Analysis of diffusion tensor magnetic resonance imaging data using principal component analysis

An analysis method for diffusion tensor (DT) magnetic resonance imaging data is described, which, contrary to the standard method (multivariate fitting), does not require a specific functional model for diffusion-weighted (DW) signals. The method uses principal component analysis (PCA) under the assumption of a single fibre per pixel. PCA and the standard method were compared using simulations and human brain data. The two methods were equivalent in determining fibre orientation. PCA-derived fractional anisotropy and DT relative anisotropy had similar signal-to-noise ratio (SNR) and dependence on fibre shape. PCA-derived mean diffusivity had similar SNR to the respective DT scalar, and it depended on fibre anisotropy. Appropriate scaling of the PCA measures resulted in very good agreement between PCA and DT maps. In conclusion, the assumption of a specific functional model for DW signals is not necessary for characterization of anisotropic diffusion in a single fibre.

The global distribution of phytoplankton size spectrum and size classes from their light-absorption spectra derived from satellite data

The absorption spectra of phytoplankton in the visible domain hold implicit information on the phytoplankton community structure. Here we use this information to retrieve quantitative information on phytoplankton size structure by developing a novel method to compute the exponent of an assumed power-law for their particle-size spectrum. This quantity, in combination with total chlorophyll-a concentration, can be used to estimate the fractional concentration of chlorophyll in any arbitrarily-defined size class of phytoplankton. We further define and derive expressions for two distinct measures of cell size of mixed populations, namely, the average spherical diameter of a bio-optically equivalent homogeneous population of cells of equal size, and the average equivalent spherical diameter of a population of cells that follow a power-law particle-size distribution. The method relies on measurements of two quantities of a phytoplankton sample: the concentration of chlorophyll-a, which is an operational index of phytoplankton biomass, and the total absorption coefficient of phytoplankton in the red peak of visible spectrum at 676 nm. A sensitivity analysis confirms that the relative errors in the estimates of the exponent of particle size spectra are reasonably low. The exponents of phytoplankton size spectra, estimated for a large set of in situ data from a variety of oceanic environments (~ 2400 samples), are within a reasonable range; and the estimated fractions of chlorophyll in pico-, nano- and micro-phytoplankton are generally consistent with those obtained by an independent, indirect method based on diagnostic pigments determined using high-performance liquid chromatography. The estimates of cell size for in situ samples dominated by different phytoplankton types (diatoms, prymnesiophytes, Prochlorococcus, other cyanobacteria and green algae) yield nominal sizes consistent with the taxonomic classification. To estimate the same quantities from satellite-derived ocean-colour data, we combine our method with algorithms for obtaining inherent optical properties from remote sensing. The spatial distribution of the size-spectrum exponent and the chlorophyll fractions of pico-, nano- and micro-phytoplankton estimated from satellite remote sensing are in agreement with the current understanding of the biogeography of phytoplankton functional types in the global oceans. This study contributes to our understanding of the distribution and time evolution of phytoplankton size structure in the global oceans.

Fractional order and non-linear system identification algorithms for biomedical applications

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

Parametrizing the horizontal inhomogeneity of ice water content using CloudSat data products

In order to calculate unbiased microphysical and radiative quantities in the presence of a cloud, it is necessary to know not only the mean water content but also the distribution of this water content. This article describes a study of the in-cloud horizontal inhomogeneity of ice water content, based on CloudSat data. In particular, by focusing on the relations with variables that are already available in general circulation models (GCMs), a parametrization of inhomogeneity that is suitable for inclusion in GCM simulations is developed. Inhomogeneity is defined in terms of the fractional standard deviation (FSD), which is given by the standard deviation divided by the mean. The FSD of ice water content is found to increase with the horizontal scale over which it is calculated and also with the thickness of the layer. The connection to cloud fraction is more complicated; for small cloud fractions FSD increases as cloud fraction increases while FSD decreases sharply for overcast scenes. The relations to horizontal scale, layer thickness and cloud fraction are parametrized in a relatively simple equation. The performance of this parametrization is tested on an independent set of CloudSat data. The parametrization is shown to be a significant improvement on the assumption of a single-valued global FSD

