Two more things about compositional biplots: quality of projection and inclusion of supplementary elements

The biplot is a widely and powerful methodology used with multidimensional data sets to describe and display the relationships between observations and variables in an easy way. Compositional data consist of positive vectors each of which is constrained to have a constant sum; due to this property standard biplots can not be performed with compositional data, instead of a previous transformation of the data is performed. Due to this constant sum constraint, a transformation of data is needed before performing a biplot and, consequently, special interpretation rules are required. However, these rules can only be safely applied when the elements of a biplot have a good quality of projection, for which a new measure is introduced in this paper. Also, we extend the compositional biplot defined by Aitchison and Greenacre on 2002, in order to include the display supplementary elements that are not used in the definition of the compositional biplot. Different types of supplementary elements are considered: supplementary parts of the composition, supplementary continuous variables external to the composition, supplementary categorical variables and supplementary observations. The projection of supplementary parts of the composition is done by means of the equivalence of clr and lr biplots. The other supplementary projections are done by classical methodology. Both the qualities of projections and the supplementary projections are explained using real geological data: a sample of 72 observations of soil in an area about 20 km west of Kiev in the area south of Kiev Polessie

Could CODA methodology be useful in control chart techniques?

On standard control charts, the hypothesis of normality is usually assumed without any additional veri cation. Nevertheless, in some cases this assumption is not accurate and might cause errors in process quality monitoring. In particular, for the control of the proportion of nonconforming units (p-chart) the normality is doubtful when p is small and consequently, lower control limit less than or equal to zero are frequent. Some authors have proposed new techniques to de ne limits in the p-chart. Others have proposed transformations to improve the detection of special causes

Intravoxel Incoherent Motion Metrics as Potential Biomarkers for Survival in Glioblastoma.

Intravoxel incoherent motion (IVIM) is an MRI technique with potential applications in measuring brain tumor perfusion, but its clinical impact remains to be determined. We assessed the usefulness of IVIM-metrics in predicting survival in newly diagnosed glioblastoma. Fifteen patients with glioblastoma underwent MRI including spin-echo echo-planar DWI using 13 b-values ranging from 0 to 1000 s/mm2. Parametric maps for diffusion coefficient (D), pseudodiffusion coefficient (D*), and perfusion fraction (f) were generated for contrast-enhancing regions (CER) and non-enhancing regions (NCER). Regions of interest were manually drawn in regions of maximum f and on the corresponding dynamic susceptibility contrast images. Prognostic factors were evaluated by Kaplan-Meier survival and Cox proportional hazards analyses. We found that fCER and D*CER correlated with rCBFCER. The best cutoffs for 6-month survival were fCER>9.86% and D*CER>21.712 x10-3mm2/s (100% sensitivity, 71.4% specificity, 100% and 80% positive predictive values, and 80% and 100% negative predictive values; AUC:0.893 and 0.857, respectively). Treatment yielded the highest hazard ratio (5.484; 95% CI: 1.162-25.88; AUC: 0.723; P = 0.031); fCER combined with treatment predicted survival with 100% accuracy. The IVIM-metrics fCER and D*CER are promising biomarkers of 6-month survival in newly diagnosed glioblastoma

Size fraction effects on planktonic foraminifera assemblages: a compositional contribution to the golden sieve rush

A comparative study of Last Glacial to Holocene planktonic foraminiferal assemblages obtained from >150 to >106 μm size fractions of a Tyrrhenian sea core was carried out by means of compositional data analysis methods. The results show a major loss of small-sized species in the>150μmsize fraction, resulting in underdetection limit values for several Holocene samples. Statistical tests, performed by means of contrast and bootstrap, indicate that the assemblages obtained differ statistically. Nevertheless, despite the drawbacks of the analysis based on the >150 μm fraction, these differences do not imply, in the compositional data analysis approach, a significant change in covariance structure. Under compositional data analysis, covariancebased analysis should give similar results regardless of the size fraction adopted, while distance-based ones may give partly different results. The >106 μm size fraction, in which both large and small-sized species are sufficiently represented, is proposed for adoption in future studies focussing on palaeoclimatic reconstruction

Оцінка антропогенного навантаження на дендропарк “Тростянець” НАН України методом біогеохімічної індикації

The method of biogeochemical indication was used for the assessment of the anthropogenic geochemical impact on the specially protected territory of an important monument of nature, culture and history of Ukraine – Trostyanets arboretum. As bioindicators of chemical elements content in the atmosphere the epiphytic lichens of Parmelia sulcata Tayl., Parmelina tiliacea (Hoffm.) Hale, Xanthoria parietina (L.) Th. Fr., Hypogymnia physodes (L.) Nyl. and Evernia prunastri (L.) Ach. were used. For the biogeochemical indication of soil and groundwater conditions the leaves of Norway maple (Acer platanoides L.) were used. In the above-mentioned indicator plants the content of 20 micro- and macroelements (Al, Cd, Cr, Cu, Fe, Ni, Pb, V, Zn, Ba, Ca, Co, K, Mg, Mn, Na, S, Sr, Ti, Se) was detected (by ICP OE spectrometry). The obtained data of biogeochemical indication of the content of chemical elements have been processed and interpreted using the geostatistical method of composite biplot and the method of triangular diagrams. Atmogeochemical and lithohydrogeochemical fields were studied and the causes of formation of anthropogenic geochemical loads were elucidated and their potential impact on the unique landscapes of Trostyanets arboretum was shown.Методом біогеохімічної індикації проведено оцінку антропогенного геохімічного впливу на територію, яка особливо охороняється, важливу пам’ятку природи, історії та культури України – дендропарк “Тростянець” НАН України. Як біоіндикатори вмісту хімічних елементів у повітрі використано епіфітні лишайники Parmelia sulcata Tayl., Parmelina tiliacea (Hoffm.) Hale, Xanthoria parietina (L.) Th. Fr., Hypogymnia physodes (L.) Nyl. та Evernia prunastri (L.) Ach. Для біогеохімічної індикації стану ґрунтів і ґрунтових вод використано листя клену гостролистого (Acer platanoides L.). У зазначених рослинах-індикаторах визначено методом індукційно-зв’язаної плазми – оптико-емісійної спектрометрії вміст 20 мікро- та макроелементів (Al, Cd, Cr, Cu, Fe, Ni, Pb, V, Zn, Ba, Ca, Co, K, Mg, Mn, Na, S, Sr, Ti, Se). Дані щодо вмісту хімічних елементів оброблено та інтерпретовано за допомогою геостатистичного методу “композиційний біплот” і методу трикутних діаграм. Вивчено атмогеохімічні і літо гідрогеохімічні поля, встановлено причини формування антропогенних геохімічних навантажень, показано їх можливий вплив на унікальні садово-паркові ландшафти дендропарку