978 resultados para Exponential Sum


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Arenaviruses are a large and diverse family of viruses that merit significant attention as causative agents of severe hemorrhagic fevers in humans. Lassa virus (LASV) in Africa and the South American hemorrhagic fever viruses Junin (JUNV), Machupo (MACV), and Guanarito (GTOV) have emerged as important human pathogens and represent serious public health problems in their respective endemic areas. A hallmark of fatal arenaviruses hemorrhagic fevers is a marked immunosuppression of the infected patients. Antigen presenting cells (APCs) such as macrophages and in particular dendritic cells (DCs) are early and preferred targets of arenaviruses infection. Instead of being recognized and presented as foreign antigens by DCs, arenaviruses subvert the normal mechanisms of pathogen recognition, invade DCs and establish a productive infection. Viral replication perturbs the DCs' ability to present antigens and to activate T and B cells, contributing to the marked virus-induced immunosuppression observed in fatal disease. Considering their crucial role in the development of an anti-viral immune response, the mechanisms by which arenaviruses, and in particular LASV, invade DCs are of particular interest. The C-type lectin DC-specific Intercellular adhesion molecule-3-grabbing nonintegrin (DC-SIGN) was recently identified as a potential entry receptor for LASV. The first project of my thesis focused therefore on the investigation of the role of DC-SIGN in LASV entry into primary human DCs. My data revealed that DC-SIGN serves as an attachment factor for LASV on human DCs and can facilitate capture of free virus and subsequent cell entry. However, in contrast to other emerging viruses, of the phlebovirus family, I found that DC-SIGN does likely not function as an authentic entry receptor for LASV. Moreover, I was able to show that LASV enters DCs via an unusually slow pathway that depends on actin, but is independent of clathrin and dynamin. Considering the lack of effective treatments and the limited public health infrastructure in endemic regions, the development of protective vaccines against arenaviruses is an urgent need. To address this issue, the second project of my thesis aimed at the development of a novel recombinant arenavirus vaccine based on a nanoparticle (NPs) platform and its evaluation in a small animal model. During the first phase of the project I designed, produced, and characterized suitable vaccine antigens. In the second phase of the project, I generated antigen-conjugated NPs, developed vaccine formulations, and tested the NPs for their ability to elicit anti-viral T cell responses as well as anti-viral antibodies. I demonstrated that the NPs platform is able to activate both cellular and humoral branches of the adaptive anti-viral immunity, providing proof-of-principle. In sum, my first project will allow, in a long term perspective, a better understanding of the viral pathogenesis and contribute to the development of novel antiviral strategies. The second project will expectidly offer a new treatment option against arenaviruses.

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To measure the contribution of individual transactions inside the total risk of a credit portfolio is a major issue in financial institutions. VaR Contributions (VaRC) and Expected Shortfall Contributions (ESC) have become two popular ways of quantifying the risks. However, the usual Monte Carlo (MC) approach is known to be a very time consuming method for computing these risk contributions. In this paper we consider the Wavelet Approximation (WA) method for Value at Risk (VaR) computation presented in [Mas10] in order to calculate the Expected Shortfall (ES) and the risk contributions under the Vasicek one-factor model framework. We decompose the VaR and the ES as a sum of sensitivities representing the marginal impact on the total portfolio risk. Moreover, we present technical improvements in the Wavelet Approximation (WA) that considerably reduce the computational effort in the approximation while, at the same time, the accuracy increases.

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Report for the scientific sojourn carried out at the Darmouth College, from august 2007 until february 2008. It has been very successful, from different viewpoints: scientific, philosophical, human. We have definitely advanced, during the past six months, towards the comprehension of the behaviour of the fluctuations of the quantum vacuum in the presence of boundaries, moving and non-moving, and also in situations where the topology of space-time changes: the dynamical Casimir effect, regularization problems, particle creation statistics, according to different BC, etc. We have solved some longstanding problems and got in this subject quite remarkable results (as we will explain in more detail below). We also pursued a general approach towards a viable modified f(R) gravity in both the Jordan and the Einstein frames (which are known to be mathematically equivalent, but physically not so). A class of exponential, realistic modified gravities has been introduced by us and investigated with care. Special focus was made on step-class models, most promising from the phenomenological viewpoint and which provide a natural way to classify all viable modified gravities. One- and two-steps models were considered, but the analysis is extensible to N-step models. Both inflation in the early universe and the onset of recent accelerated expansion arise in these models in a natural, unified way, what makes them very promising. Moreover, it is monstrated in our work that models in this category easily pass all local tests, including stability of spherical body solution, non-violation of Newton's law, and generation of a very heavy positive mass for the additional scalar degree of freedom.

