On The Breakdown Properties of some Multivariate M-Functionals

For probability distributions on ℝq, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler's [Ann. Statist. 15 (1987) 234] ‘distribution-free’ M-functional of scatter is given. These include a symmetrized version of Tyler's M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for ‘smooth’ distributions, the (contamination) breakdown point of Tyler's M-functional of scatter and of its symmetrized version are 1/q and inline image, respectively. For the multivariate t M-functional which arises from the maximum likelihood estimate for the parameters of an elliptical t distribution on ν ≥ 1 degrees of freedom the breakdown point at smooth distributions is 1/(q + ν). Breakdown points are also obtained for general distributions, including empirical distributions. Finally, the sources of breakdown are investigated. It turns out that breakdown can only be caused by contaminating distributions that are concentrated near low-dimensional subspaces.

Spatial Distribution of Stem Cell-Like Keratinocytes in Dissected Compound Hair Follicles of the Dog

Hair cycle disturbances are common in dogs and comparable to some alopecic disorders in humans. A normal hair cycle is maintained by follicular stem cells which are predominately found in an area known as the bulge. Due to similar morphological characteristics of the bulge area in humans and dogs, the shared particularity of compound hair follicles as well as similarities in follicular biomarker expression, the dog is a promising model to study human hair cycle and stem cell disorders. To gain insight into the spatial distribution of follicular keratinocytes with stem cell potential in canine compound follicles, we microdissected hair follicles in anagen and telogen from skin samples of freshly euthanized dogs. The keratinocytes isolated from different locations were investigated for their colony forming efficiency, growth and differentiation potential as well as clonal growth. Our results indicate that i) compound and single hair follicles exhibit a comparable spatial distribution pattern with respect to cells with high growth potential and stem cell-like characteristics, ii) the lower isthmus (comprising the bulge) harbors most cells with high growth potential in both, the anagen and the telogen hair cycle stage, iii) unlike in other species, colonies with highest growth potential are rather small with an irregular perimeter and iv) the keratinocytes derived from the bulbar region exhibit characteristics of actively dividing transit amplifying cells. Our results now provide the basis to conduct comparative studies of normal dogs and those with hair cycle disorders with the possibility to extend relevant findings to human patients.

Body fat distribution and serum lipids in children and adolescents

Previous studies of normal children have linked body fat but not body fat distribution (BFD), to higher blood pressures, lipids, and insulin resistance (Berenson et al., 1988) BFD is a well-established risk factor for cardiovascular disease in adults (Björntorp, 1988). This study investigates the relation of BFD and serum lipids at baseline in children from Project HeartBeat!, a study of the growth and development of cardiovascular risk factors in 678 children in three cohorts measured initially at ages 8, 11, and 14 years. Initially, two of four indices of BFD were significantly related to the lipids: ratio of upper to lower body skinfolds (ln US:LS) and conicity (C Index). A factor analysis reduced the information in the serum lipids to two vectors: (1) total cholesterol + LDL-cholesterol and (2) HDL-cholesterol − triglycerides, which together accounted for 85% of the lipid variation. Using each serum lipid and vector as separate dependent variables, linear and quadratic regression models were constructed to examine the predictive ability of the two BFD variables, controlling for total body fat, gender, ethnicity (Black, non-Black) and maturation. Linear models provided an acceptable fit. Percent body fat (%BF) was a significant predictor in each and every lipid model, independent of age, maturation, or ethnicity (p ≤ 0.05). No BFD variable entered the equation for total or LDL-cholesterol, although there was a significant maturity by BFD interaction for LDL (ln US:LS was a significant predictor in more mature individuals). Both %BF and BFD (by way of Conicity) were significant predictors of HDL-cholesterol and triglycerides (p ≤ 0.01). All models were statistically significant at a high level (p ≤ 0.01), but adjusted R 2's for all models were low (0.05–0.15). Body fat distribution is a significant predictor of lipids in normal children, but secondarily to %BF, and for LDL-cholesterol in particular, the relation is dependent on maturity status. ^

