Análisis composicional de datos en Ciencias Geoambientales

Compositional data (concentrations) are common in geosciences. Neglecting its character mey lead to erroneous conclusions. Spurious correlation (K. Pearson, 1897) has disastrous consequences. On the basis of the pioneering work by J. Aitchison in the 1980s, a methodology free of these drawbacks is now available. The geometry of the símplex allows the representation of compositions using orthogonal co-ordinares, to which usual statistical methods can be applied, thus facilating computation ans analysis. The use of (log) ratios precludes the interpretation of single concentrations disregarding their relative character. A hydro-chemical data set is used to illustrate the point

An R Library for Compositional Data Analysis in Archaeometry

Compositional data naturally arises from the scientific analysis of the chemical composition of archaeological material such as ceramic and glass artefacts. Data of this type can be explored using a variety of techniques, from standard multivariate methods such as principal components analysis and cluster analysis, to methods based upon the use of log-ratios. The general aim is to identify groups of chemically similar artefacts that could potentially be used to answer questions of provenance. This paper will demonstrate work in progress on the development of a documented library of methods, implemented using the statistical package R, for the analysis of compositional data. R is an open source package that makes available very powerful statistical facilities at no cost. We aim to show how, with the aid of statistical software such as R, traditional exploratory multivariate analysis can easily be used alongside, or in combination with, specialist techniques of compositional data analysis. The library has been developed from a core of basic R functionality, together with purpose-written routines arising from our own research (for example that reported at CoDaWork'03). In addition, we have included other appropriate publicly available techniques and libraries that have been implemented in R by other authors. Available functions range from standard multivariate techniques through to various approaches to log-ratio analysis and zero replacement. We also discuss and demonstrate a small selection of relatively new techniques that have hitherto been little-used in archaeometric applications involving compositional data. The application of the library to the analysis of data arising in archaeometry will be demonstrated; results from different analyses will be compared; and the utility of the various methods discussed

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 models between 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 that lay 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 hidden components, 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 total variance, 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. Graphical representation 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 analysis of 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, except fertilisers 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 are intrinsic to the relative nature of compositional data

Multivariate ARIMA Compositional Time Series Analysis

A compositional time series is obtained when a compositional data vector is observed at different points in time. Inherently, then, a compositional time series is a multivariate time series with important constraints on the variables observed at any instance in time. Although this type of data frequently occurs in situations of real practical interest, a trawl through the statistical literature reveals that research in the field is very much in its infancy and that many theoretical and empirical issues still remain to be addressed. Any appropriate statistical methodology for the analysis of compositional time series must take into account the constraints which are not allowed for by the usual statistical techniques available for analysing multivariate time series. One general approach to analyzing compositional time series consists in the application of an initial transform to break the positive and unit sum constraints, followed by the analysis of the transformed time series using multivariate ARIMA models. In this paper we discuss the use of the additive log-ratio, centred log-ratio and isometric log-ratio transforms. We also present results from an empirical study designed to explore how the selection of the initial transform affects subsequent multivariate ARIMA modelling as well as the quality of the forecasts

Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index

Parent, L. E., Natale, W. and Ziadi, N. 2009. Compositional nutrient diagnosis of corn using the Mahalanobis distance as nutrient imbalance index. Can. J. Soil Sci. 89: 383-390. Compositional nutrient diagnosis (CND) provides a plant nutrient imbalance index (CND - r(2)) with assumed chi(2) distribution. The Mahalanobis distance D(2), which detects outliers in compositional data sets, also has a chi(2) distribution. The objective of this paper was to compare D(2) and CND - r(2) nutrient imbalance indexes in corn (Zea mays L.). We measured grain yield as well as N, P, K, Ca, Mg, Cu, Fe, Mn, and Zn concentrations in the ear leaf at silk stage for 210 calibration sites in the St. Lawrence Lowlands [2300-2700 corn thermal units (CTU)] as well as 30 phosphorus (2300-2700 CTU; 10 sites) and 10 nitrogen (1900-2100 CTU; one site) replicated fertilizer treatments for validation. We derived CND norms as mean, standard deviation, and the inverse covariance matrix of centred log ratios (clr) for high yielding specimens (>= 9.0 Mg grain ha(-1) at 150 g H(2)O kg(-1) moisture content) in the 2300-2700 CTU zone. Using chi(2) = 17 (P < 0.05) with nine degrees of freedom (i.e., nine nutrients) as a rejection criterion for outliers and a yield threshold of 8.6 Mg ha(-1) after Cate-Nelson partitioning between low- and high-yielders in the P validation data set, D(2) misclassified two specimens compared with nine for CND -r(2). The D(2) classification was not significantly different from a chi(2) classification (P > 0.05), but the CND - r(2) classification differed significantly from chi(2) or D(2) (P < 0.001). A threshold value for nutrient imbalance could thus be derived probabilistically for conducting D(2) diagnosis, while the CND - r(2) nutrient imbalance threshold must be calibrated using fertilizer trials. In the proposed CND - D(2) procedure, D(2) is first computed to classify the specimen as possible outlier. Thereafter, nutrient indices are ranked in their order of limitation. The D(2) norms appeared less effective in the 1900-2100 CTU zone.

