based on visible and near infrared spectroscopy. The model provided accuracy suitable for labeling, under the rules in force in the European Union. The error was generally much lower than the tolerance., J. A. Cayuela expresses gratitude to the European Regional Development Fund, aswell to the Ministry of Economy and Competitiveness of Spain for funding parts of this study, which was developed within the project Recupera 2020 1.4.4., and to the Spanish Council for Scientific Research, for co-funding the grant 20137R065 corresponding to this project. J. Palarea-Albaladejo was partly supported by the Scottish Government's Rural and Environment Science and Analytical Services Division (RESAS) and by the Spanish Ministry of Economy and Competitiveness under the project CODA-RETOS MTM2015-65016-C2-1(2)-R.

Ore deposits usually consist of ore materials with different discrete (e.g. rock and alteration types) and continuous (e.g. geochemical and mineral composition) features. Financial feasibility studies are highly dependent on the modelling of these features and their associated joint uncertainties. Few geostatistical techniques have been developed for the joint modelling of high-dimensional mixed data (continuous and categorical) or constrained data, such as compositional data. The compositional nature of the mineral and geochemical data induces several challenges for multivariate geostatistical techniques, because such data carry relative information and are known for spurious statistical and spatial correlation effects. This paper investigates the application of the direct sampling algorithm for joint modelling of compositional and categorical data. In some mining projects the amount of available data may be enormous in some parts of the deposit and if the density of measurements is sufficient, multivariate geospatial patterns can be derived from that data and be simulated (without model inference) at other undersampled areas of the deposit with similar characteristics. In this context, the direct sampling multiple-point simulation method can be implemented for this reconstruction process. The compositional nature of the data is addressed via implementing an isometric log-ratio transformation. The approach is illustrated through two case studies, one synthetic and one real. The accuracy of the results is checked against a set of validation data, revealing the potential of the proposed methodology for joint modelling of compositional and categorical information. The direct sampling technique can be considered as a smart move to assess the future risk and uncertainty of a resource by making use of all the information hidden within the early data.

Time spent in different glucose ranges indicate the occurrence of adverse events and measure the quality of glucose control in type one diabetes (T1D) patients. This work proposes a Compositional Data (CoDa) approach applied to glucose profiles obtained from six T1D patients using continuous glucose monitor (CGM). Glucose profiles limited to 6-h duration were analyzed at four different times of the day These glucose profiles were distributed into time spent in five glucose ranges, which determine the composition. The log-ratio coordinates of the compositions were categorized through a clustering algorithm, which later made possible the obtainment of a linear model that should be used to predict the category of a 6-h period in different times of day. Leave-one-out cross-validation was performed, achieving an average above 90% of correct classification. A probabilistic model of transition between the category of the past 6-h of glucose to the category of the future 6-h period was obtained. Results show that the CoDa approach not only works as new analysis tool and is suitable for the categorization of glucose profiles, but also is a complementary tool for the prediction of different categories of glucose control. This prediction could assist patients to take correction measures in advance to adverse situations.

Combined analyses of the surface elemental composition and mineralogy of Vesta and Ceres provide insights into their interior evolution, crustal formation, and regolith processes. Compositional data acquired by Dawn's Visible to Infrared Mapping Spectrometer (VIR) and Gamma Ray and Neutron Detector (GRaND) are sensitive to different depths and spatial scales. To compare these data sets, high-resolution maps of absorption band strengths from VIR are degraded to the broad spatial scales sampled by GRaND using a physics-based smoothing algorithm that accounts for the shape and topography of Vesta and Ceres. On Vesta, the distributions of elemental hydrogen and hydroxyl are similar, which implies that hydrogen is primarily in the form of hydroxyl, likely as phyllosilicates delivered by the infall of carbonaceous chondrite impactors. Small differences in the spatial patterns of hydroxyl and hydrogen imply that hydrogen is layered in some locations. In Vesta's dark hemisphere, hydrogen deposits are more extensive than hydroxyl, which indicates higher concentrations of hydrated minerals at depth. In contrast, the distributions of elemental hydrogen and hydrogen-bearing species (OH and NH_4^+) on Ceres are dissimilar. High concentrations of hydrogen in the Ceres’ polar regions (approaching 30 wt.% equivalent H_2O) indicate the presence of subsurface ice as predicted by ice stability theory. The concentration of iron follows a water-dilution trend when plotted as a function of regolith hydrogen content, consistent with the presence of subsurface water ice. The VIR and GRaND data jointly constrain aspects of Ceres’ surface chemistry and evolution. GRaND iron measurements place a firm upper bound on magnetite content, which supports graphitized carbon as an alternative to magnetite as a darkening agent. Lower-bounds on the concentration of carbon in carbonates implied by VIR, together with the ratio of carbonates to organics in carbonaceous chondrite meteorite analogs suggest high concentrations of carbon within Ceres’ regolith. GRaND neutron measurements permit elevated carbon concentrations, equal to or in excess of that found in CI chondrites (greater than a few wt.%). Organic matter, detected by VIR at Ernutet crater, might be widespread and may have been converted to graphite, e.g. via UV exposure, elsewhere on the surface. Furthermore, elevated concentrations of carbonaceous material can explain the difference between iron and hydrogen concentrations measured by GRaND and the CI carbonaceous chondrites, which are representative of the materials from which Ceres accreted. The elemental measurements indicate that ice and rock fractionated during Ceres’ evolution producing a crust that differs in composition from the whole body.