Multivariate methods for correlated effects sizes

Current statistical methods for estimation of parametric effect sizes from a series of experiments are generally restricted to univariate comparisons of standardized mean differences between two treatments. Multivariate methods are presented for the case in which effect size is a vector of standardized multivariate mean differences and the number of treatment groups is two or more. The proposed methods employ a vector of independent sample means for each response variable that leads to a covariance structure which depends only on correlations among the $p$ responses on each subject. Using weighted least squares theory and the assumption that the observations are from normally distributed populations, multivariate hypotheses analogous to common hypotheses used for testing effect sizes were formulated and tested for treatment effects which are correlated through a common control group, through multiple response variables observed on each subject, or both conditions.^ The asymptotic multivariate distribution for correlated effect sizes is obtained by extending univariate methods for estimating effect sizes which are correlated through common control groups. The joint distribution of vectors of effect sizes (from $p$ responses on each subject) from one treatment and one control group and from several treatment groups sharing a common control group are derived. Methods are given for estimation of linear combinations of effect sizes when certain homogeneity conditions are met, and for estimation of vectors of effect sizes and confidence intervals from $p$ responses on each subject. Computational illustrations are provided using data from studies of effects of electric field exposure on small laboratory animals. ^

Selection of body fat distribution indices in adults and associations with plasma lipid metabolism variables

Body fat distribution is a cardiovascular health risk factor in adults. Body fat distribution can be measured through various methods including anthropometry. It is not clear which anthropometric index is suitable for epidemiologic studies of fat distribution and cardiovascular disease. The purpose of the present study was to select a measure of body fat distribution from among a series of indices (those traditionally used in the literature and others constructed from the analysis) that is most highly correlated with lipid-related variables and is independent of overall fatness. Subjects were Mexican-American men and women (N = 1004) from a study of gallbladder disease in Starr County, Texas. Multivariate associations were sought between lipid profile measures (lipids, lipoproteins, and apolipoproteins) and two sets of anthropometric variables (4 circumferences and 6 skinfolds). This was done to assess the association between lipid-related measures and the two sets of anthropometric variables and guide the construction of indices.^ Two indices emerged from the analysis that seemed to be highly correlated with lipid profile measures independent of obesity. These indices are: 2*arm circumference-thigh skinfold in pre- and post-menopausal women and arm/thigh circumference ratio in men. Next, using the sum of all skinfolds to represent obesity and the selected body fat distribution indices, the following hypotheses were tested: (1) state of obesity and centrally/upper distributed body fat are equally predictive of lipids, lipoproteins and apolipoproteins, and (2) the correlation among the lipid-related measures is not altered by obesity and body fat distribution.^ With respect to the first hypothesis, the present study found that most lipids, lipoproteins and apolipoproteins were significantly associated with both overall fatness and anatomical location of body fat in both sex and menopausal groups. However, within men and post-menopausal women, certain lipid profile measures (triglyceride and HDLT among post-menopausal women and apos C-II, CIII, and E among men) had substantially higher correlation with body fat distribution as compared with overall fatness.^ With respect to the second hypothesis, both obesity and body fat distribution were found to alter the association among plasma lipid variables in men and women. There was a suggestion from the data that the pattern of correlations among men and post-menopausal women are more comparable. Among men correlations involving apo A-I, HDLT, and HDL$\sb2$ seemed greatly influenced by obesity, and A-II by fat distribution; among post-menopausal women correlations involving apos A-I and A-II were highly affected by the location of body fat.^ Thus, these data point out that not only can obesity and fat distribution affect levels of single measures, they also can markedly influence the pattern of relationship among measures. The fact that such changes are seen for both obesity and fat distribution is significant, since the indices employed were chosen because they were independent of one another. ^