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ICEclc is a mobile genetic element found in two copies on the chromosome of the bacterium Pseudomonas knackmussii B13. ICEclc harbors genes encoding metabolic pathways for the degradation of chlorocatechols (CLC) and 2-aminophenol (2AP). At low frequencies, ICEclc excises from the chromosome, closes into a circular DNA molecule which can transfer to another bacterium via conjugation. Once in the recipient cell, ICEclc can reintegrate into the chromosome by site-specific recombination. This thesis aimed at identifying the regulatory network underlying the decisions for ICEclc horizontal transfer (HGT). The first chapter is an introduction on integrative and conjugative elements (ICEs) more in general, of which ICEclc is one example. In particular I emphasized the current knowledge of regulation and conjugation machineries of the different classes of ICE. In the second chapter, I describe a transcriptional analysis using microarrays and other experiments to understand expression of ICEclc in exponential and stationary phase. By overlaying transcriptomic profiles with Northern hybridizations and RT- PCR data, we established a transcription map for the entire core region of ICEclc, a region assumed to encode the ICE conjugation process. We also demonstrated how transcription of the ICEclc core is maximal in stationary phase, which correlates to expression of reporter genes fused to key ICEclc promoters. In the third chapter, I present a transcriptome analysis of ICEclc in a variety of different host species, in order to explore whether there are species-specific differences. In the fourth chapter, I focus on the role of a curious ICEclc-encoded TetR-type transcriptional repressor. We find that this gene, which we name mfsR, not only controls its own expression but that of a set of genes for a putative multi-drug efflux pump (mfsABC) as well. By using a combination of biochemical and molecular biology techniques, I could show that MfsR specifically binds to operator boxes in two ICEclc promoters (PmfsR and PmfsA), inhibiting the transcription of both the mfsR and mfsABC-orf38184 operons. Although we could not detect a clear phenotype of an mfsABC deletion, we discuss the implications of pump gene reorganizations in ICEclc and close relatives. In the fifth chapter, we find that mfsR not only controls its own expression and that of the mfsABC operon, but is also indirectly controlling ICEclc transfer. Using gene deletions, microarrays, transfer assays and microscopy-based reporter fusions, we demonstrate that mfsR actually controls a small operon of three regulatory genes. The last gene of this mfsR operon, orf17162, encodes a LysR-type activator that when deleted strongly impairs ICEclc transfer. Interestingly, deletion of mfsR leads to transfer competence in almost all cells, thereby overruling the bistability process in the wild-type. In the final sixth chapter, I discuss the relevance of the present thesis and the resulting perspectives for future studies.

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BACKGROUND: Greater tobacco smoking and alcohol consumption and lower body mass index (BMI) increase odds ratios (OR) for oral cavity, oropharyngeal, hypopharyngeal, and laryngeal cancers; however, there are no comprehensive sex-specific comparisons of ORs for these factors. METHODS: We analyzed 2,441 oral cavity (925 women and 1,516 men), 2,297 oropharynx (564 women and 1,733 men), 508 hypopharynx (96 women and 412 men), and 1,740 larynx (237 women and 1,503 men) cases from the INHANCE consortium of 15 head and neck cancer case-control studies. Controls numbered from 7,604 to 13,829 subjects, depending on analysis. Analyses fitted linear-exponential excess ORs models. RESULTS: ORs were increased in underweight (<18.5 BMI) relative to normal weight (18.5-24.9) and reduced in overweight and obese categories (>/=25 BMI) for all sites and were homogeneous by sex. ORs by smoking and drinking in women compared with men were significantly greater for oropharyngeal cancer (p < 0.01 for both factors), suggestive for hypopharyngeal cancer (p = 0.05 and p = 0.06, respectively), but homogeneous for oral cavity (p = 0.56 and p = 0.64) and laryngeal (p = 0.18 and p = 0.72) cancers. CONCLUSIONS: The extent that OR modifications of smoking and drinking by sex for oropharyngeal and, possibly, hypopharyngeal cancers represent true associations, or derive from unmeasured confounders or unobserved sex-related disease subtypes (e.g., human papillomavirus-positive oropharyngeal cancer) remains to be clarified.

