Application of compositional data analysis to geochemical data of marine sediments

In an earlier investigation (Burger et al., 2000) five sediment cores near the RodriguesTriple Junction in the Indian Ocean were studied applying classical statistical methods(fuzzy c-means clustering, linear mixing model, principal component analysis) for theextraction of endmembers and evaluating the spatial and temporal variation ofgeochemical signals. Three main factors of sedimentation were expected by the marinegeologists: a volcano-genetic, a hydro-hydrothermal and an ultra-basic factor. Thedisplay of fuzzy membership values and/or factor scores versus depth providedconsistent results for two factors only; the ultra-basic component could not beidentified. The reason for this may be that only traditional statistical methods wereapplied, i.e. the untransformed components were used and the cosine-theta coefficient assimilarity measure.During the last decade considerable progress in compositional data analysis was madeand many case studies were published using new tools for exploratory analysis of thesedata. Therefore it makes sense to check if the application of suitable data transformations,reduction of the D-part simplex to two or three factors and visualinterpretation of the factor scores would lead to a revision of earlier results and toanswers to open questions . In this paper we follow the lines of a paper of R. Tolosana-Delgado et al. (2005) starting with a problem-oriented interpretation of the biplotscattergram, extracting compositional factors, ilr-transformation of the components andvisualization of the factor scores in a spatial context: The compositional factors will beplotted versus depth (time) of the core samples in order to facilitate the identification ofthe expected sources of the sedimentary process.Kew words: compositional data analysis, biplot, deep sea sediments

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Quantifying rock fabrics: a test of autocorrelation of the spatial distribution of cristals

A novel test of spatial independence of the distribution of crystals or phases in rocksbased on compositional statistics is introduced. It improves and generalizes the commonjoins-count statistics known from map analysis in geographic information systems.Assigning phases independently to objects in RD is modelled by a single-trial multinomialrandom function Z(x), where the probabilities of phases add to one and areexplicitly modelled as compositions in the K-part simplex SK. Thus, apparent inconsistenciesof the tests based on the conventional joins{count statistics and their possiblycontradictory interpretations are avoided. In practical applications we assume that theprobabilities of phases do not depend on the location but are identical everywhere inthe domain of de nition. Thus, the model involves the sum of r independent identicalmultinomial distributed 1-trial random variables which is an r-trial multinomialdistributed random variable. The probabilities of the distribution of the r counts canbe considered as a composition in the Q-part simplex SQ. They span the so calledHardy-Weinberg manifold H that is proved to be a K-1-affine subspace of SQ. This isa generalisation of the well-known Hardy-Weinberg law of genetics. If the assignmentof phases accounts for some kind of spatial dependence, then the r-trial probabilitiesdo not remain on H. This suggests the use of the Aitchison distance between observedprobabilities to H to test dependence. Moreover, when there is a spatial uctuation ofthe multinomial probabilities, the observed r-trial probabilities move on H. This shiftcan be used as to check for these uctuations. A practical procedure and an algorithmto perform the test have been developed. Some cases applied to simulated and realdata are presented.Key words: Spatial distribution of crystals in rocks, spatial distribution of phases,joins-count statistics, multinomial distribution, Hardy-Weinberg law, Hardy-Weinbergmanifold, Aitchison geometry

Bilinear models for spatio-temporal point distribution analysis: application to extrapolation of left ventricular, biventricular and whole heart cardiac dynamics

In this work we describe the usage of bilinear statistical models as a means of factoring the shape variability into two components attributed to inter-subject variation and to the intrinsic dynamics of the human heart. We show that it is feasible to reconstruct the shape of the heart at discrete points in the cardiac cycle. Provided we are given a small number of shape instances representing the same heart atdifferent points in the same cycle, we can use the bilinearmodel to establish this. Using a temporal and a spatial alignment step in the preprocessing of the shapes, around half of the reconstruction errors were on the order of the axial image resolution of 2 mm, and over 90% was within 3.5 mm. From this, weconclude that the dynamics were indeed separated from theinter-subject variability in our dataset.