Twenty-six samples of mortar used for various construction applications (joint mortars, floor mortars, filling mortars and plasters) were collected from different areas of the archaeological site of Pompeii (Campania - Sothern Italy). The mortar samples belong to various historical periods covering approximately 2000 years, from the 2nd century BC to the post excavation period (18–19th century). The samples were characterized employing Optical Microscopy (OM), X-ray Powder Diffraction (XRPD), X-ray Fluorescence (XRF), Electron Probe Micro Analysis (EPMA) and Raman Spectroscopy. Moreover, image analysis was carried out using JMicroVision software in order to determine the percentages of binder, macropores and aggregate, in terms of crushed ceramic fragments (cocciopesto), rock fragments and monocrystals. The application of these techniques allowed obtaining a complete chemical and minero-petrographic characterization of the samples, which may prove useful for preparing compatible repair mortars for future restoration works. The archaeometric study provided new data on the production technology of the mortars and the analogies and differences observed among the samples, enabled us to distinguish different constructive phases, thus confirming or rebutting the archaeological hypothesis on the dating of some samples. By combining compositional variables through the discriminant analysis, it was also possible to analyse the time evolution of the materials and to construct preliminary multivariate statistical models, helpful to identify the various typologies of mortars used in the different historical periods.

Generation of sediments from crystalline rocks is the result of a complex and incompletely understood suite of processes. The time evolution of the rock-fragment assemblage in sands derived from granitoids is determined by the relative strengths of crystal interfaces and their abundances in the parent rock. In this study we highlight the role of crystal-interface frequencies in granitoids. Strong evidence for non-random texture with significant implications for predicted interface frequencies have been reported in previous studies. We analysed available interface-frequency data from granitoids using methods of compositional data analysis, and connected our results to existing texture classifications. On average, granitoids display a high degree of ordering with significant depletion of isomineralic interfaces relative to expectations based on random texture. Analysis of 210 normalized interface frequency distributions from nine different granitoids reveals a consistent pattern of variation among interface frequencies, which suggests a single underlying petrogenetic process related to the combined effects of nucleation and textural equilibration (“coarsening”). In view of the large scatter of relative interface frequencies within and among granitoids, we propose to model their distribution empirically for the purpose of calibrating sediment-generation studies. Multivariate normal distributions of centred log-ratio transformed relative frequencies are capable of capturing ~95% of the observed variability with a limited number of dimensions. As a rule of thumb, the number of dimensions needed to approximate interface-frequency counts can be taken equal to the number of mineral classes, which is (much) smaller than the number of interface classes. Mathematical analysis shows that the joint variability of rock texture and composition may be factorized into three statistically independent measures: modal composition, crystal-size probability density functions, and normalized interface frequencies. The potential independence of these measures permits objective identification of petrogenetically significant correlations among them, which will be indicated by statistically significant cross-covariances. At this stage, inferences from microscopic texture analysis cannot be extrapolated to the scale of entire drainage basins in which sediments are generated, because insufficient data are available on the large-scale spatial heterogeneity of texture and composition of granitoid parent rocks.

Unsupervised and supervised machine learning techniques are used to classify and predict the alteration facies of the Rosemont skarn deposit. The deposit comprises three major geological domains informally named the Lower Plate, Upper Plate, and West Block. Over 1 billion tons of Cu-Mo-Ag mineralization are primarily hosted within the Lower Plate and West Block, concealed under poorly mineralized rocks of the Upper Plate. A training dataset comprising 882 drill core samples analyzed for X-ray powder diffraction (XRD) mineralogy and multi-element geochemistry is used to improve the classification and recognition of the skarn alteration. The XRD-mineralogy is used for unsupervised learning in which hierarchical and K-means cluster analysis is applied to devise a classification of the skarn alteration using a compositional data analysis approach. The complex alteration at the Rosemont deposit is simplified into garnet-pyroxene-wollastonite-vesuvianite (GrtPxWoVes) skarn, serpentine-amphibole (SrpAm) skarn, epidote (Ep) skarn, and least altered (LAlt) rock. These four classes are coded into a categorical variable named Alteration Facies. The supervised learning uses the multi-element geochemical data to predict Alteration Facies. Several predictive models are fitted using different machine learning algorithms including support vector machines with linear (SVM-linear) and radial (SVM-radial) kernels, linear discriminant analysis (LDA), quadratic discriminant analysis (QDA), classification and regression trees (CART), and random forests (RF). Each predictive model is fitted onto three predictor spaces including raw geochemical data, isometric log-ratios (ilr), and centered log-ratios (clr) to evaluate the effect of compositional representations on the performance of the predictive models. The analysis shows that the RF algorithm yields predictive models that outperform all other algorithms using any of the predictor spaces. The RF test set prediction accuracy after 10-fold cross-validation is 79%; which is significantly higher than an accuracy of 45% obtained from visual core logging classification of the skarn alteration. Hypothesis testing, using multilevel linear modeling, suggests that there are no statistically significant differences in the quality of the predictive models fitted onto the raw, ilr, and clr geochemical data. Therefore, compositional representations of the geochemical data do not improve the performance of the predictive models. The best RF model is used to predict Alteration Facies on 33,000 drill core samples in which multi-element geochemistry is available but the skarn alteration is uncertain due to the lack of XRD-mineralogy. The predicted alteration shows that the Ep skarn facies occurs above the economic mineralization within Mesozoic siliciclastic and volcanic rocks of the Upper plate. The GrtPxWoVes skarn and SrpAm skarn occur within Paleozoic carbonate rocks of the Lower Plate and West Block. Accordingly, the Ep skarn facies can be used to target blind Cu-Mo-Ag rich porphyry-skarn mineralization in areas where the Paleozoic carbonate rocks are concealed under the Mesozoic siliciclastic and volcanic rocks.

