Biplots of compositional data

The singular value decomposition and its interpretation as alinear biplot has proved to be a powerful tool for analysing many formsof multivariate data. Here we adapt biplot methodology to the specifficcase of compositional data consisting of positive vectors each of whichis constrained to have unit sum. These relative variation biplots haveproperties relating to special features of compositional data: the studyof ratios, subcompositions and models of compositional relationships. Themethodology is demonstrated on a data set consisting of six-part colourcompositions in 22 abstract paintings, showing how the singular valuedecomposition can achieve an accurate biplot of the colour ratios and howpossible models interrelating the colours can be diagnosed.

Tradition, Change and Variation : Past and Present Trends in Public Old-age Care

The general aim of this dissertation is to describe and analyse how public old-age care in Sweden has developed and changed during the last century. The study applies a provider perspective on how care has been planned and professionally carried out. A broader social policy perspective, studying old-age care at central/national as well as local/municipal level, is also developed. A special focus is directed at the large local variation in care and services for the elderly. The empirical base is comprised of official documents and other public sources, survey data from interviews with elderly recipients of public old-age care, and official statistics on publicly financed and controlled old-age care and services. Study I addresses the development of old-age care in Sweden during the twentieth century by studying an important occupation in this field – the supervisors and their professional roles, tasks and working conditions. Throughout, the roles of supervisors have followed the prevailing official policy on the proper way to provide care for elderly people in Sweden; from poor relief at the beginning of the 1900s, via a generous level of services in the 1960s and 1970s, to today’s restricted and economy-controlled mode of operation. Study II describes and compares two main forms of public old-age care in Sweden today, home help services and institutional care. The care-load found in home-based care was comparable to and sometimes even larger than in service-homes and other institutions, indicating that large care needs among elderly people in Sweden today can be met in their homes as well as in institutional settings. Studies III and IV analyse the local variation in public old-age care in Sweden. During the last decades there has been an overall decline in home help services. The coverage of home help for elderly people shows large differences between municipalities throughout this period, and the relative variation has increased. The local disparity seems to depend more on historical factors, e.g., previous coverage rates, than on the present municipal situation in levels of need or local economy and politics. In an introductory part the four papers are linked together by an outline of the demographic situation and the social policy model for old-age care in Sweden. Trends that have been apparent over time, e.g. professionalisation and market orientation, are traced and discussed. Conflicts between prevailing ideologies are analysed, in regards to for instance home-based and institution-based care, social and medical culture, and local and central levels of decision-making. ’Welfare municipality’, ‘path dependency’, and ‘decentralisation’ are suggested as a conceptual framework for describing the large and increasing local variations in old-age care. Finally, implications of the four studies with regard to old-age care policy and further research are discussed.

On the mass determination of super-Earths orbiting active stars: the CoRoT-7 system

Context. Star activity makes the mass determination of CoRoT-7b and CoRoT 7c uncertain. Investigators of the CoRoT team proposed several solutions, but all but one of them are larger than the initial determinations of 4.8 +/- 0.8 M(Earth) for CoRoT-7b and 8.4 +/- 0.9 M(Earth) for CoRoT 7c. Aims. This investigation uses the excellent HARPS radial velocity measurements of CoRoT-7 to redetermine the planet masses and to explore techniques for determining mass and orbital elements of planets discovered around active stars when the relative variation in the radial velocity due to the star activity cannot be considered as just noise and can exceed the variation due to the planets. Methods. The main technique used here is a self-consistent version of the high-pass filter used by Queloz et al. (2009, A&A, 506, 303) in the first mass determination of CoRoT-7b and CoRoT-7c. The results are compared to those given by two alternative techniques: (1) the approach proposed by Hatzes et al. (2010, A&A, 520, A93) using only those nights in which two or three observations were done; (2) a pure Fourier analysis. In all cases, the eccentricities are taken equal to zero as indicated by the study of the tidal evolution of the system. The periods are also kept fixed at the values given by Queloz et al. Only the observations done in the time interval BJD 2 454 847-873 are used because they include many nights with multiple observations; otherwise, it is not possible to separate the effects of the rotation fourth harmonic (5.91 d = P(rot)/4) from the alias of the orbital period of CoRoT-7b (0.853585 d). Results. The results of the various approaches are combined to give planet mass values 8.0 +/- 1.2 M(Earth) for CoRoT-7b and 13.6 +/- 1.4 M(Earth) for CoRoT 7c. An estimation of the variation of the radial velocity of the star due to its activity is also given. Conclusions. The results obtained with three different approaches agree to give higher masses than those in previous determinations. From the existing internal structure models they indicate that CoRoT-7b is a much denser super-Earth. The bulk density is 11 +/- 3.5 g cm(-3), so CoRoT-7b may be rocky with a large iron core.

