Dynamic graphics of parametrically linked multivariate methods used in compositional data analysis

Many multivariate methods that are apparently distinct can be linked by introducing one or more parameters in their definition. Methods that can be linked in this way are correspondence analysis, unweighted or weighted logratio analysis (the latter also known as "spectral mapping"), nonsymmetric correspondence analysis, principal component analysis (with and without logarithmic transformation of the data) and multidimensional scaling. In this presentation I will show how several of these methods, which are frequently used in compositional data analysis, may be linked through parametrizations such as power transformations, linear transformations and convex linear combinations. Since the methods of interest here all lead to visual maps of data, a "movie" can be made where where the linking parameter is allowed to vary in small steps: the results are recalculated "frame by frame" and one can see the smooth change from one method to another. Several of these "movies" will be shown, giving a deeper insight into the similarities and differences between these methods

Alternatives to Reparations in International Investment Arbitration– A Debate Between Theory and Practice

An analysis of the alternatives of compensation in relation to international investment disputes is relevant, because a pecuniary award is not always the appropriate remedy to solve disputes arising between investors and States. This is the case because States may be increasingly interested in opting for a different type of compensation. Furthermore, it is still not clear whether arbitral tribunals have recognised alternative types of awarding damages in respect of international investments disputes. This analysis comprises two principal components, the first, is to identify whether or not the tribunals may render an award that not only demands the payment of a sum of money but also considers some other means of compensation. The second, centres on how compliance with these non-pecuniary awards may be demanded. Our approach to these two principal components will always revolve around the idea of respecting the sovereignty of the State, bearing in mind that the execution of an arbitral award, which obliges the State to refrain from or to perform an act in its territory, relies precisely on the sovereignty of the State to execute it. 

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2 H4+ X̃2B 3u←C2 H4X̃1 Ag band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B 3u←C2H4X̃1 Ag band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2 D4 results to be not as good as those for C2 H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required.

Phenetic analysis of anemone coronaria (ranunculaceae) and related species

This study clarifies the taxonomic status of Anemone coronaria and segregates the species and A. coronaria infraspecific variants using morphological and morphometric analyses. Principal component analysis of the coronaria group was performed on 25 quantitative and qualitative characters, and morphometric analysis of the A. coronaria infraspecific variants was performed on 21 quantitative and qualitative characters. The results showed that the A. coronaria group clustered into four major groups: A. coronaria L., A. biflora DC, A. bucharica (Regel) Juz.ex Komarov, and a final group including A. eranthioides Regel and A. tschernjaewii Regel. The data on the A. coronaria infraspecific variants clustered into six groups: A. coronaria L. var. coronaria L., var. cyanea Ard., var. albiflora Rouy & Fouc., var. parviflora Regel, var. ventreana Ard., and var. rissoana Ard. © 2007 The Linnean Society of London

Rapid quality assessment of wheat cultivars registered in Poland using the 2-g mixograph and multivariate statistical analysis

Baking and 2-g mixograph analyses were performed for 55 cultivars (19 spring and 36 winter wheat) from various quality classes from the 2002 harvest in Poland. An instrumented 2-g direct-drive mixograph was used to study the mixing characteristics of the wheat cultivars. A number of parameters were extracted automatically from each mixograph trace and correlated with baking volume and flour quality parameters (protein content and high molecular weight glutenin subunit [HMW-GS] composition by SDS-PAGE) using multiple linear regression statistical analysis. Principal component analysis of the mixograph data discriminated between four flour quality classes, and predictions of baking volume were obtained using several selected mixograph parameters, chosen using a best subsets regression routine, giving R-2 values of 0.862-0.866. In particular, three new spring wheat strains (CHD 502a-c) recently registered in Poland were highly discriminated and predicted to give high baking volume on the basis of two mixograph parameters: peak bandwidth and 10-min bandwidth.