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Desde el inicio del proyecto del genoma humano y su éxito en el año 2001 se han secuenciado genomas de multitud de especies. La mejora en las tecnologías de secuenciación ha generado volúmenes de datos con un crecimiento exponencial. El proyecto Análisis bioinformáticos sobre la tecnología Hadoop abarca la computación paralela de datos biológicos como son las secuencias de ADN. El estudio ha sido encauzado por la naturaleza del problema a resolver. El alineamiento de secuencias genéticas con el paradigma MapReduce.

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PURPOSE: The aim of this study was to compare VO2 kinetics during constant power cycle exercise measured using a conventional facemask (CM) or a respiratory snorkel (RS) designed for breath-by-breath analysis in swimming. METHODS: VO2 kinetics parameters-obtained using CM or RS, in randomized counterbalanced order-were compared in 10 trained triathletes performing two submaximal heavy-intensity cycling square-wave transitions. These VO2 kinetics parameters (ie, time delay: td1, td2; time constant: τ1, τ2; amplitude: A1, A2, for the primary phase and slow component, respectively) were modeled using a double exponential function. In the case of the RS data, this model incorporated an individually determined snorkel delay (ISD). RESULTS: Only td1 (8.9 ± 3.0 vs 13.8 ± 1.8 s, P < .01) differed between CM and RS, whereas all other parameters were not different (τ1 = 24.7 ± 7.6 vs 21.1 ± 6.3 s; A1 = 39.4 ± 5.3 vs 36.8 ± 5.1 mL x min(-1) x kg(-1); td2 = 107.5 ± 87.4 vs 183.5 ± 75.9 s; A2' (relevant slow component amplitude) = 2.6 ± 2.4 vs 3.1 ± 2.6 mL x min(-1) x kg(-1) for CM and RS, respectively). CONCLUSIONS: Although there can be a small mixture of breaths allowed by the volume of the snorkel in the transition to exercise, this does not appear to significantly influence the results. Therefore, given the use of an ISD, the RS is a valid instrument for the determination of VO2 kinetics within submaximal exercise.

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The synthesis of poly(RboP), the main Bacillus subtilis W23 teichoic acid, is encoded by tarDF-tarABIJKL operons, the latter being controlled by two promoters designated PtarA-int and PtarA-ext. Analysis by lacZ fusions reveals that PtarA-int activity exhibits sharp increases at the beginning and end of the transition between exponential and stationary growth phase. As confirmed by mRNA quantification, these increases are mediated by ECF sigma factors sigmaX and sigmaM respectively. In liquid media, strain W23 sigX sigM double mutants experience serious difficulties in the transition and stationary growth phases. Inactivation of sigmaX- and sigmaM-controlled regulons, which precludes transcription from PtarA-int, leads to (i) delays in chromosome segregation and septation and (ii) a transient loss of up to 30% of the culture OD or lysis. However, specific inactivation of PtarA-int, leading mainly to a shortage of poly(RboP), does not affect growth while, nevertheless, interfering with normal septation, as revealed by electron microscopy. The different sigM transcription in strains W23 and 168 is discussed. In W23, expression of tarA and sigM, which is shown to control divIC, is inversely correlated with growth rate, suggesting that the sigM regulon is involved in the control of cell division.

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Tropical cyclones are affected by a large number of climatic factors, which translates into complex patterns of occurrence. The variability of annual metrics of tropical-cyclone activity has been intensively studied, in particular since the sudden activation of the North Atlantic in the mid 1990’s. We provide first a swift overview on previous work by diverse authors about these annual metrics for the North-Atlantic basin, where the natural variability of the phenomenon, the existence of trends, the drawbacks of the records, and the influence of global warming have been the subject of interesting debates. Next, we present an alternative approach that does not focus on seasonal features but on the characteristics of single events [Corral et al., Nature Phys. 6, 693 (2010)]. It is argued that the individual-storm power dissipation index (PDI) constitutes a natural way to describe each event, and further, that the PDI statistics yields a robust law for the occurrence of tropical cyclones in terms of a power law. In this context, methods of fitting these distributions are discussed. As an important extension to this work we introduce a distribution function that models the whole range of the PDI density (excluding incompleteness effects at the smallest values), the gamma distribution, consisting in a powerlaw with an exponential decay at the tail. The characteristic scale of this decay, represented by the cutoff parameter, provides very valuable information on the finiteness size of the basin, via the largest values of the PDIs that the basin can sustain. We use the gamma fit to evaluate the influence of sea surface temperature (SST) on the occurrence of extreme PDI values, for which we find an increase around 50 % in the values of these basin-wide events for a 0.49 C SST average difference. Similar findings are observed for the effects of the positive phase of the Atlantic multidecadal oscillation and the number of hurricanes in a season on the PDI distribution. In the case of the El Niño Southern oscillation (ENSO), positive and negative values of the multivariate ENSO index do not have a significant effect on the PDI distribution; however, when only extreme values of the index are used, it is found that the presence of El Niño decreases the PDI of the most extreme hurricanes.