Model - data comparison of western African rainfall evolutions during the Last Interglacial (130-115 ka)

This dataset characterizes the evolution of western African precipitation indicated by marine sediment geochemical records in comparison to transient simulations using CCSM3 global climate model throughout the Last Interglacial (130-115 ka). It contains (1) defined tie-points (age models), newly published stable isotopes of benthic foraminifera and Al/Si log-ratios of eight marine sediment cores from the western African margin and (2) annual and seasonal rainfall anomalies (relative to pre-industrial values) for six characteristic latitudinal bands in western Africa simulated by CCSM3 (two transient simulations: one non-accelerated and one accelerated experiment).

X-ray fluorescence scanning of discrete samples on the Schwalbenberg II loess-paleosol sequence, raw data, magnetic susceptibility, organic carbon and U-ratio as grainsize index

The Schwalbenberg II loess-paleosol sequence (LPS) denotes a key site for Marine Isotope Stage (MIS 3) in Western Europe owing to eight succeeding cambisols, which primarily constitute the Ahrgau Subformation. Therefore, this LPS qualifies as a test candidate for the potential of temporal high-resolution geochemical data obtained X-ray fluorescence (XRF) scanning of discrete samplesproviding a fast and non-destructive tool for determining the element composition. The geochemical data is first contextualized to existing proxy data such as magnetic susceptibility (MS) and organic carbon (Corg) and then aggregated to element log ratios characteristic for weathering intensity [LOG (Ca/Sr), LOG (Rb/Sr), LOG (Ba/Sr), LOG (Rb/K)] and dust provenance [LOG (Ti/Zr), LOG (Ti/Al), LOG (Si/Al)]. Generally, an interpretation of rock magnetic particles is challenged in western Europe, where not only magnetic enhancement but also depletion plays a role. Our data indicates leaching and top-soil erosion induced MS depletion at the Schwalbenberg II LPS. Besides weathering, LOG (Ca/Sr) is susceptible for secondary calcification. Thus, also LOG (Rb/Sr) and LOG (Ba/Sr) are shown to be influenced by calcification dynamics. Consequently, LOG (Rb/K) seems to be the most suitable weathering index identifying the Sinzig Soils S1 and S2 as the most pronounced paleosols for this site. Sinzig Soil S3 is enclosed by gelic gleysols and in contrast to S1 and S2 only initially weathered pointing to colder climate conditions. Also the Remagen Soils are characterized by subtle to moderate positive excursions in the weathering indices. Comparing the Schwalbenberg II LPS with the nearby Eifel Lake Sediment Archive (ELSA) and other more distant German, Austrian and Czech LPS while discussing time and climate as limiting factors for pedogenesis, we suggest that the lithologically determined paleosols are in-situ soil formations. The provenance indices document a Zr-enrichment at the transition from the Ahrgau to the Hesbaye Subformation. This is explained by a conceptual model incorporating multiple sediment recycling and sorting effects in eolian and fluvial domains.

Grain-size distributions and bulk chemistry of sediment core MD00-2361

The terrigenous fraction of sediments from a deep-sea sediment core recovered from the northwestern Western Australian continental slope offshore North West Cape, SE Indian Ocean, reveals a history of Western Australian climate throughout the last 550 ka. End-member modelling of a data set of grain-size distributions (n = 438) of the terrigenous sediment fraction allows to interpret the record in terms of aeolian and fluvial sediment deposition, both related to palaeo-environmental conditions in the North West Cape area. The data set can be best described by two aeolian end members and one fluvial one. Changes in the ratio of the two aeolian end members over the fluvial one are interpreted as aridity variations in northwestern Western Australia. These grain-size data are compared with bulk geochemical data obtained by XRF scans of the core. Log-ratios of the elements Zr/Fe and Ti/Ca, which indicate a terrigenous origin, corroborate the grain-size data. We postulate that the mid- to late Quaternary near North West Cape climate was relatively arid during the glacial and relatively humid during the interglacial stages, owing to meridional shifts in the atmospheric circulation system. Opposite to published palaeo-environmental records from the same latitude (20°S) offshore Chile and offshore Namibia, the Australian aridity record does not show the typical southern hemisphere climate variability of humid glacials and dry interglacials, which we interpret to be the result of the relatively large land mass of the Australian continent, which emphasises a strong monsoonal climatic system.