Public health expenditure and spatial interactions in a decentralized national health system

One of the limitations of cross-country health expenditure analysis refers to the fact that the financing, the internal organization and political restraints of health care decision-making are country-specific and heterogeneous. Yet, a potential solution is to examine the influence of such effects in those countries that have undertaken decentralization processes. In such a setting, it is possible to examine potential expenditure spillovers across the geography of a country as well as the influence of the political ideology of regional incumbents on public health expenditure. This paper examines the determinants of public health expenditure within Spanish region-states (Autonomous Communities, ACs), most of them subject to similar financing structures although exhibiting significant heterogeneity as a result of the increasing decentralization, region-specific political factors along with different use of health care inputs, economic dimension and spatial interactions

The empirics of spatial competition: evidence from European regions

The New Economic Geography literature allows detailed analysis of the factors that determine the location decisions of firms in integrated markets. However, the competitive process is modelled in a rather rudimentary way, and the empirical evidence has usually been obtained from reduced-form econometric specifications. This study describes a structural model that takes into account strategic interactions between firms. We investigate the relationship between the degree of perceived competition ¿ not only from local firms but from firms in other regions ¿ and geographic concentration. The preliminary results indicate that, in aggregate terms, local firms present stronger competition than firms in other regions. Moreover, it is confirmed that greater geographical concentration of production reduces market power, due to the intensification of local competition; however, its impact on production costs is unclear.

The empirics of spatial competition: evidence from European regions

The New Economic Geography literature allows detailed analysis of the factors that determine the location decisions of firms in integrated markets. However, the competitive process is modelled in a rather rudimentary way, and the empirical evidence has usually been obtained from reduced-form econometric specifications. This study describes a structural model that takes into account strategic interactions between firms. We investigate the relationship between the degree of perceived competition ¿ not only from local firms but from firms in other regions ¿ and geographic concentration. The preliminary results indicate that, in aggregate terms, local firms present stronger competition than firms in other regions. Moreover, it is confirmed that greater geographical concentration of production reduces market power, due to the intensification of local competition; however, its impact on production costs is unclear.

Agglomeration and labour productivity in Spanish industry: a long-term analysis

This paper analyzes the relationship between spatial density of economic activity and interregional differences in the productivity of industrial labour in Spain during the period 1860-1999. In the spirit of Ciccone and Hall (1996) and Ciccone (2002), we analyze the evolution of this relationship over the long term in Spain. Using data on the period 1860-1999 we show the existence of an agglomeration effect linking the density of economic activity with labour productivity in the industry. This effect was present since the beginning of the industrialization process in the middle of the 19th century but has been decreasing over time. The estimated elasticity of labour productivity with respect to employment density was close to 8% in the subperiod 1860-1900, reduces to a value of around 7% in the subperiod 1914-1930, to 4% in the subperiod 1965-1979 and becomes insignificant in the final subperiod 1985-1999. At the end of the period analyzed there is no evidence of the existence of net agglomeration effects in the industry. This result could be explained by an important increase in the congestion effects in large industrial metropolitan areas that would have compensated the centripetal or agglomeration forces at work. Furthermore, this result is also consistent with the evidence of a dispersion of industrial activity in Spain during the last decades.

Public health expenditure and spatial interactions in a decentralized national health system

One of the limitations of cross-country health expenditure analysis refers to the fact that the financing, the internal organization and political restraints of health care decision-making are country-specific and heterogeneous. Yet, a potential solution is to examine the influence of such effects in those countries that have undertaken decentralization processes. In such a setting, it is possible to examine potential expenditure spillovers across the geography of a country as well as the influence of the political ideology of regional incumbents on public health expenditure. This paper examines the determinants of public health expenditure within Spanish region-states (Autonomous Communities, ACs), most of them subject to similar financing structures although exhibiting significant heterogeneity as a result of the increasing decentralization, region-specific political factors along with different use of health care inputs, economic dimension and spatial interactions

Species resolved analysis of the expansion of hydroxyapatite laser ablation plumes

The plume generated by ablation of hydroxyapatite targets under ArF excimer laser irradiation has been investigated by means of fast intensified CCD-imaging and optical emission spectroscopy. Results have shown that the plume splits into two plasma clouds as it expands. Time and spatial resolved spectra have revealed that under the experiment conditions emission is mostly due to calcium neutral atoms and calcium oxide molecular radicals. Imaging of the plume with the aid of bandpass filters has demonstrated that the emissive species in the larger and faster plasma cloud are calcium neutral atoms, whereas in the smaller and slower one they are calcium oxide molecular radicals