The performance of WD-XRF and NAA set-ups has been examined by comparing compositional data obtained by the two methods on 36 clay samples collected in Central and Eastern Crete. While the two methods determine a different range of elements – 26 are determined by WD-XRF, 27 by NAA, of which 15 are measured with both methods – with different precisions, a similar grouping, and level of resolution when examining the same set of clays could be achieved using WD-XRF data in comparison with NAA data. These results highlight the WD-XRF routine's potential of discrimination even in regions which have proved to be challenging for provenance studies in the past.

Hydrogeochemical and isotopic data were used to improve the understanding of 1) Groundwater flow in a complex fractured aquifer system, 2) Surface water – groundwater interactions, and 3) Groundwater evolution within the La Linea Massif in the Cordillera Central of the Colombian Andes, using two roadway tunnels drilled there as a natural laboratory. The La Linea Massif is a crystalline structure formed by two igneous-metamorphic fractured complexes (Cajamarca Group and Quebradagrande Group), plus andesitic porphyry rocks from the Cenozoic period. The tunnels traverse eight main fault zones, where higher infiltrations of groundwater into the tunnels were reported. Water samples were collected at the surface and within the tunnels in three different sampling rounds in 2010, 2014 and 2015. Major ion concentrations and δ 18 O and δ 2 H stable isotopic ratios were measured. This database is a unique opportunity to investigate water-rock interaction processes through time in a dewatering crystalline rock massif in such an important area in the Colombian Andes. Compositional data analysis (CoDa) techniques were implemented on the major ion data before a multivariate statistical analysis (MSA). The MSA included a compositional principal component analysis (PCA) and a compositional hierarchical cluster analysis (HCA), combined with more classical graphical methods for the classification of water chemistry data, such as Piper and Stiff diagrams. According to the compositional HCA and PCA, the obtained components and clusters are first related to the location of the samples (surface or tunnel samples) followed by the geochemical processes. The geochemical variability of the massif is associated with the weathering of silicates and pyrite oxidation that generates carbonate dissolution as a result of the drainage caused by the tunnels. A temporal evolution characterized by a decrease in pH, conductivity and Mg2+ concentrations was observed. The analysis of the stable isotopes, 2H and 18O, suggests that the sampled groundwater has a common origin: recharge waters with specific signatures for the east and west watersheds that exhibit alterations due to hydration because of the dissolution of plagioclases and rock-water interactions with materials exposed to hydrothermal fluids.

The research presented here evaluates the applicability of energy-dispersive X-ray fluorescence (EDXRF) for characterizing steatite. We present compositional data from an assemblage of 100 steatite beads and pipes deriving from 11 Northern Iroquoian sites in southern Ontario and New York State. Percentages of major elemental constituents and principal components analysis define two compositional groups and various non-steatite artifacts. Our results suggest that EDXRF is an expedient means of characterizing steatite based on major oxides and trace elements. The results support the assertion that individual Iroquoian communities were involved in distinct interaction networks that linked groups in southern Ontario and the St. Lawrence Valley region.

