Robust Factor Analysis for Compositional Data

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

Brain network analysis of patients with Temporal Lobe Epilepsy

Patients with Temporal Lobe Epilepsy (TLE) suffer from widespread subtle white matter abnormalities and abnormal functional connectivity extending beyond the affected lobe, as revealed by Diffusion Tensor MR Imaging, volumetric and functional MRI studies. Diffusion Spectrum Imaging (DSI) is a diffusion imaging technique with high angular resolution for improving the mapping of white matter pathways. In this study, we used DSI, connectivity matrices and topological measures to investigate how the alteration in structural connectivity influences whole brain structural networks. Eleven patients with right-sided TLE and hippocampal sclerosis and 18 controls underwent our DSI protocol at 3T. The cortical and subcortical grey matters were parcellated into 86 regions of interest and the connectivity between every region pair was estimated using global tractography and a connectivity matrix (the adjacency matrix of the structural network). We then compared the networks of patients and controls using topological measures. In patients, we found a higher characteristic path length and a lower clustering coefficient compared to controls. Local measures at node level of the clustering and efficiency showed a significant difference after a multiple comparison correction (Bonferroni). These significant nodes were located within as well outside the temporal lobe, and the localisation of most of them was consistent with regions known to be part of epileptic networks in TLE. Our results show altered connectivity patterns that are concordant with the mapping of functional epileptic networks in patients with TLE. Further studies are needed to establish the relevance of these findings for the propagation of epileptic activity, cognitive deficits in medial TLE and outcome of epilepsy surgery in individual patients.

Compositional data analysis in archaeometry

We shall call an n × p data matrix fully-compositional if the rows sum to a constant, and sub-compositional if the variables are a subset of a fully-compositional data set1. Such data occur widely in archaeometry, where it is common to determine the chemical composition of ceramic, glass, metal or other artefacts using techniques such as neutron activation analysis (NAA), inductively coupled plasma spectroscopy (ICPS), X-ray fluorescence analysis (XRF) etc. Interest often centres on whether there are distinct chemical groups within the data and whether, for example, these can be associated with different origins or manufacturing technologies

New insights on river water chemistry by using non-centred simplicial principal component analysis: a case study

The use of perturbation and power transformation operations permits the investigation of linear processes in the simplex as in a vectorial space. When the investigated geochemical processes can be constrained by the use of well-known starting point, the eigenvectors of the covariance matrix of a non-centred principalcomponent analysis allow to model compositional changes compared with a reference point.The results obtained for the chemistry of water collected in River Arno (central-northern Italy) have open new perspectives for considering relative changes of the analysed variables and to hypothesise the relative effect of different acting physical-chemical processes, thus posing the basis for a quantitative modelling

Compositional Data Analysis with R

R from http://www.r-project.org/ is ‘GNU S’ – a language and environment for statistical computingand graphics. The environment in which many classical and modern statistical techniques havebeen implemented, but many are supplied as packages. There are 8 standard packages and many moreare available through the cran family of Internet sites http://cran.r-project.org .We started to develop a library of functions in R to support the analysis of mixtures and our goal isa MixeR package for compositional data analysis that provides support foroperations on compositions: perturbation and power multiplication, subcomposition with or withoutresiduals, centering of the data, computing Aitchison’s, Euclidean, Bhattacharyya distances,compositional Kullback-Leibler divergence etc.graphical presentation of compositions in ternary diagrams and tetrahedrons with additional features:barycenter, geometric mean of the data set, the percentiles lines, marking and coloring ofsubsets of the data set, theirs geometric means, notation of individual data in the set . . .dealing with zeros and missing values in compositional data sets with R procedures for simpleand multiplicative replacement strategy,the time series analysis of compositional data.We’ll present the current status of MixeR development and illustrate its use on selected data sets

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

In-depth analysis of hyaline fibromatosis syndrome frameshift mutations at the same site reveal the necessity of personalized therapy.

Hyaline fibromatosis syndrome is an autosomal recessive disease caused by mutations in ANTXR2, a gene involved in extracellular matrix homeostasis. Sixty percent of patients carry frameshift mutations at a mutational hotspot in exon 13. We show in patient cells that these mutations lead to low ANTXR2 mRNA and undetectable protein levels. Ectopic expression of the proteins encoded by the mutated genes reveals that a two base insertion leads to the synthesis of a protein that is rapidly targeted to the ER-associated degradation pathway due to the modified structure of the cytosolic tail, which instead of being hydrophilic and highly disordered as in wild type ANTXR2, is folded and exposes hydrophobic patches. In contrast, one base insertion leads to a truncated protein that properly localizes to the plasma membrane and retains partial function. We next show that targeting the nonsense mediated mRNA decay pathway in patient cells leads to a rescue of ANTXR2 protein in patients carrying one base insertion but not in those carrying two base insertions. This study highlights the importance of in-depth analysis of the molecular consequences of specific patient mutations, which even when they occur at the same site can have drastically different consequences.