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Introduction Lesion detection in multiple sclerosis (MS) is an essential part of its clinical diagnosis. In addition, radiological characterisation of MS lesions is an important research field that aims at distinguishing different MS types, monitoring drug response and prognosis. To date, various MR protocols have been proposed to obtain optimal lesion contrast for early and comprehensive diagnosis of the MS disease. In this study, we compare the sensitivity of five different MR contrasts for lesion detection: (i) the DIR sequence (Double Inversion Recovery, [4]), (ii) the Dark-fluid SPACE acquisition schemes, a 3D variant of a 2D FLAIR sequence [1], (iii) the MP2RAGE [2], an MP-RAGE variant that provides homogeneous T1 contrast and quantitative T1-values, and the sequences currently used for clinical MS diagnosis (2D FLAIR, MP-RAGE). Furthermore, we investigate the T1 relaxation times of cortical and sub-cortical regions in the brain hemispheres and the cerebellum at 3T. Methods 10 early-stage female MS patients (age: 31.64.7y; disease duration: 3.81.9y; disability score, EDSS: 1.80.4) and 10 healthy controls (age and gender-matched: 31.25.8y) were included in the study after obtaining informed written consent according to the local ethic protocol. All experiments were performed at 3T (Magnetom Trio a Tim System, Siemens, Germany) using a 32-channel head coil [5]. The imaging protocol included the following sequences, (all except for axial FLAIR 2D with 1x1x1.2 mm3 voxel and 256x256x160 matrix): DIR (TI1/TI2/TR XX/3652/10000 ms, iPAT=2, TA 12:02 min), MP-RAGE (TI/TR 900/2300 ms, iPAT=3, TA 3:47 min); MP2RAGE (TI1/TI2/TR 700/2500/5000 ms, iPAT=3, TA 8:22 min, cf. [2]); 3D FLAIR SPACE (only for patient 4-6, TI/TR 1800/5000 ms, iPAT=2, TA=5;52 min, cf. [1]); Axial FLAIR (0.9x0.9x2.5 mm3, 256x256x44 matrix, TI/TR 2500/9000 ms, iPAT=2, TA 4:05 min). Lesions were identified by two experienced neurologist and radiologist, manually contoured and assigned to regional locations (s. table 1). Regional lesion masks (RLM) from each contrast were compared for number and volumes of lesions. In addition, RLM were merged in a single "master" mask, which represented the sum of the lesions of all contrasts. T1 values were derived for each location from this mask for patients 5-10 (3D FLAIR contrast was missing for patient 1-4). Results & Discussion The DIR sequence appears the most sensitive for total lesions count, followed by the MP2RAGE (table 1). The 3D FLAIR SPACE sequence turns out to be more sensitive than the 2D FLAIR, presumably due to reduced partial volume effects. Looking for sub-cortical hemispheric lesions, the DIR contrast appears to be equally sensitive to the MP2RAGE and SPACE, but most sensitive for cerebellar MS plaques. The DIR sequence is also the one that reveals cortical hemispheric lesions best. T1 relaxation times at 3T in the WM and GM of the hemispheres and the cerebellum, as obtained with the MP2RAGE sequence, are shown in table 2. Extending previous studies, we confirm overall longer T1-values in lesion tissue and higher standard deviations compared to the non-lesion tissue and control tissue in healthy controls. We hypothesize a biological (different degree of axonal loss and demyelination) rather than technical origin. Conclusion In this study, we applied 5 MR contrasts including two novel sequences to investigate the contrast of highest sensitivity for early MS diagnosis. In addition, we characterized for the first time the T1 relaxation time in cortical and sub-cortical regions of the hemispheres and the cerebellum. Results are in agreement with previous publications and meaningful biological interpretation of the data.