Multivariate analysis of regional-scale geochemical data for environmental monitoring

A compositional multivariate approach is used to analyse regional scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey Northern Ireland (GSNI). The multi-element total concentration data presented comprise XRF analyses of 6862 rural soil samples collected at 20cm depths on a non-aligned grid at one site per 2 km2. Censored data were imputed using published detection limits. Using these imputed values for 46 elements (including LOI), each soil sample site was assigned to the regional geology map provided by GSNI initially using the dominant lithology for the map polygon. Northern Ireland includes a diversity of geology representing a stratigraphic record from the Mesoproterozoic, up to and including the Palaeogene. However, the advance of ice sheets and their meltwaters over the last 100,000 years has left at least 80% of the bedrock covered by superficial deposits, including glacial till and post-glacial alluvium and peat. The question is to what extent the soil geochemistry reflects the underlying geology or superficial deposits. To address this, the geochemical data were transformed using centered log ratios (clr) to observe the requirements of compositional data analysis and avoid closure issues. Following this, compositional multivariate techniques including compositional Principal Component Analysis (PCA) and minimum/maximum autocorrelation factor (MAF) analysis method were used to determine the influence of underlying geology on the soil geochemistry signature. PCA showed that 72% of the variation was determined by the first four principal components (PC’s) implying “significant” structure in the data. Analysis of variance showed that only 10 PC’s were necessary to classify the soil geochemical data. To consider an improvement over PCA that uses the spatial relationships of the data, a classification based on MAF analysis was undertaken using the first 6 dominant factors. Understanding the relationship between soil geochemistry and superficial deposits is important for environmental monitoring of fragile ecosystems such as peat. To explore whether peat cover could be predicted from the classification, the lithology designation was adapted to include the presence of peat, based on GSNI superficial deposit polygons and linear discriminant analysis (LDA) undertaken. Prediction accuracy for LDA classification improved from 60.98% based on PCA using 10 principal components to 64.73% using MAF based on the 6 most dominant factors. The misclassification of peat may reflect degradation of peat covered areas since the creation of superficial deposit classification. Further work will examine the influence of underlying lithologies on elemental concentrations in peat composition and the effect of this in classification analysis.

Quantitative analysis of vascular to cardiac selectivity of L- and T-type voltage-operated calcium channel antagonists in human tissues

1. Classical L-type voltage-operated calcium channel (VOCC) antagonists dilate blood vessels, depress myocardial contractility and slow cardiac conduction. 2. We compared four L-type VOCC antagonists and a novel tetralol derivative, mibefradil, reportedly 10-fold more selective for T- (transient) over L-type VOCC in two in vitro assays of human tissue, namely isolated small arteries from the aortic vasa vasorum in a myograph and right atrial trabeculae muscle under isometric force conditions. 3. In arteries contracted with K+ (62 mmol/L), the relaxation pIC(50) values for the VOCC antagonists felodipine, nifedipine, amlodipine, verapamil and mibefradil were 8.30, 7.78, 6.64, 6.26 and 6.22, respectively. In atrial trabeculae, the pIC(50) values to inhibit the inotropic response to a submaximal concentration of isoprenaline (6 nmol/L) for felodipine, nifedipine, verapamil, amlodipine and mibefradil were 7.21, 6.95, 6.91, 5.94 and 4.61, respectively. 4. Taking the anti-log (pIC(50) vessel - pIC(50) atrium) the vascular relaxation to cardiac depression potency ratios for mibefradil, felodipine, nifedipine, amlodipine and verapamil were 41, 12, 7, 5 and 0.22, respectively. 5. We conclude that, in human tissue assays, perhaps T- over L-type VOCC selectivity confers the most favourable vascular selectivity on mibefradil. Alternatively, splice variants of L-type VOCC in the vasculature (CaV1.2b) may be more sensitive to mibefradil than the splice variants in the heart (CaV1.2a).