Comparison of Tumor Shrinkage and Cumulative Dose Distribution for Lung Cancers

Background: The physical characteristic of protons is that they deliver most of their radiation dose to the target volume and deliver no dose to the normal tissue distal to the tumor. Previously, numerous studies have shown unique advantages of proton therapy over intensity-modulated radiation therapy (IMRT) in conforming dose to the tumor and sparing dose to the surrounding normal tissues and the critical structures in many clinical sites. However, proton therapy is known to be more sensitive to treatment uncertainties such as inter- and intra-fractional variations in patient anatomy. To date, no study has clearly demonstrated the effectiveness of proton therapy compared with the conventional IMRT under the consideration of both respiratory motion and tumor shrinkage in non-small cell lung cancer (NSCLC) patients. Purpose: This thesis investigated two questions for establishing a clinically relevant comparison of the two different modalities (IMRT and proton therapy). The first question was whether or not there are any differences in tumor shrinkage between patients randomized to IMRT versus passively scattered proton therapy (PSPT). Tumor shrinkage is considered a standard measure of radiation therapy response that has been widely used to gauge a short-term progression of radiation therapy. The second question was whether or not there are any differences between the planned dose and 5D dose under the influence of inter- and intra-fractional variations in the patient anatomy for both modalities. Methods: A total of 45 patients (25 IMRT patients and 20 PSPT patients) were used to quantify the tumor shrinkage in terms of the change of the primary gross tumor volume (GTVp). All patients were randomized to receive either IMRT or PSPT for NSCLC. Treatment planning goals were identical for both groups. All patients received 5 to 8 weekly repeated 4-dimensional computed tomography (4DCT) scans during the course of radiation treatments. The original GTVp contours were propagated to T50 of weekly 4DCT images using deformable image registration and their absolute volumes were measured. Statistical analysis was performed to compare the distribution of tumor shrinkage between the two population groups. In order to investigate the difference between the planned dose and the 5D dose with consideration of both breathing motion and anatomical change, we re-calculated new dose distributions at every phase of the breathing cycle for all available weekly 4DCT data sets which resulted 50 to 80 individual dose calculations for each of the 7 patients presented in this thesis. The newly calculated dose distributions were then deformed and accumulated to T50 of the planning 4DCT for comparison with the planned dose distribution. Results: At the end of the treatment, both IMRT and PSPT groups showed mean tumor volume reductions of 23.6% ( 19.2%) and 20.9% ( 17.0 %) respectively. Moreover, the mean difference in tumor shrinkage between two groups is 3% along with the corresponding 95% confidence interval, [-8%, 14%]. The rate of tumor shrinkage was highly correlated with the initial tumor volume size. For the planning dose and 5D dose comparison study, all 7 patients showed a mean difference of 1 % in terms of target coverage for both IMRT and PSPT treatment plans. Conclusions: The results of the tumor shrinkage investigation showed no statistically significant difference in tumor shrinkage between the IMRT and PSPT patients, and the tumor shrinkage between the two modalities is similar based on the 95% confidence interval. From the pilot study of comparing the planned dose with the 5D dose, we found the difference to be only 1%. Overall impression of the two modalities in terms of treatment response as measured by the tumor shrinkage and 5D dose under the influence of anatomical change that were designed under the same protocol (i.e. randomized trial) showed similar result.

An individual based model spatial distribution, production and biomass for Calanus finmarchicus in the Norwegian Sea

The copepod Calanus finmarchicus is the dominant species of the meso-zooplankton in the Norwegian Sea, and constitutes an important link between the phytoplankton and the higher trophic levels in the Norwegian Sea food chain. An individualbased model for C. finmarchicus, based on super-individuals and evolving traits for behaviour, stages, etc., is two-way coupled to the NORWegian ECOlogical Model system (NORWECOM). One year of modelled C. finmarchicus spatial distribution, production and biomass are found to represent observations reasonably well. High C. finmarchicus abundance is found along the Norwegian shelf-break in the early summer, while the overwintering population is found along the slope and in the deeper Norwegian Sea basins. The timing of the spring bloom is generally later than in the observations. Annual Norwegian Sea production is found to be 29 million tonnes of carbon and a production to biomass (P/B) ratio of 4.3 emerges. Sensitivity tests show that the modelling system is robust to initial values of behavioural traits and with regards to the number of super-individuals simulated given that this is above about 50,000 individuals. Experiments with the model system indicate that it provides a valuable tool for studies of ecosystem responses to causative forces such as prey density or overwintering population size. For example, introducing C. finmarchicus food limitations reduces the stock dramatically, but on the other hand, a reduced stock may rebuild in one year under normal conditions. The NetCDF file contains model grid coordinates and bottom topography.