Wastes from the world's largest manufacturer of DDT (1-chloro-4-[2,2,2-trichloro-1-(4-chlorophenyl)ethyl]benzene) were released into the Los Angeles County municipal sewer system from 1947 to 1971. Following primary treatment, the effluent was discharged through a submarine outfall system whereupon a portion of the DDT and associated degradation products were deposited in sediments of the Palos Verdes Shelf (PVS). Parent DDT is present only in trace amounts in the sediments today, the vast majority having been transformed to DDE (1-chloro-4-[2,2-dichloro-1-(4-chlorophenyl)ethenyl]benzene) shortly following deposition. Previously believed to be inert, DDE is slowly being converted to DDMU (1-chloro-4-[2-chloro-1-(4-chlorophenyl)ethenyl]benzene) and DDMU to DDNU (1-chloro-4-[1-(4-chlorophenyl)ethenyl]benzene) via microbially-mediated reductive dechlorination (RDC). Kinetic and compositional data suggest that this process began sometime in the mid- to late 1970s. Rates of DDE RDC in shelf sediments are spatially variable and have proven difficult to determine accurately. This limits our ability to understand the factors controlling RDC rates and to predict the course of natural recovery. In the present study, concentrations of ten DDT compounds and twelve PCB (polychlorinated biphenyl) congeners were determined in cores collected at two locations on the PVS (stations 3C, 6C, ~ 7 km and ~ 2 km downcurrent from the outfalls, respectively). DDE inventories, normalized to those of non-degrading PCB congeners having similar physico-chemical properties , were modeled to yield first-order RDC rates for the period 1981–2010. Average rates at stations 3C and 6C were 0.044 ± 0.004 and 0.008 ± 0.002 yr− 1, respectively, with depth-dependent RDC rates at station 3C (1992–2003) ranging from 0.0025 to 0.102 yr− 1. Comparison of RDC and total loss (i.e., RDC + physical loss) rates suggests that the average per cent loss of DDE due to RDC is ~ 90% at station 3C (1981–2010) and ~ 57% at station 6C (1992–2010). Trajectories of adjusted molar inventories of DDE, DDMU, and DDNU were forecast using a first-order multi-step reaction series (M-SRS) model. The results for DDE are consistent with the normalization procedure; RDC rates at stations 3C and 6C were 0.036 ± 0.002 yr− 1 and 0.010 ± 0.001 yr− 1, respectively. At station 6C, the DDE to DDMU transformation appears to be the rate limiting step in the reaction sequence, DDE k 1 → DDMU k 2 → DDNU k 3 → unidentified compound(s), whereas at station 3C RDC rates for DDE and DDMU are roughly equivalent. At both locations the transformation rate of DDNU is 7–20 times that of the other steps. Estimated half-lives of DDE at stations 3C and 6C based on the M-SRS model results are ~ 19 and 72 years, respectively.

This paper focuses on the implementation of a methodology for identifying chemical groups, the search for data patterns and the determination of outliers in a collection of ceramic samples after compositional analysis. In order to obtain the chemical composition, pottery samples from the archaeological site of Xalasco were analyzed by means of a portable XRF technique. The discrimination of groups was based on the methodology proposed by Aitchison in 1986 for the analysis of compositional data. First, we applied a stepwise method for the selection of variables with the use of biplots. The detection of outliers was managed by using the method known as FAST-MCD. In a second stage, the detected groups and their components were analyzed in a supervised manner using the PLS-DA method. Once the groups were validated, we obtained the balances and the CoDa-dendrogram with the isometric transformation to appreciate the differences in their chemical composition. The results showed a high degree of accuracy in the discrimination between groups, which can be interpreted as different manufacturing processes. The chemical differences among the samples can be understood in terms of the cultural influences reflected in the preparation of the ceramics pastes through time, the availability of raw materials and the organization of pottery production.

The Athabasca Basin in northern Saskatchewan, Canada, hosts the world's largest high-grade U resources near the unconformity between sandstones and underlying crystalline basement rocks. Finding U deposits is difficult in the interior of the Athabasca Basin where the sandstone cover can reach 1400 m. This study uses the lithogeochemistry of sandstones obtained from drill cores to identify elements associated with U using principal component analysis (PCA) from three areas; samples directly above the Phoenix U deposit, those in Denison Mine's Wheeler River property and background areas in the basin. The sandstone data from the Wheeler River property shows that U is positively associated with Y-Cu-Zn-Na-W-Co-Ni-B-Mg-HREEs-Cr-Sc-Mo-V-LREEs due to uraniferous hydrothermal alteration. In contrast, the principal components derived from the lithogeochemistry of sandstones far from known mineralization in the basin shows that U is positively associated with Th-Ti-Zr-Hf, suggesting that U is hosted in refractory detrital minerals. Linear discriminant analysis (LDA) and random forest (RF) analysis based on principal components of elements associated with U show three classes of sandstones with clear discrimination between samples; those above the Phoenix ore (Class Phoenix), in the Wheeler River (Class Wheeler River), and regional background (Class Regional Background). The class Phoenix contains most of the sandstone samples overlying the Phoenix deposit and a few samples in the Wheeler River property. This study shows that PCA, LDA and RF are able to detect geochemical footprints of uraniferous hydrothermal alteration >500 m from the ore and differentiate sandstones spatially associated with the mineralization from those in barren areas. Based on the performance of the two discrimination methods, we suggest that RF is a preferred method as it better differentiates altered sandstones from regional background samples. The classification analysis used in this study may be useful in U exploration in Athabasca Basin and other sedimentary basins.