Neurofuzzy state identification using prefiltering

A new state estimator algorithm is based on a neurofuzzy network and the Kalman filter algorithm. The major contribution of the paper is recognition of a bias problem in the parameter estimation of the state-space model and the introduction of a simple, effective prefiltering method to achieve unbiased parameter estimates in the state-space model, which will then be applied for state estimation using the Kalman filtering algorithm. Fundamental to this method is a simple prefiltering procedure using a nonlinear principal component analysis method based on the neurofuzzy basis set. This prefiltering can be performed without prior system structure knowledge. Numerical examples demonstrate the effectiveness of the new approach.

Integrated cytokine and metabolic analysis of pathological responses to parasite exposure in rodents

Parasitic infections cause a myriad of responses in their mammalian hosts, on immune as well as on metabolic level. A multiplex panel of cytokines and metabolites derived from four parasite-rodent models, namely, Plasmodium berghei-mouse, Trypanosoma brucei brucei-mouse, Schistosoma mansoni-mouse, and Fasciola hepatica-rat were statistically coanalyzed. 1H NMR spectroscopy and multivariate statistical analysis were used to characterize the urine and plasma metabolite profiles in infected and noninfected animals. Each parasite generated a unique metabolic signature in the host. Plasma cytokine concentrations were obtained using the ‘Meso Scale Discovery’ multi cytokine assay platform. Multivariate data integration methods were subsequently used to elucidate the component of the metabolic signature which is associated with inflammation and to determine specific metabolic correlates with parasite-induced changes in plasma cytokine levels. For example, the relative levels of acetyl glycoproteins extracted from the plasma metabolite profile in the P. berghei-infected mice were statistically correlated with IFN-γ, whereas the same cytokine was anticorrelated with glucose levels. Both the metabolic and the cytokine data showed a similar spatial distribution in principal component analysis scores plots constructed for the combined murine data, with samples from all infected animals clustering according to the parasite species and whereby the protozoan infections (P. berghei and T. b. brucei) grouped separately from the helminth infection (S. mansoni). For S. mansoni, the main infection-responsive cytokines were IL-4 and IL-5, which covaried with lactate, choline, and D-3-hydroxybutyrate. This study demonstrates that the inherently differential immune response to single and multicellular parasites not only manifests in the cytokine expression, but also consequently imprints on the metabolic signature, and calls for in-depth analysis to further explore direct links between immune features and biochemical pathways.

Gut microbial catabolism of grape seed flavan-3-ols by human faecal microbiota. Targetted analysis of precursor compounds, intermediate metabolites and end-products.

In vitro batch culture fermentations were conducted with grape seed polyphenols and human faecal microbiota, in order to monitor both changes in precursor flavan-3-ols and the formation of microbial-derived metabolites. By the application of UPLC-DAD-ESI-TQ MS, monomers, and dimeric and trimeric procyanidins were shown to be degraded during the first 10 h of fermentation, with notable inter-individual differences being observed between fermentations. This period (10 h) also coincided with the maximum formation of intermediate metabolites, such as 5-(3′,4′-dihydroxyphenyl)-γ-valerolactone and 4-hydroxy-5-(3′,4′-dihydroxyphenyl)-valeric acid, and of several phenolic acids, including 3-(3,4-dihydroxyphenyl)-propionic acid, 3,4-dihydroxyphenylacetic acid, 4-hydroxymandelic acid, and gallic acid (5–10 h maximum formation). Later phases of the incubations (10–48 h) were characterised by the appearance of mono- and non-hydroxylated forms of previous metabolites by dehydroxylation reactions. Of particular interest was the detection of γ-valerolactone, which was seen for the first time as a metabolite from the microbial catabolism of flavan-3-ols. Changes registered during fermentation were finally summarised by a principal component analysis (PCA). Results revealed that 5-(3′,4′-dihydroxyphenyl)-γ-valerolactone was a key metabolite in explaining inter-individual differences and delineating the rate and extent of the microbial catabolism of flavan-3-ols, which could finally affect absorption and bioactivity of these compounds.