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The proprotein convertase subtilisin kexin isozyme 1 (SKI-1)/site 1 protease (S1P) plays crucial roles in cellular homeostatic functions and is hijacked by pathogenic viruses for the processing of their envelope glycoproteins. Zymogen activation of SKI-1/S1P involves sequential autocatalytic processing of its N-terminal prodomain at sites B'/B followed by the herein newly identified C'/C sites. We found that SKI-1/S1P autoprocessing results in intermediates whose catalytic domain remains associated with prodomain fragments of different lengths. In contrast to other zymogen proprotein convertases, all incompletely matured intermediates of SKI-1/S1P showed full catalytic activity toward cellular substrates, whereas optimal cleavage of viral glycoproteins depended on B'/B processing. Incompletely matured forms of SKI-1/S1P further process cellular and viral substrates in distinct subcellular compartments. Using a cell-based sensor for SKI-1/S1P activity, we found that 9 amino acid residues at the cleavage site (P1-P8) and P1' are necessary and sufficient to define the subcellular location of processing and to determine to what extent processing of a substrate depends on SKI-1/S1P maturation. In sum, our study reveals novel and unexpected features of SKI-1/S1P zymogen activation and subcellular specificity of activity toward cellular and pathogen-derived substrates.

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Altitudinal tree lines are mainly constrained by temperature, but can also be influenced by factors such as human activity, particularly in the European Alps, where centuries of agricultural use have affected the tree-line. Over the last decades this trend has been reversed due to changing agricultural practices and land-abandonment. We aimed to combine a statistical land-abandonment model with a forest dynamics model, to take into account the combined effects of climate and human land-use on the Alpine tree-line in Switzerland. Land-abandonment probability was expressed by a logistic regression function of degree-day sum, distance from forest edge, soil stoniness, slope, proportion of employees in the secondary and tertiary sectors, proportion of commuters and proportion of full-time farms. This was implemented in the TreeMig spatio-temporal forest model. Distance from forest edge and degree-day sum vary through feed-back from the dynamics part of TreeMig and climate change scenarios, while the other variables remain constant for each grid cell over time. The new model, TreeMig-LAb, was tested on theoretical landscapes, where the variables in the land-abandonment model were varied one by one. This confirmed the strong influence of distance from forest and slope on the abandonment probability. Degree-day sum has a more complex role, with opposite influences on land-abandonment and forest growth. TreeMig-LAb was also applied to a case study area in the Upper Engadine (Swiss Alps), along with a model where abandonment probability was a constant. Two scenarios were used: natural succession only (100% probability) and a probability of abandonment based on past transition proportions in that area (2.1% per decade). The former showed new forest growing in all but the highest-altitude locations. The latter was more realistic as to numbers of newly forested cells, but their location was random and the resulting landscape heterogeneous. Using the logistic regression model gave results consistent with observed patterns of land-abandonment: existing forests expanded and gaps closed, leading to an increasingly homogeneous landscape.

