Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Psychometric properties of the French version of the Zuckerman-Kuhlman Personality Questionnaire

This instrumental study was designed to investigate the psychometric properties of the French version and the cross-language replicability of the Zuckerman-Kuhlman Personality Questionnaire (ZKPQ) at the factor- and at the facet-level. The ZKPQ is an instrument aimed at assessing the five basic factors of Zuckerman's Alternative Five-Factor Model (AFFM). Subjects were 843 French-speaking Swiss, mainly students. At the factor-level, the reliability ranged from .73 to .87 and at the facet level, the reliability ranged from .57 to .77. Differences between genders are congruent with those found in the American sample. Women scored higher on N-Anx, and lower on ImpSS, and Act. A series of exploratory factor analyses supported the overall five-factor structure and the structure at the facet-level. The correlations among the scales support that the five basic factors of the AFFM are orthogonal. Targeted factor analyses and congruence coefficients show high cross-language replicability at the factor- and at the facet-level. The adequacy of the model at the factor- and facet-level was tested using confirmatory factor analyses. The results show that the French version of the ZKPQ is a reliable and valid instrument and has a high cross-language replicability.

Economic growth and inequality: the role of fiscal policies

This paper analyses the impact of different instruments of fiscal policy on economic growth as well as on income inequality, using an unbalanced panel of 43 upper-middle and high income countries for the period 1972-2006. We consider and estimate two individual equations explaining growth and inequality in order to assess the incidence of different fiscal policies. Firstly, our approach considers imposing orthogonal assumptions between growth and inequality in both equations, and secondly, it allows growth to be included in the inequality equation, and inequality to be included in the growth equation. The empirical results suggest that an increase in the size of government measured through current expenditures and direct taxes diminishes economic growth while reducing inequality, being public investment the only fiscal policy that may break this trade-off between efficiency and equity, since increases in this item reduces inequality without harming output. Therefore, the results reflect that the trade-off between efficiency and equity that governments often confront when designing their fiscal policies may be avoided.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.

Inexperienced sonographers can successfully visualize and assess a three-dimensional image of the fetal face using a standardized ultrasound protocol

Introduction: A standardized three-dimensional ultrasonographic (3DUS) protocol is described that allows fetal face reconstruction. Ability to identify cleft lip with 3DUS using this protocol was assessed by operators with minimal 3DUS experience. Material and Methods: 260 stored volumes of fetal face were analyzed using a standardized protocol by operators with different levels of competence in 3DUS. The outcomes studied were: (1) the performance of post-processing 3D face volumes for the detection of facial clefts; (2) the ability of a resident with minimal 3DUS experience to reconstruct the acquired facial volumes, and (3) the time needed to reconstruct each plane to allow proper diagnosis of a cleft. Results: The three orthogonal planes of the fetal face (axial, sagittal and coronal) were adequately reconstructed with similar performance when acquired by a maternal-fetal medicine specialist or by residents with minimal experience (72 vs. 76%, p = 0.629). The learning curve for manipulation of 3DUS volumes of the fetal face corresponds to 30 cases and is independent of the operator's level of experience. Discussion: The learning curve for the standardized protocol we describe is short, even for inexperienced sonographers. This technique might decrease the length of anatomy ultrasounds and improve the ability to visualize fetal face anomalies.

Perfusion measurement in brain gliomas with intravoxel incoherent motion MRI.