Physiological, biochemical and transcriptional analysis of onion bulbs during storage

Abstract: During the transition from endo-dormancy to eco-dormancy and subsequent growth, the onion bulb undergoes the transition from sink organ to source, to sustain cell division in the meristematic tissue. The mechanisms controlling these processes are not fully understood. Here, a detailed analysis of whole onion bulb physiological, biochemical and transcriptional changes in response to sprouting is reported, enabling a better knowledge of the mechanisms regulating post-harvest onion sprout development. Biochemical and physiological analyses were conducted on different cultivars ('Wellington', 'Sherpa' and 'Red Baron') grown at different sites over 3 years, cured at different temperatures (20, 24 and 28 degrees C) and stored under different regimes (1, 3, 6 and 6 1 degrees C). In addition, the first onion oligonucleotide microarray was developed to determine differential gene expression in onion during curing and storage, so that transcriptional changes could support biochemical and physiological analyses. There were greater transcriptional differences between samples at harvest and before sprouting than between the samples taken before and after sprouting, with some significant changes occurring during the relatively short curing period. These changes are likely to represent the transition from endo-dormancy to sprout suppression, and suggest that endo-dormancy is a relatively short period ending just after curing. Principal component analysis of biochemical and physiological data identified the ratio of monosaccharides (fructose and glucose) to disaccharide (sucrose), along with the concentration of zeatin riboside, as important factors in discriminating between sprouting and pre-sprouting bulbs. These detailed analyses provide novel insights into key regulatory triggers for sprout dormancy release in onion bulbs and provide the potential for the development of biochemical or transcriptional markers for sprout initiation. Evidence presented herein also suggests there is no detrimental effect on bulb storage life and quality caused by curing at 20 degrees C, producing a considerable saving in energy and costs.

Reduced-order dynamics of the Martian atmospheric dynamics

In this paper we explore the possibility of deriving low-dimensional models of the dynamics of the Martian atmosphere. The analysis consists of a Proper Orthogonal Decomposition (POD) of the atmospheric streamfunction after first decomposing the vertical structure with a set of eigenmodes. The vertical modes were obtained from the quasi-geostrophic vertical structure equation. The empirical orthogonal functions (EOFs) were optimized to represent the atmospheric total energy. The total energy was used as the criterion to retain those modes with large energy content and discard the rest. The principal components (PCs) were analysed by means of Fourier analysis, so that the dominant frequencies could be identified. It was possible to observe the strong influence of the diurnal cycle and to identify the motion and vacillation of baroclinic waves.

Advanced multivariate analysis to assess remediation of hydrocarbons in soils

Accurate monitoring of degradation levels in soils is essential in order to understand and achieve complete degradation of petroleum hydrocarbons in contaminated soils. We aimed to develop the use of multivariate methods for the monitoring of biodegradation of diesel in soils and to determine if diesel contaminated soils could be remediated to a chemical composition similar to that of an uncontaminated soil. An incubation experiment was set up with three contrasting soil types. Each soil was exposed to diesel at varying stages of degradation and then analysed for key hydrocarbons throughout 161 days of incubation. Hydrocarbon distributions were analysed by Principal Coordinate Analysis and similar samples grouped by cluster analysis. Variation and differences between samples were determined using permutational multivariate analysis of variance. It was found that all soils followed trajectories approaching the chemical composition of the unpolluted soil. Some contaminated soils were no longer significantly different to that of uncontaminated soil after 161 days of incubation. The use of cluster analysis allows the assignment of a percentage chemical similarity of a diesel contaminated soil to an uncontaminated soil sample. This will aid in the monitoring of hydrocarbon contaminated sites and the establishment of potential endpoints for successful remediation.