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Notre étude consiste en une recherche longitudinale pour laquelle une cohorte d'élèves a été suivie depuis la Grande Section de l'école maternelle française (élèves de 5-6 ans) jusqu'au Cours Élémentaire 1re année de l'école élémentaire française (élèves de 7-8 ans) dans des situations ordinaires de classe. À ces niveaux scolaires, l'un des principaux objectifs du curriculum est l'apprentissage de la lecture. Nous considérons que l'élève construit les compétences de lecture à acquérir, i.e. les compétences caractérisant son développement potentiel, en s'appuyant sur les compétences caractérisant son développement actuel (Vygotski, 1934/1997). Lorsqu'il apprend à lire, l'élève a à sa disposition des moyens sémiotiques relatifs à la connaissance des objets et leurs usages, ainsi qu'aux gestes et leur signification (Moro & Rodriguez, 2005), ce que nous appelons globalement la matérialité. En conséquence, dans cette recherche, nous faisons l'hypothèse que ces premières habiletés relatives à la matérialité, constituent une ressource dans les situations d'enseignement- apprentissage de la lecture. Nous réalisons une étude de cas dont le recueil des données, à caractère ethnographique, est constitué de moments de classe enregistrés en vidéo, et ce, quatre fois par année scolaire. Ces douze enregistrements vidéo sont complétés par deux entretiens semi-directifs et un entretien d'auto- confrontation ; ils sont aussi mis en lien avec les Instructions officielles (programmes scolaires). L'analyse est à la fois macrogénétique et microgénétique. Pour chaque observation, concernant l'analyse macrogénétique, nous réalisons le synopsis à partir duquel nous sélectionnons des épisodes significatifs porteurs de matérialité. Les épisodes significatifs sont constitués des événements remarquables dont les analyses microgénétiques nécessitent l'utilisation d'outils, à savoir les tableaux des matérialités et les photogrammes. Notre étude montre que la matérialité permet aux élèves de devenir lecteurs et que les formes de cette matérialité changent en fonction de l'avancée des acquisitions des élèves et des dimensions de la lecture (code et compréhension) à apprendre. - Our research consists of a longitudinal study in which one group of pupils in ordinary classroom situations has been followed from the top level of French pre-elementary school (5- to 6 year-old pupils) to the second level of French primary school (7- to 8 year-old pupils). For these three school grades, one of the main objectives in the curriculum is learning to read. We consider that pupils build their new reading skills, i.e. the skills characterizing their potential development, by relying on skills characterizing their actual development (Vygotski, 1934/1997). When learning to read, pupils yet have at their disposal semiotic abilities related to knowledge both of material objects and their uses, and of basic gestures and their meaning (Moro & Rodriguez, 2005), all of this we sum up under the term of materiality. Consequently, in our research, we make the hypothesis that the children's basic abilities related to materiality constitute a resource in teaching-learning situations. We have chosen to carry out a case study. The data collected consist of videos of class sequences carried out four times a year for three years. These twelve videos are supplemented by two semi- structured interviews with the teacher, one "self-confronting" interview in which the teacher is brought to discuss her actions and by the analysis of the ministry's school curricula. Our analysis is both macrogenetic and microgenetic. For each teaching sequence, on the level of macrogenetic analysis, we have made up the synopsis from which we have selected significant episodes in terms of materiality. The significant episodes are composed of remarkable events the microgenetic analysis of which requires the use of tools such as materiality boards and photograms. Our study shows that materiality enables pupils to develop reading skills and that the forms that materiality takes on change according to the pupils' acquisition progress and the aspects of reading (code and comprehension) still to be learned.

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BACKGROUND: Plasma free and urinary metanephrines are recognized biomarkers for the assessment of pheochromocytoma. Plasma total metanephrines with a long half-life may represent another useful biomarker. OBJECTIVE: The aim of this study is to evaluate the diagnostic performances of plasma total metanephrines alone or combined with free metanephrines and fractionated 24-h urinary metanephrines. METHODS: A retrospective, case-control diagnostic test study was conducted between 1999 and 2007 in two university hospitals in Switzerland and two institutions in France. The patients included 46 cases with histologically proven pheochromocytoma, and 181 controls suspected of tumor with negative investigations and 3-year follow-up. None had renal dysfunction. Sensitivity and specificity were compared after expressing each measurement result as a ratio over its upper reference limit, adding the ratios of normetanephrine and metanephrine, and defining cut-off values of 1 or 2 for this sum. RESULTS: Applying a cut-off value of 1, plasma free and total metanephrines and urinary fractionated metanephrines had similar sensitivities of 96% (95% confidence interval, 86-99%), 95% (85-99%), and 95% (84-99%) along with similar specificities of 89% (83-94%), 91% (84-95%), and 86% (80-91%). A cut-off of 2 for the sum of ratios over reference limit improves the specificity, and it can be used for a confirmation test based on another biomarker taken among the three biomarkers. CONCLUSION: All three metanephrine-based tests perform equivalently for diagnosing pheochromocytoma in the absence of renal insufficiency, and can be conveniently associated two by two for confirming/excluding tumor.

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We extend PML theory to account for information on the conditional moments up to order four, but without assuming a parametric model, to avoid a risk of misspecification of the conditional distribution. The key statistical tool is the quartic exponential family, which allows us to generalize the PML2 and QGPML1 methods proposed in Gourieroux et al. (1984) to PML4 and QGPML2 methods, respectively. An asymptotic theory is developed. The key numerical tool that we use is the Gauss-Freud integration scheme that solves a computational problem that has previously been raised in several fields. Simulation exercises demonstrate the feasibility and robustness of the methods [Authors]