BACKGROUND AND PURPOSE: Intravoxel incoherent motion MRI has been proposed as an alternative method to measure brain perfusion. Our aim was to evaluate the utility of intravoxel incoherent motion perfusion parameters (the perfusion fraction, the pseudodiffusion coefficient, and the flow-related parameter) to differentiate high- and low-grade brain gliomas. MATERIALS AND METHODS: The intravoxel incoherent motion perfusion parameters were assessed in 21 brain gliomas (16 high-grade, 5 low-grade). Images were acquired by using a Stejskal-Tanner diffusion pulse sequence, with 16 values of b (0-900 s/mm(2)) in 3 orthogonal directions on 3T systems equipped with 32 multichannel receiver head coils. The intravoxel incoherent motion perfusion parameters were derived by fitting the intravoxel incoherent motion biexponential model. Regions of interest were drawn in regions of maximum intravoxel incoherent motion perfusion fraction and contralateral control regions. Statistical significance was assessed by using the Student t test. In addition, regions of interest were drawn around all whole tumors and were evaluated with the help of histograms. RESULTS: In the regions of maximum perfusion fraction, perfusion fraction was significantly higher in the high-grade group (0.127 ± 0.031) than in the low-grade group (0.084 ± 0.016, P < .001) and in the contralateral control region (0.061 ± 0.011, P < .001). No statistically significant difference was observed for the pseudodiffusion coefficient. The perfusion fraction correlated moderately with dynamic susceptibility contrast relative CBV (r = 0.59). The histograms of the perfusion fraction showed a "heavy-tailed" distribution for high-grade but not low-grade gliomas. CONCLUSIONS: The intravoxel incoherent motion perfusion fraction is helpful for differentiating high- from low-grade brain gliomas.

Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte

CoDa-dendrogram: A new exploratory too

The use of orthonormal coordinates in the simplex and, particularly, balance coordinates, has suggested the use of a dendrogram for the exploratory analysis of compositional data. The dendrogram is based on a sequential binary partition of a compositional vector into groups of parts. At each step of a partition, one group of parts isdivided into two new groups, and a balancing axis in the simplex between both groupsis defined. The set of balancing axes constitutes an orthonormal basis, and the projections of the sample on them are orthogonal coordinates. They can be represented in adendrogram-like graph showing: (a) the way of grouping parts of the compositional vector; (b) the explanatory role of each subcomposition generated in the partition process;(c) the decomposition of the total variance into balance components associated witheach binary partition; (d) a box-plot of each balance. This representation is useful tohelp the interpretation of balance coordinates; to identify which are the most explanatory coordinates; and to describe the whole sample in a single diagram independentlyof the number of parts of the sample

Compositional analysis of bivariate discrete probabilities

A joint distribution of two discrete random variables with finite support can be displayed as a two way table of probabilities adding to one. Assume that this table hasn rows and m columns and all probabilities are non-null. This kind of table can beseen as an element in the simplex of n · m parts. In this context, the marginals areidentified as compositional amalgams, conditionals (rows or columns) as subcompositions. Also, simplicial perturbation appears as Bayes theorem. However, the Euclideanelements of the Aitchison geometry of the simplex can also be translated into the tableof probabilities: subspaces, orthogonal projections, distances.Two important questions are addressed: a) given a table of probabilities, which isthe nearest independent table to the initial one? b) which is the largest orthogonalprojection of a row onto a column? or, equivalently, which is the information in arow explained by a column, thus explaining the interaction? To answer these questionsthree orthogonal decompositions are presented: (1) by columns and a row-wise geometric marginal, (2) by rows and a columnwise geometric marginal, (3) by independenttwo-way tables and fully dependent tables representing row-column interaction. Animportant result is that the nearest independent table is the product of the two (rowand column)-wise geometric marginal tables. A corollary is that, in an independenttable, the geometric marginals conform with the traditional (arithmetic) marginals.These decompositions can be compared with standard log-linear models.Key words: balance, compositional data, simplex, Aitchison geometry, composition,orthonormal basis, arithmetic and geometric marginals, amalgam, dependence measure,contingency table

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Gap probabilities for the cardinal sine

We study the zero set of random analytic functions generated by a sum of the cardinal sine functions which form an orthogonal basis for the Paley-Wiener space. As a model case, we consider real-valued Gaussian coefficients. It is shown that the asymptotic probability that there is no zero in a bounded interval decays exponentially as a function of the length.

How to confirm C.E.R.A. doping in athletes' blood?