Exploratory factor analysis of the Brazilian OHIP for edentulous subjects

P>The use of seven domains for the Oral Health Impact Profile (OHIP)-EDENT was not supported for its Brazilian version, making data interpretation in clinical settings difficult. Thus, the aim of this study was to assess patients` responses for the translated OHIP-EDENT in a group of edentulous subjects and to develop factor scales for application in future studies. Data from 103 conventional and implant-retained complete denture wearers (36 men, mean age of 69 center dot 1 +/- 10 center dot 3 years) were assessed using the Brazilian version of the OHIP-EDENT. Oral health-related quality of life domains were identified by factor analysis using principal component analysis as the extraction method, followed by varimax rotation. Factor analysis identified four factors that accounted for 63% of the 19 items total variance, named masticatory discomfort and disability (four items), psychological discomfort and disability (five items), social disability (five items) and oral pain and discomfort (five items). Four factors/domains of the Brazilian OHIP-EDENT version represent patient-important aspects of oral health-related quality of life.

PCA Tomography: how to extract information from data cubes

Astronomy has evolved almost exclusively by the use of spectroscopic and imaging techniques, operated separately. With the development of modern technologies, it is possible to obtain data cubes in which one combines both techniques simultaneously, producing images with spectral resolution. To extract information from them can be quite complex, and hence the development of new methods of data analysis is desirable. We present a method of analysis of data cube (data from single field observations, containing two spatial and one spectral dimension) that uses Principal Component Analysis (PCA) to express the data in the form of reduced dimensionality, facilitating efficient information extraction from very large data sets. PCA transforms the system of correlated coordinates into a system of uncorrelated coordinates ordered by principal components of decreasing variance. The new coordinates are referred to as eigenvectors, and the projections of the data on to these coordinates produce images we will call tomograms. The association of the tomograms (images) to eigenvectors (spectra) is important for the interpretation of both. The eigenvectors are mutually orthogonal, and this information is fundamental for their handling and interpretation. When the data cube shows objects that present uncorrelated physical phenomena, the eigenvector`s orthogonality may be instrumental in separating and identifying them. By handling eigenvectors and tomograms, one can enhance features, extract noise, compress data, extract spectra, etc. We applied the method, for illustration purpose only, to the central region of the low ionization nuclear emission region (LINER) galaxy NGC 4736, and demonstrate that it has a type 1 active nucleus, not known before. Furthermore, we show that it is displaced from the centre of its stellar bulge.

SIZE AS A LINE OF LEAST RESISTANCE II: DIRECT SELECTION ON SIZE OR CORRELATED RESPONSE DUE TO CONSTRAINTS?

Evolutionary change in New World Monkey (NWM) skulls occurred primarily along the line of least resistance defined by size (including allometric) variation (g(max)). Although the direction of evolution was aligned with this axis, it was not clear whether this macroevolutionary pattern results from the conservation of within population genetic covariance patterns (long-term constraint) or long-term selection along a size dimension, or whether both, constraints and selection, were inextricably involved. Furthermore, G-matrix stability can also be a consequence of selection, which implies that both, constraints embodied in g(max) and evolutionary changes observed on the trait averages, would be influenced by selection Here, we describe a combination of approaches that allows one to test whether any particular instance of size evolution is a correlated by-product due to constraints (g(max)) or is due to direct selection on size and apply it to NWM lineages as a case study. The approach is based on comparing the direction and amount of evolutionary change produced by two different simulated sets of net-selection gradients (beta), a size (isometric and allometric size) and a nonsize set. Using this approach it is possible to distinguish between the two hypotheses (indirect size evolution due to constraints or direct selection on size), because although both may produce an evolutionary response aligned with g(max), the amount of change produced by random selection operating through the variance/covariance patterns (constraints hypothesis) will be much smaller than that produced by selection on size (selection hypothesis). Furthermore, the alignment of simulated evolutionary changes with g(max) when selection is not on size is not as tight as when selection is actually on size, allowing a statistical test of whether a particular observed case of evolution along the line of least resistance is the result of selection along it or not. Also, with matrix diagonalization (principal components [PC]) it is possible to calculate directly the net-selection gradient on size alone (first PC [PC1]) by dividing the amount of phenotypic difference between any two populations by the amount of variation in PC1, which allows one to benchmark whether selection was on size or not