Ultrastructural and molecular analysis of Bowman's layer corneal dystrophies: an epithelial origin?

PURPOSE: Two mutations (R555Q and R124L) in the BIGH3 gene have been described in anterior or Bowman's layer dystrophies (CDB). The clinical, molecular, and ultrastructural findings of five families with CDB was reviewed to determine whether there is a consistent genotype:phenotype correlation. METHODS: Keratoplasty tissue from each patient was examined by light and electron microscopy (LM and EM). DNA was obtained, and exons 4 and 12 of BIGH3 were analyzed by polymerase chain reaction and single-stranded conformation polymorphism/heteroduplex analysis. Abnormally migrating products were analyzed by direct sequencing. RESULTS: In two families with type I CDB (CDBI), the R124L mutation was defined. There were light and ultrastructural features of superficial granular dystrophy and atypical banding of the "rod-shaped bodies" ultrastructurally. Patients from three families with "honeycomb" dystrophy were found to carry the R555Q mutation and had characteristic features of Bowman's dystrophy type II (CDBII). CONCLUSIONS: There is a strong genotype:phenotype correlation among CBDI (R124L) and CDBII (R555Q). LM and EM findings suggest that epithelial abnormalities may underlie the pathology of both conditions. The findings clarify the confusion over classification of the Bowman's layer dystrophies.

Analysis and quantification of vitamin D metabolites in serum by ultra-performance liquid chromatography coupled to tandem mass spectrometry and high-resolution mass spectrometry: a method comparison and validation.

RATIONALE: The aim of the work was to develop and validate a method for the quantification of vitamin D metabolites in serum using ultra-high-pressure liquid chromatography coupled to mass spectrometry (LC/MS), and to validate a high-resolution mass spectrometry (LC/HRMS) approach against a tandem mass spectrometry (LC/MS/MS) approach using a large clinical sample set. METHODS: A fast, accurate and reliable method for the quantification of the vitamin D metabolites, 25-hydroxyvitamin D2 (25OH-D2) and 25-hydroxyvitamin D3 (25OH-D3), in human serum was developed and validated. The C3 epimer of 25OH-D3 (3-epi-25OH-D3) was also separated from 25OH-D3. The samples were rapidly prepared via a protein precipitation step followed by solid-phase extraction (SPE) using an HLB μelution plate. Quantification was performed using both LC/MS/MS and LC/HRMS systems. RESULTS: Recovery, matrix effect, inter- and intra-day reproducibility were assessed. Lower limits of quantification (LLOQs) were determined for both 25OH-D2 and 25OH-D3 for the LC/MS/MS approach (6.2 and 3.4 µg/L, respectively) and the LC/HRMS approach (2.1 and 1.7 µg/L, respectively). A Passing & Bablok fit was determined between both approaches for 25OH-D3 on 662 clinical samples (1.11 + 1.06x). It was also shown that results can be affected by the inclusion of the isomer 3-epi-25OH-D3. CONCLUSIONS: Quantification of the relevant vitamin D metabolites was successfully developed and validated here. It was shown that LC/HRMS is an accurate, powerful and easy to use approach for quantification within clinical laboratories. Finally, the results here suggest that it is important to separate 3-epi-25OH-D3 from 25OH-D3. Copyright © 2012 John Wiley & Sons, Ltd.

In vitro heat exposure induces a redistribution of nuclear matrix proteins in human K562 erythroleukemia cells.

By using both conventional and confocal laser scanning microscopy with three monoclonal antibodies recognizing nuclear matrix proteins we have investigated by means of indirect fluorescence whether an incubation of isolated nuclei at the physiological temperature of 37 degrees C induces a redistribution of nuclear components in human K562 erythroleukemia cells. Upon incubation of isolated nuclei for 45 min at 37 degrees C, we have found that two of the antibodies, directed against proteins of the inner matrix network (M(r) 125 and 160 kDa), gave a fluorescent pattern different from that observed in permeabilized cells. By contrast, the fluorescent pattern did not change if nuclei were kept at 0 degrees C. The difference was more marked in case of the 160-kDa polypeptide. The fluorescent pattern detected by the third antibody, which recognizes the 180-kDa nucleolar isoform of DNA topoisomerase II, was unaffected by heat exposure of isolated nuclei. When isolated nuclear matrices prepared from heat-stabilized nuclei were stained by means of the same three antibodies, it was possible to see that the distribution of the 160-kDa matrix protein no longer corresponded to that observable in permeabilized cells, whereas the fluorescent pattern given by the antibody to the 125-kDa polypeptide resembled that detectable in permeabilized cells. The 180-kDa isoform of topoisomerase II was still present in the matrix nucleolar remnants. We conclude that a 37 degrees C incubation of isolated nuclei induces a redistribution of some nuclear matrix antigens and cannot prevent the rearrangement in the spatial organization of one of these antigens that takes place during matrix isolation in human erythroleukemia cells. The practical relevance of these findings is discussed.