Modelling of topsoil geochemical data using discriminant function analysis, along with a set of corresponding geochemical maps, portray a legacy of environmental contamination in the city of Sisak. Based on centred log-ratio (clr) transformed compositional data from topsoil samples collected on Kupa-Odra and Sava River floodplain sediments and loess, underlying the Sisak urban area, and regrouped according to their land use characteristics (urban, industrial and agricultural areas), a few element clusters emerged accounting for discrimination between the defined groups. The most prominent feature of the lithological model, as suggested by the first discriminant function, is the carbonate group (Mg, Ca, Sr) versus anthropogenic sourced elements/transition metals (e.g., Sn, Zn, Ba, Mn, Pb, U, Ag, Cr, V) dichotomy separating soil developed on floodplain sediments of Sava and Kupa-Odra Rivers from those evolved on loess. The major attribute of the land use model, according to the main discriminant function, is differentiation between urban/industrial and rural (agricultural) samples based on contrast provided by the carbonate component and other anthropogenic sourced element clusters (predominantly alkaline and concentrated over the loess substrate), in contrast to fertiliser trace and transition element clusters (predominantly acid and disseminated over Kupa-Odra and Sava River floodplain sediments). In both cases, the second discriminant function provides additional information on the secondary level, i.e., in the lithology model the Kupa-Odra sediment group is distinguished from other lithological groupings owing to its predominantly transition element signature. In the land use model, urban soil samples are separated from industrial ones based on the characteristic Na-Sr-Ca-pH(KCl) element association (urban waste) against a typical ‘industrial’ element signature (Zn-Cd-Mn-Pb-Mo).

In this paper we construct a hierarchical model for spatial compositional data which is used to reconstruct past land-cover compositions (in terms of coniferous forest, broadleaved forest, and unforested/open land) for five time periods during the past 6000 years over Europe. The model consists of a Gaussian Markov Random Field (GMRF) with Dirichlet observations. A block updated Markov chain Monte Carlo (MCMC), including an adaptive Metropolis adjusted Langevin step, is used to estimate model parameters. The sparse precision matrix in the GMRF provides computational advantages leading to a fast MCMC algorithm. Reconstructions are obtained by combining pollen-based estimates of vegetation cover at a limited number of locations with scenarios of past deforestation and output from a dynamic vegetation model. To evaluate uncertainties in the predictions a novel way of constructing joint confidence regions for the entire composition at each prediction location is proposed. The hierarchical model’s ability to reconstruct past land cover is evaluated through cross validation for all time periods, and by comparing reconstructions for the recent past to a present day European forest map. The evaluation results are promising, and the model is able to capture known structures in past land-cover compositions.

Different features of geochemical information were studied by comparing spatial distribution of concentration values and compositional data values. Geochemical data are compositional and should be treated as such to avoid spurious correlations and misleading interpretations. However, geochemists are also interested to discuss in terms of elemental concentrations. In this work the spatial distribution of Fe, Mn, Ti, Co, Cr, Ni and V based on 3535 topsoil samples collected in Campania region (Southern Italy) and analysed by ICP-MS after aqua regia digestion, is studied. Unielement maps and CoDA based maps, namely of ilr-transformed data and of two subcompositions of 3 components have been produced and interpreted. Results show that the ilr maps often show different geochemical patterns from those provided by the maps based on raw concentrations, namely for V, Fe and Co. This is not surprising as each studied ilr is a (log)ratio of an element against the others and account for the compositional variability. Nevertheless, the geochemical patterns of both raw and ilr based maps relate mostly with the geolithological features of the region: (1) (Ti, Ni, Cr)log-ratio variables are the best pathfinder in differentiating between volcanic (relative enrichment in Ti) and non-volcanic (relative enrichment in Ni and Cr) areas. (2) Soil alteration phenomena could locally enhance log-ratios of Ti due its high geochemical stability. (3) The spatial analysis of ilr-Fe and ilr Mn variables amplifies their relative degree of enrichment in correspondence of silici-clastic formations suggesting that Mn-Fe oxides of clay minerals mainly dominate the geochemical composition of the soils of the survey area. (4) Local enrichments of Cr and Ni at the main rivers' mouths and in the metropolitan areas of Naples and Salerno, possibly of anthropogenic origin, are highlighted in the 3-part subcomposition analysis. The developed exploration methodology of uni-element geochemical data under a compositional perspective leads to deeper insight and the gain is a more accurate interpretation of processes controlling soils geochemical variability.

A simulation model is developed for pulsed laser remelting that captures the homogenization of surface chemical composition and height variations that occur due to silicon (Si) precipitates in a hypereutectic aluminum-silicon (Al-Si) casting alloy. The model simulates remelting pulse-by-pulse with two sequential and repeated steps: it first predicts surface homogenization by areal averaging within a laser spot and then generates and adds a surface feature, due to thermocapillary flow, whose size depends on the concentration of Si within the homogenized spot. Compositional data of remelted lines was collected with energy-dispersive x-ray spectroscopy and used to verify the homogenization step of the simulation model. It was found that Si precipitates get redistributed by the laser with the peak in Si concentration occurring in the direction opposite that of beam travel. Height data from remelted lines were measured using white light interferometry to verify the accuracy of the remelting model in simulating surface topographical modifications. It was found that variations of approximately ± 1 μm are induced in the Al-Si alloy during pulsed laser remelting due to the Si proeutectic precipitates. This is attributed to differences in laser absorption of Si and Al. Because the Si precipitates absorb more energy from the laser, they experience higher temperatures and temperature gradients, which cause larger thermocapillary flow. The results provide insights into approaches to model surface compositional homogenization that occurs during laser remelting and provides an understanding of surface microstructural and topographical features often seen in laser polished Al-Si casting alloys.