Compositional analysis of archaeological glasses

At CoDaWork'03 we presented work on the analysis of archaeological glass composi-tional data. Such data typically consist of geochemical compositions involving 10-12variables and approximates completely compositional data if the main component, sil-ica, is included. We suggested that what has been termed `crude' principal componentanalysis (PCA) of standardized data often identi ed interpretable pattern in the datamore readily than analyses based on log-ratio transformed data (LRA). The funda-mental problem is that, in LRA, minor oxides with high relative variation, that maynot be structure carrying, can dominate an analysis and obscure pattern associatedwith variables present at higher absolute levels. We investigate this further using sub-compositional data relating to archaeological glasses found on Israeli sites. A simplemodel for glass-making is that it is based on a `recipe' consisting of two `ingredients',sand and a source of soda. Our analysis focuses on the sub-composition of componentsassociated with the sand source. A `crude' PCA of standardized data shows two clearcompositional groups that can be interpreted in terms of di erent recipes being used atdi erent periods, reected in absolute di erences in the composition. LRA analysis canbe undertaken either by normalizing the data or de ning a `residual'. In either case,after some `tuning', these groups are recovered. The results from the normalized LRAare di erently interpreted as showing that the source of sand used to make the glassdi ered. These results are complementary. One relates to the recipe used. The otherrelates to the composition (and presumed sources) of one of the ingredients. It seemsto be axiomatic in some expositions of LRA that statistical analysis of compositionaldata should focus on relative variation via the use of ratios. Our analysis suggests thatabsolute di erences can also be informative

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completelyabsent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and byMartín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involvedparts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method isintroduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that thetheoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approachhas reasonable properties from a compositional point of view. In particular, it is “natural” in the sense thatit recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in thesame paper a substitution method for missing values on compositional data sets is introduced

Markov chain montecarlo method applied to rounding zeros of compositional data: first approach

As stated in Aitchison (1986), a proper study of relative variation in a compositional data set should be based on logratios, and dealing with logratios excludes dealing with zeros. Nevertheless, it is clear that zero observations might be present in real data sets, either because the corresponding part is completely absent –essential zeros– or because it is below detection limit –rounded zeros. Because the second kind of zeros is usually understood as “a trace too small to measure”, it seems reasonable to replace them by a suitable small value, and this has been the traditional approach. As stated, e.g. by Tauber (1999) and by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000), the principal problem in compositional data analysis is related to rounded zeros. One should be careful to use a replacement strategy that does not seriously distort the general structure of the data. In particular, the covariance structure of the involved parts –and thus the metric properties– should be preserved, as otherwise further analysis on subpopulations could be misleading. Following this point of view, a non-parametric imputation method is introduced in Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2000). This method is analyzed in depth by Martín-Fernández, Barceló-Vidal, and Pawlowsky-Glahn (2003) where it is shown that the theoretical drawbacks of the additive zero replacement method proposed in Aitchison (1986) can be overcome using a new multiplicative approach on the non-zero parts of a composition. The new approach has reasonable properties from a compositional point of view. In particular, it is “natural” in the sense that it recovers the “true” composition if replacement values are identical to the missing values, and it is coherent with the basic operations on the simplex. This coherence implies that the covariance structure of subcompositions with no zeros is preserved. As a generalization of the multiplicative replacement, in the same paper a substitution method for missing values on compositional data sets is introduced