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By anessential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur inmany compositional situations, such as household budget patterns, time budgets,palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful insuch situations. From consideration of such examples it seems sensible to build up amodel in two stages, the first determining where the zeros will occur and the secondhow the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

Altered structural connectivity in patients with medial temporal lobe epilepsy: A Diffusion Spectrum Imaging and Graph Analysis study

In this study we investigated the effect of medial temporal lobe epilepsy (MTLE) on the global characteristics of brain connectivity estimated by topological measures. We used DSI (Diffusion Spectrum Imaging) to construct a connectivity matrix where the nodes represents the anatomical ROIs and the edges are the connections between any pair of ROIs weighted by the mean GFA/FA values. A significant difference was found between the patient group vs control group in characteristic path length, clustering coefficient and small-worldness. This suggests that the MTLE network is less efficient compared to the network of the control group.

Intracellular nanomanipulation by a photonic-force microscope with real-time acquisition of a 3D stiffness matrix.

A traditional photonic-force microscope (PFM) results in huge sets of data, which requires tedious numerical analysis. In this paper, we propose instead an analog signal processor to attain real-time capabilities while retaining the richness of the traditional PFM data. Our system is devoted to intracellular measurements and is fully interactive through the use of a haptic joystick. Using our specialized analog hardware along with a dedicated algorithm, we can extract the full 3D stiffness matrix of the optical trap in real time, including the off-diagonal cross-terms. Our system is also capable of simultaneously recording data for subsequent offline analysis. This allows us to check that a good correlation exists between the classical analysis of stiffness and our real-time measurements. We monitor the PFM beads using an optical microscope. The force-feedback mechanism of the haptic joystick helps us in interactively guiding the bead inside living cells and collecting information from its (possibly anisotropic) environment. The instantaneous stiffness measurements are also displayed in real time on a graphical user interface. The whole system has been built and is operational; here we present early results that confirm the consistency of the real-time measurements with offline computations.

Body fluid and tissue analysis using filter paper sampling support prior to LC-MS/MS: application to fatal overdose with colchicine

Because of the various matrices available for forensic investigations, the development of versatile analytical approaches allowing the simultaneous determination of drugs is challenging. The aim of this work was to assess a liquid chromatography-tandem mass spectrometry (LC-MS/MS) platform allowing the rapid quantification of colchicine in body fluids and tissues collected in the context of a fatal overdose. For this purpose, filter paper was used as a sampling support and was associated with an automated 96-well plate extraction performed by the LC autosampler itself. The developed method features a 7-min total run time including automated filter paper extraction (2 min) and chromatographic separation (5 min). The sample preparation was reduced to a minimum regardless of the matrix analyzed. This platform was fully validated for dried blood spots (DBS) in the toxic concentration range of colchicine. The DBS calibration curve was applied successfully to quantification in all other matrices (body fluids and tissues) except for bile, where an excessive matrix effect was found. The distribution of colchicine for a fatal overdose case was reported as follows: peripheral blood, 29 ng/ml; urine, 94 ng/ml; vitreous humour and cerebrospinal fluid, < 5 ng/ml; pericardial fluid, 14 ng/ml; brain, < 5 pg/mg; heart, 121 pg/mg; kidney, 245 pg/mg; and liver, 143 pg/mg. Although filter paper is usually employed for DBS, we report here the extension of this alternative sampling support to the analysis of other body fluids and tissues. The developed platform represents a rapid and versatile approach for drug determination in multiple forensic media.

The effect of sodium tetrathionate stabilization on the distribution of three nuclear matrix proteins in human K562 erythroleukemia cells.

Using both conventional fluorescence and confocal laser scanning microscopy we have investigated whether or not stabilization of isolated human erythroleukemic nuclei with sodium tetrathionate can maintain in the nuclear matrix the same spatial distribution of three polypeptides (M(r) 160 kDa and 125 kDa, previously shown to be components of the internal nuclear matrix plus the 180-kDa nucleolar isoform of DNA topoisomerase II) as seen in permeabilized cells. The incubation of isolated nuclei in the presence of 2 mM sodium tetrathionate was performed at 0 degrees C or 37 degrees C. The matrix fraction retained 20-40% of nuclear protein, depending on the temperature at which the chemical stabilization was executed. Western blot analysis revealed that the proteins studied were completely retained in the high-salt resistant matrix. Indirect immunofluorescence experiments showed that the distribution of the three antigens in the final matrix closely resembled that detected in permeabilized cells, particularly when the stabilization was performed at 37 degrees C. This conclusion was also strengthened by analysis of cells, isolated nuclei and the nuclear matrix by means of confocal laser scanning microscopy. We conclude that sodium tetrathionate stabilization of isolated nuclei does not alter the spatial distribution of some nuclear matrix proteins.