Older adults' health has been linked with time in moderate-to-vigorous physical activity (MVPA), and recent studies suggest time in sedentary behaviour may also be important. Time-use behaviours (MVPA, light physical activity, sedentary time and sleep) are co-dependent, and therefore their associations with health should be examined in an integrated manner. This is the first study to investigate the relationship between older adults' reallocation of time among these time-use behaviours and markers of cardio-respiratory fitness, obesity and cardio-metabolic risk.Cross-sectional study of 122 Australians (65 ± 3 y, 61% female).Daily time use: average daily minutes spent in MVPA, light physical activity, sedentary time and sleep derived from 24-h, 7-day accelerometry, were conceptualised as a time-use composition. Cardio-respiratory fitness: graded submaximal cycle ergometer test. Obesity: objectively measured body mass index (BMI) and waist-to-hip ratio (WHR). Cardio-metabolic risk: sphygmomanometer-measured resting blood pressure and fingertip blood sampling for fasting total cholesterol and glucose.Time-use composition was significantly associated with obesity markers (BMI, p = 0.001; WHR, p 0.001). The reallocation of 15 min to MVPA from any of the other behaviours was associated with approximately +1.1 (95% confidence interval 0.2; 1.9) ml/kgThese findings reinforce the importance of MVPA for health among older adults. Interventions to maintain MVPA, even without increasing it, may be valuable.

Perovskite mineral oxides commonly exhibit extensive solid-solution, and are therefore classified on the basis of the proportions of their ideal end-members. A uniform sequence of calculation of the end-members is required if comparisons are to be made between different sets of analytical data. A Microsoft Excel spreadsheet has been programmed to assist with the classification and depiction of the minerals of the perovskite- and vapnikite-subgroups following the 2017 nomenclature of the perovskite supergroup recommended by the International Mineralogical Association (IMA). Compositional data for up to 36 elements are input into the spreadsheet as oxides in weight percent. For each analysis, the output includes the formula, the normalized proportions of 15 end-members, and the percentage of cations which cannot be assigned to those end-members. The data are automatically plotted onto the ternary and quaternary diagrams recommended by the IMA for depiction of perovskite compositions. Up to 200 analyses can be entered into the spreadsheet, which is accompanied by data calculated for 140 perovskite compositions compiled from the literature.

The data represent the first available data set on platinum group element (PGE) levels in Berlin topsoil. In 2013, over 100 topsoil samples (0–20 cm) were collected in the inner city of Berlin. The PGEs in topsoil samples were analysed by ICP-MS after a trace-matrix separation. The results were compared to analyses of PGEs in Berlin topsoil collected at the same sample sites in 1992. The data show an increased accumulation of PGE concentrations in Berlin topsoil during this two-decade interval as a result of gradual increase in the use of vehicles with catalytic converters. A comparison of PGE median concentrations show an increase by a factor of 1.5 for Pt, 3.0 for Pd, 4.3 for Rh, and 3.1 for Au, over the 20-year period. The single element distribution maps of PGEs from 2013 confirm a clear correlation with traffic density. The PGE ratios (Pt/Pd, Pt/Rh, Pd/Rh) were consistent with known catalytic converter compositions, and indicate catalytic exhausts as the main source of these elements. A comparison of the maps of measured raw PGE data with the clr-transformed maps reveals identical distribution patterns (including PGE anomalies). Principal component analysis (PCA) results obtained from the classical statistical approach (standardised) are quite similar to those from PCA carried out using the compositional data analysis (CoDA) approach. Grouping of the PGEs, based on hierarchical cluster analysis, provides a complementary treatment and confirms the PCA results, indicating that the PGE concentrations in Berlin topsoil from 2013 are mainly caused by vehicle emissions.

Bulk chemical compositions of meteorites were traditionally analyzed by wet chemical analysis, and NIPR has data for 1162 meteorites as of September 2017. We discuss the classification of meteorites on the basis of these data. Chondrite data are distributed in an anomalously wide range of compositions on the Urey-Craig diagram. One of the reasons for such wide distribution is terrestrial weathering producing Fe2O3–bearing phases from Fe-Ni metal and sulfides. Another important factor affecting the bulk compositional data is brecciation. Our observations indicate that many brecciated chondrites contain anomalously abundant opaque minerals, or are depleted in them, resulting in unusual compositions. In case of enstatite and some carbonaceous chondrites, the bulk compositions are distributed in wider ranges than reported before. The bulk compositions of HED meteorites are consistent with their mineralogy and classification. Our study suggests that wet chemical data are still significant for the meteorite classification. However, petrographic observation is indispensable for evaluating the bulk chemistry and classification of meteorites., 国立極地研究所は1162個の隕石の全岩化学組成を湿式分析法により得た。本論文ではこのデータを基に隕石の分類を検討した。コンドライトをユーレイ—クレイグ図にプロットすると異常な領域に分布するものが認められる。地球上での風化作用が一因である。また角礫岩化作用の寄与も大きい。光学顕微鏡観察によれば異常な組成の普通コンドライトの多くは角礫岩である。エンスタタイト・コンドライトや炭素質コンドライトでは従来のデータより広い範囲の全岩化学組成を持つことが明らかになった。HED隕石の全岩化学組成は鉱物組合せや分類と一致する。本研究により湿式分析法による全岩化学組成データは分類上、重要であることがわかった。これと同時に全岩化学組成や分類の議論に当たっては岩石学的観察が不可欠であることも示した。