Distribution of abundance of planktic foraminifera and calcareous nannofossils at DSDP Sites 17-167 and 62-463

New paleomagnetic and paleontologic data from Pacific DSDP Sites 463 and 167 define the magnetic reversals that predate the Cretaceous Normal Polarity Superchron (K-N). Data from Mid-Pacific Mountain Site 463 provide the first definition of polarity chron M0 in the Pacific deep-sea sedimentary record. Foraminiferal biostratigraphy suggests that polarity chron M0 is contained entirely within the lower Aptian Hedbergella similis Zone, in agreement with foraminiferal data from the Italian Southern Alps and Atlantic Ocean. Nannofossil assemblages also suggest an early Aptian age for polarity chron M0, contrary to results from the Italian Umbrian Apennines and Southern Alps, which place polarity chron M0 on the Barremian-Aptian boundary. Biostratigraphic dating discrepancies caused by the time-transgressive, preservational, or provincial nature of paleontological species might be reconciled by the use of magnetostratigraphy, specifically polarity chron M0 which lies close to the Barremian-Aptian boundary. At Magellan Rise Site 167, five reversed polarity zones are recorded in Hauterivian to Aptian sediments. Correlation with M-anomalies is complicated by synsedimentary and postsedimentary sliding about 25 m.y. after basement formation, producing gaps in, and duplications of, the stratigraphic sequence. The magnitude and timing of such sliding must be addressed when evaluating the stratigraphy of these oceanic-rise environments.

Distribution of benthos in late Quaternary turbidite layers of sediment cores from the North-West African continental margin

The CaCO3-contents and the fractions > 40 µm have been analysed from 5 kastenloten, one piston core and two kastengreifer taken between Senegal and Cape Verde Islands. Numerous benthonic and planktonic organisms and different terrigenous components have been distinguished. The four cores off Senegal reach middle Wuerm sediments; cores GIK12329-6 and TAG72-1 reach the V-zone and core GIK12331-4 the X-zone (Eem); the two kastengreifer contain sediments of Holocene age. Correlation of the cores has been made. Holocene sedimentation rates decrease from the shallow cores (6-11 cm/1000 years) to the deep-sea (1-2 cm/1000 years). The following climatic variations could be deduced from the sediments off the Senegal: during Holocene climate was in general as today, the Senegal river transporting fine grained material to the sea. The upper Wuerm was arid with no river influence but with red dune sand transported to the continental slope. During middle Wuerm the climate was humid again. The deep-sea cores have been influenced by eolian material from arid regions during glacial and interglacial periods, indicated by relatively high "Wuestenquarz-numbers". However, during Wuerm "Wuestenquarz-numbers" are higher than during Holocene and Eem, indicating that more intensely red coloured sediment was exposed to wind activity on the continent during this period. Varying amounts of terrigenous material and CaCO3-contents indicate varying wind strengths (lower in Holocene and Eem than during Wuerm). The boundary between humid and arid Wuerm climate was at approximately 20 °N. Influence of upwelling is difficult to establish in the sediments off Senegal, because river influence, while increasing fertility also dilutes the diatoms which are typical for upwelling. High amounts of organic carbon, low plankton/benthos ratios of foraminifers and low plankton foraminifer/radiolarian ratios in Holocene sections might be interpreted as influenced by upwelling. Turbidites occur in cores 72 and 31 and at the Holocene/Pleistocene boundary of core GIK12329-6. Their composition indicates provenance from the continental shelf of the Cape Verde Islands for core 31 and the continental shelf and slope off Senegal for core TAG72-1. Volcanic material, rare in the normal pelagic sediment of core GIK12331-4 is more frequent in the turbidites.

Making genetic biodiversity measurable : a review of statistical multivariate methods to study variability at gene level

Measures of agro-ecosystems genetic variability are essential to sustain scientific-based actions and policies tending to protect the ecosystem services they provide. To build the genetic variability datum it is necessary to deal with a large number and different types of variables. Molecular marker data is highly dimensional by nature, and frequently additional types of information are obtained, as morphological and physiological traits. This way, genetic variability studies are usually associated with the measurement of several traits on each entity. Multivariate methods are aimed at finding proximities between entities characterized by multiple traits by summarizing information in few synthetic variables. In this work we discuss and illustrate several multivariate methods used for different purposes to build the datum of genetic variability. We include methods applied in studies for exploring the spatial structure of genetic variability and the association of genetic data to other sources of information. Multivariate techniques allow the pursuit of the genetic variability datum, as a unifying notion that merges concepts of type, abundance and distribution of variability at gene level.