Compositional analysis of archaeological glasses

At CoDaWork'03 we presented work on the analysis of archaeological glass composi- tional data. Such data typically consist of geochemical compositions involving 10-12 variables and approximates completely compositional data if the main component, sil- ica, is included. We suggested that what has been termed `crude' principal component analysis (PCA) of standardized data often identi ed interpretable pattern in the data more readily than analyses based on log-ratio transformed data (LRA). The funda- mental problem is that, in LRA, minor oxides with high relative variation, that may not be structure carrying, can dominate an analysis and obscure pattern associated with variables present at higher absolute levels. We investigate this further using sub- compositional data relating to archaeological glasses found on Israeli sites. A simple model for glass-making is that it is based on a `recipe' consisting of two `ingredients', sand and a source of soda. Our analysis focuses on the sub-composition of components associated with the sand source. A `crude' PCA of standardized data shows two clear compositional groups that can be interpreted in terms of di erent recipes being used at di erent periods, re ected in absolute di erences in the composition. LRA analysis can be undertaken either by normalizing the data or de ning a `residual'. In either case, after some `tuning', these groups are recovered. The results from the normalized LRA are di erently interpreted as showing that the source of sand used to make the glass di ered. These results are complementary. One relates to the recipe used. The other relates to the composition (and presumed sources) of one of the ingredients. It seems to be axiomatic in some expositions of LRA that statistical analysis of compositional data should focus on relative variation via the use of ratios. Our analysis suggests that absolute di erences can also be informative

Myocardial contractile dysfunction contributes to the development of heart failure in rats with aortic stenosis

Objectives: To analyze the potential contribution of contractility state and ventricular geometry to the development of heart failure in rats with aortic stenosis.Methods: Rats were divided into three groups: compensated aortic stenosis (AS, n = 11), heart failure AS (n = 12) and control rats (C, n = 13).Results: After 21 weeks, failing AS rats presented higher systolic (C = 36.6 +/- 3.1, AS-78.6 +/- 4.8*, failing AS = 104.6 +/- 7.8*) and diastolic meridian stress (C = 6.9 +/- 0.4, AS = 20.1 +/- 1.1*, failing AS = 43.2 +/- 3.2*(dagger)), hydroxyproline (C = 3.6 +/- 0.7 mg/g, AS = 6.6 +/- 0.6* mg/g, failing AS = 9.2 +/- 1.4*(dagger) mg/g) and cross-sectional area (C = 338 +/- 25 mu m(2), AS = 451 +/- 32* mu m(2), failing AS = 508 +/- 36*(dagger) mu m(2)), in comparison with control and compensated AS animals (*p < 0.05 vs. control, (dagger)p < 0.05 vs. AS). In the isometric contraction study, considering the time from peak tension to 50% relaxation (RT50), the relative variation responses, following post-rest contraction and increase in Ca2+ concentration, were higher in failing AS than compensated AS animals. In contrast, following post-rest contraction, compensated AS group presented higher values of the peak developed tension (DT) than failing AS group. Following beta-adrenergic stimulation, control animals presented higher values of +dT/dt and -dT/dt than AS animals. In addition, failing AS animals presented higher TPT values than compensated AS animals.Conclusion: Myocardial contractile dysfunction contributes to the development of heart failure in rats with aortic stenosis. (c) 2006 Elsevier B.V.. All rights reserved.

Comparative mechanical study of isolated papillary muscle from Wistar-Kyoto and Wistar rats

Isolated papillary muscles have often been used in myocardial mechanical function studies. The objective of the present study was to compare the mechanical function of papillary muscle isolated from left ventricle between Wistar (W) and Wistar-Kyoto (WKY) rats of different ages (1, 3, 6 and 12 months), in order to examine whether there is a difference in intrinsic mechanical properties of muscle between the two rat strains. Muscles were perfused with Krebs-Henseleit solution at 28°C and studied isometrically and isotonically at a stimulation rate of 0.2 Hz. The W and WKY showed statistically significant differences during both isometric and isotonic contractions. During isometric contraction? (l) the peak developed tension (DT) and + dT/dt were lower in WKY rats in the 1 mo groups, (2) the resting tension (RT) was greater in WKY at 3, 6 and 12 mo. (3) time to peak tension (TPT) was greater in WKY at 3 and 12 mo, (4) time for tension to fall from peak to 50% of peak tension (RT 1/2) was greater in WKY at 3 mo and (5) - dT/dt was lower in WKY at 1 and 3 mo. During isotonic contraction, (1) the peak shortening (PS) and -dL/dt were lower in WKY at 12 mo, (2) the time to peak shortening (TPS) was greater in WKY at 3 and 12 mo; (3) + dL/dt was lower in WKY at 3, 6, and 12 mo and (4) the relative variation of length (Lmax-PS)/Lmax was greater in WKY at 6 and 12 mo. These data showed a difference in mechanical behaviour of the papillary muscle between Wistar and Wistar-Kyoto rats of different age.