Fractional polynomial response surface models

Second-order polynomial models have been used extensively to approximate the relationship between a response variable and several continuous factors. However, sometimes polynomial models do not adequately describe the important features of the response surface. This article describes the use of fractional polynomial models. It is shown how the models can be fitted, an appropriate model selected, and inference conducted. Polynomial and fractional polynomial models are fitted to two published datasets, illustrating that sometimes the fractional polynomial can give as good a fit to the data and much more plausible behavior between the design points than the polynomial model. © 2005 American Statistical Association and the International Biometric Society.

Field and petrographic data of 1.90 to 1.88 Ga I- and A-type granitoids from the central region of the Amazonian Craton, NE Amazonas State, Brazil

O SW do município de Presidente Figueiredo, localizado no Estado do Amazonas, Nordeste do Cráton Amazônico Central, Brasil, hospeda granitoides do tipo I de idade entre 1890 a 1898 Ma (Terra Preta Granito, Suíte Água Branca), hornblenda-sienogranitos do tipo A (Sienogranito Canoas da Suíte Mapuera), rochas vulcânicas ácidas à intermediárias (Grupo Iricoumé) e granitos rapakivi de idades entre 1883 a 1889 Ma (Granito São Gabriel da Suíte Mapuera), e rochas afins (quartzo-gabro-anortosito e diorito), além de quartzo-monzonito Castanhal, milonitos e hornfels. A fácies quartzo-diorito do granito Terra Preta foi formada por processos de mistura entre um dique quartzo-gabro sinplutônico e um granodiorito hornblenda. Glóbulos parcialmente assimilados de sienogranitos hornblenda Canoas e seus contatos com o granodiorito hornblenda Terra Preta sugerem que o sienogranito Canoas é um pouco mais jovem do que o Granito Terra Preta. Xenólitos do sienogranito Canoas no interior do Granito São Gabriel mostram que o granito é mais jovem do que o sienogranito Canoas. Novas evidências geológicas e petrográficas avançam na compreensão petrológica destas rochas e sugerem que, além de cristalização fracionada, assimilação e mistura de magma, desempenharam um papel importante, pelo menos em escala local, na evolução e variação composicionais dos plutons. Tal evidência é encontrada no Granito Terra Preta misturado com materiais quartzo-diorito, félsico associado ao sienogranito Canoas e nos enclaves microgranulares intermediários, que apresentam biotita e hornblenda primárias, além de dissolução plagioclásio, corrosão de feldspatos, mantos feldspatos alcalinos, segunda geração de apatita, e elevados teores xenocristais em enclaves intermediários formados a partir da fragmentação de intrusões máficas. Análises petrográficas mostram que um evento deformacional registrado na parte Ocidental da área de estudo (com deformação progressiva de E para W) é estimado entre o magmatismo pós-colisional de 1,90 Ga e as invasões do Granito São Gabriel e rochas afins máficas/intermediárias (intraplaca). No entanto, torna-se extremamente necessário obter idades absolutas para este evento metamórfico.

Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

Rhenium and platinum-group element concentrations and Os isotope data for Philippine Sea Plate basalts from DSDP Legs 31, 58, and 59