C.E.R.A. (Continuous Erythropoietin Receptor Activator) is a new third-generation erythropoiesis-stimulating agent that has recently been linked with abuse in endurance sports. The anti-doping community rapidly reacted by releasing a high-throughput screening ELISA allowing the detection of C.E.R.A. doping in athletes' blood. In order to return adverse analytical findings, anti-doping laboratories, however, need, as far as possible, to confirm the presence of the drug in athletes' samples through orthogonal methods. This article focuses on the comparison of 2 proposed confirmation assays based on gel electrophoresis that were coupled with a new sample immunopurification method. IEF, the classical method used to target erythropoietin (EPO) and its recombinant analogues in athletes' samples, and SARKOSYL-PAGE were applied to the plasma samples of subjects having received a single injection of C.E.R.A. It was demonstrated that SARKOSYL-PAGE was at least 6 times more sensitive than IEF, with comparable specificity. A longer detection window coupled with easier interpretation criteria led us to recommend the use of SARKOSYL-PAGE to confirm C.E.R.A. presence in athletes' blood.

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing modelsbetween end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework.We present here a possible solution based on factor analysis of compositions illustrated with a case study.We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables thatlay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hiddencomponents, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members.We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained totalvariance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphicalrepresentation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysisof diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, exceptfertilisers due to the heterogeneity of their composition.This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations areintrinsic to the relative nature of compositional data

Magnetic and in vitro heating properties of implants formed in situ from injectable formulations and containing superparamagnetic iron oxide nanoparticles (SPIONs) embedded in silica microparticles for magnetically induced local hyperthermia

The biological and therapeutic responses to hyperthermia, when it is envisaged as an anti-tumor treatment modality, are complex and variable. Heat delivery plays a critical role and is counteracted by more or less efficient body cooling, which is largely mediated by blood flow. In the case of magnetically mediated modality, the delivery of the magnetic particles, most often superparamagnetic iron oxide nanoparticles (SPIONs), is also critically involved. We focus here on the magnetic characterization of two injectable formulations able to gel in situ and entrap silica microparticles embedding SPIONs. These formulations have previously shown suitable syringeability and intratumoral distribution in vivo. The first formulation is based on alginate, and the second on a poly(ethylene-co-vinyl alcohol) (EVAL). Here we investigated the magnetic properties and heating capacities in an alternating magnetic field (141 kHz, 12 mT) for implants with increasing concentrations of magnetic microparticles. We found that the magnetic properties of the magnetic microparticles were preserved using the formulation and in the wet implant at 37 degrees C, as in vivo. Using two orthogonal methods, a common SLP (20 Wg(-1)) was found after weighting by magnetic microparticle fraction, suggesting that both formulations are able to properly carry the magnetic microparticles in situ while preserving their magnetic properties and heating capacities. (C) 2010 Elsevier B.V. All rights reserved.

Line bisection by eye and by hand reveal opposite biases

The vision-for-action literature favours the idea that the motor output of an action - whether manual or oculomotor - leads to similar results regarding object handling. Findings on line bisection performance challenge this idea: healthy individuals bisect lines manually to the left of centre, and to the right of centre when using eye fixation. In case that these opposite biases for manual and oculomotor action reflect more universal compensatory mechanisms that cancel each other out to enhance overall accuracy, one would like to observe comparable opposite biases for other material. In the present study, we report on three independent experiments in which we tested line bisection (by hand, by eye fixation) not only for solid lines, but also for letter lines; the latter, when bisected manually, is known to result in a rightward bias. Accordingly, we expected a leftward bias for letter lines when bisected via eye fixation. Analysis of bisection biases provided evidence for this idea: manual bisection was more rightward for letter as compared to solid lines, while bisection by eye fixation was more leftward for letter as compared to solid lines. Support for the eye fixation observation was particularly obvious in two of the three studies, for which comparability between eye and hand action was increasingly adjusted (paper-pencil versus touch screen for manual action). These findings question the assumption that ocular motor and manual output are always inter-changeable, but rather suggest that at least for some situations ocular motor and manual output biases are orthogonal to each other, possibly balancing each other out.