Plasmodium falciparum gametocyte carriage, sex ratios and asexual parasite rates in Nigerian children before and after a treatment protocol policy change instituting the use of artemisinin-based combination therapies

The effects of artemisinin-based combination therapies (ACTs) on transmission of Plasmodium falciparum were evaluated after a policy change instituting the use of ACTs in an endemic area. P. falciparum gametocyte carriage, sex ratios and inbreeding rates were examined in 2,585 children at presentation with acute falciparum malaria during a 10-year period from 2001-2010. Asexual parasite rates were also evaluated from 2003-2010 in 10,615 children before and after the policy change. Gametocyte carriage declined significantly from 12.4% in 2001 to 3.6% in 2010 (@@χ² for trend = 44.3, p < 0.0001), but sex ratios and inbreeding rates remained unchanged. Additionally, overall parasite rates remained unchanged before and after the policy change (47.2% vs. 45.4%), but these rates declined significantly from 2003-2010 (@@χ² for trend 35.4, p < 0.0001). Chloroquine (CQ) and artemether-lumefantrine (AL) were used as prototype drugs before and after the policy change, respectively. AL significantly shortened the duration of male gametocyte carriage in individual patients after treatment began compared with CQ (log rank statistic = 7.92, p = 0.005). ACTs reduced the rate of gametocyte carriage in children with acute falciparum infections at presentation and shortened the duration of male gametocyte carriage after treatment. However, parasite population sex ratios, inbreeding rates and overall parasite rate were unaffected.

Rapid hamstrings/quadriceps strength capacity in professional soccer players with different conventional isokinetic muscle strength ratios

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Leg muscles recruitment pattern in soccer players and active individuals during isometric contractions

This study aimed to compare the torque, torque ratio (Hamstrings:Quadriceps - H:Q), electromyographic (EMG) activity and EMG ratio (knee flexors:knee extensors EMG) in soccer players (SG, N=10) and active subjects (AG, N=10). Subjects performed three maximal voluntary isometric knee extensions and flexions at 45° and 90° to determine the peak torque and EMG activity. Torque and EMG activity of the knee flexor (biceps femoris [BF] and semitendinosus [ST]) were divided by the torque and EMG activity of the knee extensor (vastuls lateralis [VL] and rectus femoris [RF]) to calculate torque ratios (H:Q) and EMG ratios (BF:VL, BF:RF, ST:VL, ST:RF). The flexion torque was significantly higher for SG (p<0.05) in 45° and 90°. EMG activity for SG was significantly higher in agonist contractions for VL, RF and ST, and significantly lower in antagonist contractions for RF and ST when compared to AG Torque and EMG ratios were similar between groups and there were good correlations between torque ratio and BF:VL ratio (r=0.71, p=0.02) and BF:RF ratio (r=0.81, p=0.004) at 45. The EMG results could overestimate the joint balance calculated using torque ratios. Differences in recruitment pattern between soccer players and non-athletes can be related to the training routines and the EMG ratios presents applicable in trained populations.

Grip and load force coordination in cyclical isometric manipulation task is not affected by the feedback type

Background: The relationship between normal and tangential force components (grip force - GF and load force - LF, respectively) acting on the digits-object interface during object manipulation reveals neural mechanisms involved in movement control. Here, we examined whether the feedback type provided to the participants during exertion of LF would influence GF-LF coordination and task performance. Methods. Sixteen young (24.7 ±3.8 years-old) volunteers isometrically exerted continuously sinusoidal FZ (vertical component of LF) by pulling a fixed instrumented handle up and relaxing under two feedback conditions: targeting and tracking. In targeting condition, FZ exertion range was determined by horizontal lines representing the upper (10 N) and lower (1 N) targets, with frequency (0.77 or 1.53 Hz) dictated by a metronome. In tracking condition, a sinusoidal template set at similar frequencies and range was presented and should be superposed by the participants' exerted FZ. Task performance was assessed by absolute errors at peaks (AEPeak) and valleys (AEValley) and GF-LF coordination by GF-LF ratios, maximum cross-correlation coefficients (r max), and time lags. Results: The results revealed no effect of feedback and no feedback by frequency interaction on any variable. AE Peak and GF-LF ratio were higher and rmax lower at 1.53 Hz than at 0.77 Hz. Conclusion: These findings indicate that the type of feedback does not influence task performance and GF-LF coordination. Therefore, we recommend the use of tracking tasks when assessing GF-LF coordination during isometric LF exertion in externally fixed instrumented handles because they are easier to understand and provide additional indices (e.g., RMSE) of voluntary force control. © 2013 Pedão et al.; licensee BioMed Central Ltd.

Automatic Labeling of Software Components and their Evolution using Log-Likelihood Ratio of Word Frequencies in Source Code

As more and more open-source software components become available on the internet we need automatic ways to label and compare them. For example, a developer who searches for reusable software must be able to quickly gain an understanding of retrieved components. This understanding cannot be gained at the level of source code due to the semantic gap between source code and the domain model. In this paper we present a lexical approach that uses the log-likelihood ratios of word frequencies to automatically provide labels for software components. We present a prototype implementation of our labeling/comparison algorithm and provide examples of its application. In particular, we apply the approach to detect trends in the evolution of a software system.