Variação genética para caracteres silviculturais e marcador molecular em uma população base de Eucalyptus camaldulensis Dehnh

Pós-graduação em Agronomia - FEIS

Variabilidade genética em progênies de guapuruvu Schizolobium parahyba (Vell.) Blake

Pós-graduação em Ciência Florestal - FCA

Geofísica aplicada no monitoramento de área de disposição de resíduos sólidos domiciliares

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variação genética para os caracteres fisiológicos, bioquímicos e nutricionais em sementes de uma população base de Myracrodruon urundeuva procedente de Aquidauana-MS

Pós-graduação em Agronomia - FEIS

(Table 1) Attenuation coefficient of lateral propagating light in sea ice, southern Beaufort Sea

The attenuation property of a lateral propagating light (LPL) in sea ice was measured using an artificial lamp in the Canadian Arctic during the 2007/2008 winter. A measurement method is proposed and applied whereby a recording instrument is buried in the sea ice and an artificial lamp is moved across the instrument. The apparent attenuation coefficient µ(lamda) for the lateral propagating light is obtained from the measured logarithmic relative variation rate. With the exception of blue and red lights, the attenuation coefficient changed little with wavelength, but changed considerably with depth. The vertical decrease of the attenuation coefficient was found to be correlated with salinity: the greater the salinity, the greater the attenuation coefficient. A clear linear relation of salinity and the lateral attenuation coefficient with R2 = 0.939 exists to address the close correlation of the attenuation of LPL with the scattering from the brine. The observed attenuation coefficient of LPL is much larger than that of the vertical propagation light, which we speculate to be caused by scattering. Part of this scattered component is transmitted out of the sea ice from the upper and lower surfaces.

Archaeological otoliths as environmental recorders: high resolution sampling of pacific cod (Gadus macrocephalus) otoliths from Kiska Island, Alaska

Archaeological fish otoliths have the potential to serve as proxies for both season of site occupation and palaeoclimate conditions. By sampling along the distinctive sub-annual seasonal bands of the otolith and completing a stable isotope (δ¹⁸O, δ¹³C) analysis, variations within the fish’s environment can be identified. Through the analysis of cod otoliths from two archaeological sites on Kiska Island, Gertrude Cove (KIS-010) and Witchcraft Point (KIS-005), this research evaluates a micromilling methodological approach to extracting climatic data from archaeological cod otoliths. In addition, δ¹⁸Ootolith data and radiocarbon dates frame a discussion of Pacific cod harvesting, site occupation, and changing climatic conditions on Kiska Island. To aid in the interpretation of the archaeological Pacific cod results, archaeological and modern Atlantic cod otoliths were also analyzed as a component of this study to develop. The Atlantic cod otoliths provided the methodological and interpretative framework for the study, and also served to assess the efficacy of this sampling strategy for archaeological materials and to add time-depth to existing datasets. The δ¹⁸Ootolith values successfully illustrate relative variation in ambient water temperature. The Pacific cod δ¹⁸O values demonstrate a weak seasonal signal identifiable up to year 3, followed by relatively stable values until year 6/7 when values continuously increase. Based on the δ¹⁸O values, the Pacific cod were exposed to the coldest water temperatures immediately prior to capture. The lack of a clear cycle of seasonal variation and the continued increase in values towards the otolith edge obscures the season of capture, and indicates that other behavioural, environmental, or methodological factors influenced the otolith δ¹⁸O values. It is suggested that Pacific cod would have been harvested throughout the year, and the presence of cod remains in Aleutian archaeological sites cannot be used as a reliable indicator of summer occupation. In addition, when the δ¹⁸O otolith values are integrated with radiocarbon dates and known climatic regimes, it is demonstrated that climatic conditions play an integral role in the pattern of occupation at Gertrude Cove. Initial site occupation coincides with the end of a neoglacial cooling period, and the most recent and continuous occupation coincides with the end of a localized warming period and the onset of the Little Ice Age (LIA).