Platinum-group elements (PGE), rhenium and osmium isotope data are reported for basalts from Deep Sea Drilling Project cores in the Philippine Sea Plate (PSP). Lithophile trace element and isotopic characteristics indicate a range of source components including DMM, EMII and subduction-enriched mantle. MORB-like basalts possess smooth, inclined chondrite-normalised PGE patterns with high palladium-PGE/iridium-PGE ratios, consistent with previously published data for MORB, and with the inferred compatibility of PGE. In contrast, while basalts with EMII-type lithophile element chemistry possess high Pt/Ir ratios, many have much lower Pd/Ir and unusually high Ru/Ir of >10. Similarly, back-arc samples from the Shikoku and Parece-Vela basins have very high Ru/Ir ratios (>30) and Pd/Ir as low as 1.1. Such extreme Pd/Ir and Ru/Ir ratios have not been previously reported in mafic volcanic suites and cannot be easily explained by variable degrees of melting, fractional crystallisation or by a shallow-level process such as alteration or degassing. The data appear most consistent with sampling of at least two mantle components with distinct PGE compositions. Peridotites with the required PGE characteristics (i.e. low Pd, but relatively high Ru and Re) have not been documented in oceanic mantle, but have been found in sub-continental mantle lithosphere and are the result of considerable melt depletion and selective metasomatic enrichment (mainly Re). The long-term presence of subduction zones surrounding the Philippine Sea Plate makes this a prime location for metasomatic enrichment of mantle, either through fluid enrichment or infiltration by small melt fractions. The Re-Os isotope data are difficult to interpret with confidence due to low Os concentrations in most samples and the uncertainty in sample age. Data for Site 444A (Shikoku Basin) give an age of 17.7+/-1.3 Ma (MSWD = 14), consistent with the proposed age of basement at the site and thus provides the first robust radiometric age for these samples. The initial 187Os/188Os of 0.1298+/-0.0069 is consistent with global MORB, and precludes significant metasomatic enrichment of Os by radiogenic slab fluids. Re-Os data for Sites 446A (two suites, Daito Basin) and 450 (Parece-Vela Basin) indicate ages of 73, 68 and 43 Ma, which are respectively, 30, 17 and >12 Ma older than previously proposed ages. The alkalic and tholeiitic suites from Site 446A define regression lines with different 187Os/188Osinitial (0.170+/-0.033 and 0.112+/-0.024, respectively) which could perhaps be explained by preferential sampling of interstitial, metasomatic sulphides (with higher time-integrated Re/Os ratios) by smaller percentage alkalic melts. One sample, with lithophile elements indistinguishable from MORB, is Os-rich (146 pg/g) and has an initial 187Os/188Os of 0.1594, which is at the upper limit of the accepted OIB range. Given the Os-rich nature of this sample and the lack of evidence for subduction or recycled crust inputs, this osmium isotope ratio likely reflects heterogeneity in the DMM. The dataset as a whole is a striking indication of the possible PGE and Os isotope variability within a region of mantle that has experienced a complex tectonic history.

A fractional vegetation cover remote sensing product on pan-arctic scale with link to geotiff image

The paper presents first results of a pan-boreal scale land cover harmonization and classification. A methodology is presented that combines global and regional vegetation datasets to extract percentage cover information for different vegetation physiognomy and barren for the pan-arctic region within the ESA Data User Element Permafrost. Based on the legend description of each land cover product the datasets are harmonized into four LCCS (Land Cover Classification System) classifiers which are linked to the MODIS Vegetation Continuous Field (VCF) product. Harmonized land cover and Vegetation Continuous Fields products are combined to derive a best estimate of percentage cover information for trees, shrubs, herbaceous and barren areas for Russia. Future work will concentrate on the expansion of the developed methodology to the pan-arctic scale. Since the vegetation builds an isolation layer, which protects the permafrost from heat and cold temperatures, a degradation of this layer due to fire strongly influences the frozen conditions in the soil. Fire is an important disturbance factor which affects vast processes and dynamics in ecosystems (e.g. biomass, biodiversity, hydrology, etc.). Especially in North Eurasia the fire occupancy has dramatically increased in the last 50 years and has doubled in the 1990s with respect to the last five decades. A comparison of global and regional fire products has shown discrepancies between the amounts of burn scars detected by different algorithms and satellite data.