(Table 2) Distribution of alkenone unsaturation index UK37 of the eastern North Atlantic

This paper reports the concentrations and within-class distributions of long-chain alkenones and alkyl alkenoates in the surface waters (0-50 m) of the eastern North Atlantic, and correlates their abundance and distribution with those of source organisms and with water temperature and other environmental variables. We collected these samples of >0.8 µm particulate material from the euphotic zone along the JGOFS 20°W longitude transect, from 61°N to 24°N, during seven cruises of the UK-JGOFS Biogeochemical Ocean Flux Study (BOFS) in 1989-1991; the biogeographical range of our 53 samples extends from the cold (<10°C), nutrient-rich and highly productive subarctic waters of the Iceland Basin to the warm (>25°C) oligotrophic subtropical waters off Africa. Surface water concentrations of total alkenone and alkenoates ranged from <50 ng/l in oligotrophic waters below 40°N to 2000-4500 ng/l in high latitude E. huxleyi blooms, and were well correlated with E. huxleyi cell densities, supporting the assumption that E. huxleyi is the predominant source of these compounds in the present day North Atlantic. The within-class distribution of the C37 and C38 alkenones and C36 alkenoates varied strongly as a function of temperature, and was largely unaffected by nutrient concentration, bloom status and other surface water properties. The biosynthetic response of the source organisms to growth temperature differed between the cold (<16°C) waters above 47°N and the warmer waters to the south. In cold (<16°C) waters above 47°N, the relative amounts of alkenoates and C38 alkenones synthesized was a strong function of growth temperature, while the unsaturation ratio of the alkenones (C37 and C38) was uncorrelated with temperature. Conversely, in warm (>16°C) waters below 47°N, the relative proportions of alkenoates and alkenones synthesized remained constant with increasing temperature while the unsaturation ratios of the C37 and C38 methyl alkenones (Uk37 and Uk38Me, respectively) increased linearly. The fitted regressions of Uk37 and Uk38Me versus temperature for waters >16°C were both highly significant (r**2 > 0.96) and had identical slopes (0.057) that were 50% higher than the slope (0.034) of the temperature calibration of Uk37 reported by Prahl and Wakeham (1987; doi:10.1038/330367a0) over the same temperature range. These observations suggest either a physiological adjustment in biochemical response to growth temperature above a 16-17°C threshold and/or variation between different E. huxleyi strains and/or related species inhabiting the cold and warm water regions of the eastern North Atlantic. Using our North Atlantic data set, we have produced multivariate temperature calibrations incorporating all major features of the alkenone and alkenoate data set. Predicted temperatures using multivariate calibrations are largely unbiased, with a standard error of approximately ±1°C over the entire data range. In contrast, simpler calibration models cannot adequately incorporate regional diversity and nonlinear trends with temperature. Our results indicate that calibrations based upon single variables, such as Uk37, can be strongly biased by unknown systematic errors arising from natural variability in the biosynthetic response of the source organisms to growth temperature. Multivariate temperature calibration can be expected to give more precise estimates of Integrated Production Temperatures (IPT) in the sedimentary record over a wider range of paleoenvironmental conditions, when derived using a calibration data set incorporating a similar range of natural variability in biosynthetic response.

Environmental variables and multivariate seabed classification maps via k means clustering of Potter Cove, Antarctica, link to input and result files in GeoTIFF format

This study subdivides the Potter Cove, King George Island, Antarctica, into seafloor regions using multivariate statistical methods. These regions are categories used for comparing, contrasting and quantifying biogeochemical processes and biodiversity between ocean regions geographically but also regions under development within the scope of global change. The division obtained is characterized by the dominating components and interpreted in terms of ruling environmental conditions. The analysis includes in total 42 different environmental variables, interpolated based on samples taken during Australian summer seasons 2010/2011 and 2011/2012. The statistical errors of several interpolation methods (e.g. IDW, Indicator, Ordinary and Co-Kriging) with changing settings have been compared and the most reasonable method has been applied. The multivariate mathematical procedures used are regionalized classification via k means cluster analysis, canonical-correlation analysis and multidimensional scaling. Canonical-correlation analysis identifies the influencing factors in the different parts of the cove. Several methods for the identification of the optimum number of clusters have been tested and 4, 7, 10 as well as 12 were identified as reasonable numbers for clustering the Potter Cove. Especially the results of 10 and 12 clusters identify marine-influenced regions which can be clearly separated from those determined by the geological catchment area and the ones dominated by river discharge.