Agglomeration and labour productivity in Spanish industry: a long-term analysis

This paper analyzes the relationship between spatial density of economic activity and interregional differences in the productivity of industrial labour in Spain during the period 1860-1999. In the spirit of Ciccone and Hall (1996) and Ciccone (2002), we analyze the evolution of this relationship over the long term in Spain. Using data on the period 1860-1999 we show the existence of an agglomeration effect linking the density of economic activity with labour productivity in the industry. This effect was present since the beginning of the industrialization process in the middle of the 19th century but has been decreasing over time. The estimated elasticity of labour productivity with respect to employment density was close to 8% in the subperiod 1860-1900, reduces to a value of around 7% in the subperiod 1914-1930, to 4% in the subperiod 1965-1979 and becomes insignificant in the final subperiod 1985-1999. At the end of the period analyzed there is no evidence of the existence of net agglomeration effects in the industry. This result could be explained by an important increase in the congestion effects in large industrial metropolitan areas that would have compensated the centripetal or agglomeration forces at work. Furthermore, this result is also consistent with the evidence of a dispersion of industrial activity in Spain during the last decades.

Public health expenditure and spatial interactions in a decentralized national health system

One of the limitations of cross-country health expenditure analysis refers to the fact that the financing, the internal organization and political restraints of health care decision-making are country-specific and heterogeneous. Yet, a potential solution is to examine the influence of such effects in those countries that have undertaken decentralization processes. In such a setting, it is possible to examine potential expenditure spillovers across the geography of a country as well as the influence of the political ideology of regional incumbents on public health expenditure. This paper examines the determinants of public health expenditure within Spanish region-states (Autonomous Communities, ACs), most of them subject to similar financing structures although exhibiting significant heterogeneity as a result of the increasing decentralization, region-specific political factors along with different use of health care inputs, economic dimension and spatial interactions

Agglomeration and labour productivity in Spanish industry: a long-term analysis

This paper analyzes the relationship between spatial density of economic activity and interregional differences in the productivity of industrial labour in Spain during the period 1860-1999. In the spirit of Ciccone and Hall (1996) and Ciccone (2002), we analyze the evolution of this relationship over the long term in Spain. Using data on the period 1860-1999 we show the existence of an agglomeration effect linking the density of economic activity with labour productivity in the industry. This effect was present since the beginning of the industrialization process in the middle of the 19th century but has been decreasing over time. The estimated elasticity of labour productivity with respect to employment density was close to 8% in the subperiod 1860-1900, reduces to a value of around 7% in the subperiod 1914-1930, to 4% in the subperiod 1965-1979 and becomes insignificant in the final subperiod 1985-1999. At the end of the period analyzed there is no evidence of the existence of net agglomeration effects in the industry. This result could be explained by an important increase in the congestion effects in large industrial metropolitan areas that would have compensated the centripetal or agglomeration forces at work. Furthermore, this result is also consistent with the evidence of a dispersion of industrial activity in Spain during the last decades.

Multiway Array Decomposition Analysis of EEGs in Alzheimer’s Disease

Methods for the extraction of features from physiological datasets are growing needs as clinical investigations of Alzheimer’s disease (AD) in large and heterogeneous population increase. General tools allowing diagnostic regardless of recording sites, such as different hospitals, are essential and if combined to inexpensive non-invasive methods could critically improve mass screening of subjects with AD. In this study, we applied three state of the art multiway array decomposition (MAD) methods to extract features from electroencephalograms (EEGs) of AD patients obtained from multiple sites. In comparison to MAD, spectral-spatial average filter (SSFs) of control and AD subjects were used as well as a common blind source separation method, algorithm for multiple unknown signal extraction (AMUSE). We trained a feed-forward multilayer perceptron (MLP) to validate and optimize AD classification from two independent databases. Using a third EEG dataset, we demonstrated that features extracted from MAD outperformed features obtained from SSFs AMUSE in terms of root mean squared error (RMSE) and reaching up to 100% of accuracy in test condition. We propose that MAD maybe a useful tool to extract features for AD diagnosis offering great generalization across multi-site databases and opening doors to the discovery of new characterization of the disease.

Spatial Polarization of the Ecological Footprint distribution

The international allocation of natural resources is determined, not by any ethical or ecological criteria, but by the dominance of market mechanisms. From a core-periphery perspective, this allocation may even be driven by historically determined structural patterns, with a core group of countries whose consumption appropriates most available natural resources, and another group, having low natural resource consumption, which plays a peripheral role. This article consists of an empirical distributional analysis of natural resource consumption (as measured by Ecological Footprints) whose purpose is to assess the extent to which the distribution of consumption responds to polarization (as opposed to mere inequality). To assess this, we estimate and decompose different polarization indices for a balanced sample of 119 countries over the period 1961 to 2007. Our results points toward a polarized distribution which is consistent with a core-periphery framework.