Several studies have investigated the wax precipitation process, focusing on the equations of state, correlations for fusion properties, and calibration of parameters. In most of them, the impact of the fluid characterization on the wax properties has not been addressed widely. In this study, we show that a single characterization scheme is not applicable to all crudes with wax precipitation. However, it is possible to categorize the crudes based on the compositional data and wax parameters to have a primary understanding of the fluid description for modeling. We employed the PC-SAFT equation of state for modeling of liquid phase behavior and the multi-solid framework to describe solid phase. The heptane plus fraction of the studied fluids is defined by the three-parameter gamma distribution of Whitson, et al. [1] , and the continuous description of the plus fraction is discretized by the pseudoization method of Whitson, et al. [2] . We also show the significance of binary interaction parameters on calculating wax appearance temperature and wax weights. The critical volumes of the precipitating hydrocarbons are adjusted to find the best binary interaction parameters values for the WAT and wax weight determination. The WAT and wax weight of eleven crude oil samples are calculated and compared to experimental and modeling results of previous studies. Our model shows considerable improvements in estimating fluid description, WAT, and wax weight compared to other available models. Moreover, we demonstrated that the number of pseudo-components and the heaviest molecular weight in the description of plus fraction highly depend on the compositional data of the heavy end and wax properties. According to our results, 15 pseudo-components with the highest molecular weight of 1200 g/mol would result in the accurate presentation of WAT and wax weight for crudes with WAT higher than 310 K and high wax weights.

The modes of occurrence for elements in coal are extremely important for deciphering geological process of coal formation and for anticipating the technological behavior and environmental and health impacts derived from coal utilization. Hierarchical clustering algorithm has been widely adopted to investigate the modes of occurrence of elements in coal. The traditional statistics (e.g., Pearson correlation, Euclidean distance) for the elemental data of coal may lead to misinterpretation because the elemental data of coal are of compositional nature and follow the rules of Aitchison geometry. This work applied log-ratio transformations in order to overcome this problem. Different hierarchical clustering algorithms with various data transformations can infer modes of occurrence for coal elements, but which algorithm is optimum deserves to be investigated. In this paper, we discuss four commonly used hierarchical clustering algorithms utilizing pivot coordinates and weighted symmetric pivot coordinates (WSPC), two types of log-ratio transformations, to infer modes of occurrence of elements in coal, based on published coal elemental data. Results showed that the Pearson correlation produces more meaningful results than the Euclidean distance in clustering rare earth elements and Y. WSPC produces more interpretable results than those from pivot coordinates transformed data for these coal elemental data. Compared with the single, complete, and centroid, the average-linkage algorithm is indeed the optimum.

The Zarshuran gold deposit as sediment-hosted Carlin-type has a total reserve of 120 million metric tonnes and an average grade of 3.5 g/t Au. The dominant hydrothermal alterations associated with gold mineralization are argillic and silicic as well as decalcification of the carbonate host rocks. The exploration geochemistry was applied to characterize the mineralization in the subsurface and peripheries of the open-pit mine at Zarshuran in order to enhance the proved reserves of the gold ores. A sampling network of a 10 × 10 m grid (n = 1720) was applied to almost unweathered surface outcrops to determine the primary geochemical haloes in the study area. Initially, the cut-off grades utilized in the exploratory data analysis were applied to identify the threshold values of the trace elements with lognormal distribution. Then, the central log ratio transformation was used to determine the robustness against outliers to characterize the closure problems with compositional data during Principle Component Analysis (PCA). The supra-ore and near-ore geochemical haloes are recognized by the indicator elements like As-Sb-Hg-Te-Au-Ag-Fe-Mn-Ba-F which are associated with mineral assemblages such as arsenical pyrite, orpiment, realgar, cinnabar, barite, and fluorite. The sub-ore geochemical haloes are characterized by index element association like Cu-Mo-Bi-W-Sn-Co-Ni-V-Cr. The ores at Zarshuran are enriched in Au, As, Sb, Ag, Te, Tl, Zn, Pb, and F but depleted in Cu, W, and Sn, as were observed in many other Carlin-type gold deposits. The enrichment factor of indicator elements (except S, Ag, and Sb) gradually decreases in value from the highly altered and mineralized zones (in proximity of the mine) toward the zones with least alteration and mineralization (in the distal parts of the mine). According to PCA analysis, two main types of ore mineralization occurred at Zarshuran, (1) Au mineralization associated with As, Sb, and Hg, and (2) Cu-Zn-Pb base-metal mineralization related to Ag. The ore-forming index was used to determine the primary axial haloes in both shallow ( −120 m) levels. The results of this study show that the main ore body may extend eastwardly and downwardly to greater depths, as was verified by the data obtained from diamond drill cores in the eastern part of the mine.

This study intends to (i) identify the potential sources of heavy metal (HM) pollution in an industrial town situated in the northwestern part of Iran and (ii) and assess whether the pollution levels discharged by HMs are significant. A suite of geochemical samples collected from the topsoil horizon of the study area were analyzed for HMs, namely Cr, Ni, Co, Cu, V, Zn, Mn, and Pb, to attain the objectives mentioned above. Compositional data analysis (CODA) techniques were employed for pinpointing the potential source of HM pollution. Initially, the centered log-ratio (clr) transformation was applied to the dataset containing raw values of chemically analyzed soil samples to address the data closure problem. Multifractal moving average interpolation was then applied to the clr-transformed data to model the spatial distribution of HMs in the study area. Maps of the spatial distribution of HMs in the study area were further classified by the concentration-area (C-A) fractal technique for identifying the potential hotspots of HM pollution in the area. It was followed by using the K-means clustering technique for classifying samples into distinct classes. This method was selected for geochemical pattern recognition owing to its simplicity and robustness in identifying subtle patterns embedded in geochemical data. The above hybrid methodology points to three anthropogenic sources discharging HM pollution into the area: leather factories, brickworks, and highways. Finally, pollution indices, namely the geo-accumulation index, pollution load index, and potential ecological risk, revealed that the elevated levels of Ni, Cr, and Co can pose serious impediments to the soil quality of the study area.

8 Páginas; 3 Tablas; 2 Figuras, This article contains processed data related to the research published in “Tentative application of compositional data analysis to fatty acid profiles of green Spanish-style Gordal table olives” (Garrido-Fernández et al., 2018) [1]. It provides information on the implementation of compositional data analysis (CoDa) to the fatty acid profiles of Spanish-style Gordal table olives vs the use of conventional statistical analysis (data composition expressed in percentages). Particularly, it includes: i) the matrix of the sequential binary partition used for the balance estimation and the isometric log-ratio transformation (ilr) of the fatty acid profiles, ii) correlation among the diverse fatty acids expressed in percentages and their significances, iii) the ilr transformed values (coordinates in the Euclidean space) obtained following the sequential binary partition previously detailed, iv) the graphical presentation in the Simplex (ternary centred plot) of the treatments as a function of the four fatty acids with the higher log-ratio variances, and v) segregation of treatments based on Cluster Analysis., This work was supported by the Spanish Government under project (AGL2010-15494/ALI, partially financed by European Regional Development Funds, ERDF) and Junta de Andalucía through financial funding to group AGR-125. We also thank Elena Nogales Hernández for technical assistance.

Plots of cumulative distribution functions (CDF) are a simple but powerful exploratory data analysis (EDA) tool to evaluate and compare statistical data distributions. Here, empirical CDF plots are used to compare results of four large (476–884 samples) national-to continental-scale inorganic water chemistry data sets: (1) European surface water, (2) European tap water, (3) European bottled waters as a proxy for groundwater and (4) Norwegian crystalline bedrock rock groundwater, all analysed at the same laboratory, albeit at different times. For many parameters (e.g., Ba, Cl−, K, SO42−) median values and ranges are, given the differing origins and, in some cases, treatment processes of the waters, surprisingly comparable. Unusually high concentrations of some other elements (e.g., B, Be, Br, Cs, F−, Ge, Li, Rb, Te and Zr) appear to be characteristic of deeper-seated, mature groundwaters. Other influences that can be inferred include contamination from well construction or plumbing materials (Cu, Pb, Zn – in tap waters, bottled waters and Norwegian groundwaters), water treatment (Fe, Mn – in tap- and Norwegian groundwater), bottle materials (Sb - bottled waters). The empirical CDF plots also reveal analytical issues for some elements (excessive rounding, element interferences). The best reference for natural and uncontaminated ’water’ is probably provided by the mineral water samples, representing ‘deep groundwater’ at the European scale.

Constraining the contribution of crustal lithologies to silicic magmas has important implications for understanding the dynamics of these potentially highly explosive systems. Low- δ 18 O rhyolite lavas erupted after caldera-forming events in Yellowstone have been interpreted as the products of bulk crustal melting of previously deposited and hydrothermally altered rhyolitic material in the down-dropped caldera roof. For lack of compositional data, the “self-cannibalisation bulk melting”-theory relies on the assumption that hydrothermally altered materials are near-cotectic and hydrous (>3 wt% H2O) and will therefore readily melt at temperatures below 850 °C. In this study, we examine the drillcores Y2, Y9 and Y13 from a USGS drilling campaign in Yellowstone in order to characterise the hydrothermally altered material in terms of major and trace elements, oxygen isotopes and water contents. Rhyolite δ 18 O values can decrease from “normal” (+5.8 to +6.1‰) on the surface to as low as −5‰ at depths of 100–160 m and probably lower as a function of increasing temperature with depth. While material in the drillcores is variably altered and silicified, oxygen isotope exchange in these samples is not accompanied by systematic changes in major and trace element composition and is independent of uptake of water. More than 75% of the drillcore samples have 1100 °C. Therefore, large-scale bulk melting is unrealistic and low- δ 18 O rhyolite magmas more likely result from assimilation of δ 18 O into a normal- δ 18 O rhyolite magma from the main reservoir. This mechanism is supported by isotopic mass-balance models as well as thermal and volumetric constraints, and may be similarly applicable to other low- δ 18 O settings worldwide.