New results on a classical operator

It is remarkable how the classical Volterra integral operator, which was one of the first operators which attracted mathematicians' attention, is still worth of being studied. In this essentially survey work, by collecting some of the very recent results related to the Volterra operator, we show that there are new (and not so new) concepts that are becoming known only at the present days. Discovering whether the Volterra operator satisfies or not a given operator property leads to new methods and ideas that are useful in the setting of Concrete Operator Theory as well as the one of General Operator Theory. In particular, a wide variety of techniques like summability kernels, theory of entire functions, Gaussian cylindrical measures, approximation theory, Laguerre and Legendre polynomials are needed to analyze different properties of the Volterra operator. We also include a characterization of the commutator of the Volterra operator acting on L-P[0, 1], 1

On solvability of linear differential equations in ${\Bbb R}^{\Bbb N}$

We construct $x^0$ in ${\Bbb R}^{\Bbb N}$ and a row-finite matrix $T=\{T_{i,j}(t)\}_{i,j\in\N}$ of polynomials of one real variable $t$ such that the Cauchy problem $\dot x(t)=T_tx(t)$, $x(0)=x^0$ in the Fr\'echet space $\R^\N$ has no solutions. We also construct a row-finite matrix $A=\{A_{i,j}(t)\}_{i,j\in\N}$ of $C^\infty(\R)$ functions such that the Cauchy problem $\dot x(t)=A_tx(t)$, $x(0)=x^0$ in ${\Bbb R}^{\Bbb N}$ has no solutions for any $x^0\in{\Bbb R}^{\Bbb N}\setminus\{0\}$. We provide some sufficient condition of solvability and of unique solvability for linear ordinary differential equations $\dot x(t)=T_tx(t)$ with matrix elements $T_{i,j}(t)$ analytically dependent on $t$.

The unit ball of the complex P(3H)

Let H be a two-dimensional complex Hilbert space and P(3H) the space of 3-homogeneous polynomials on H. We give a characterization of the extreme points of its unit ball, P(3H), from which we deduce that the unit sphere of P(3H) is the disjoint union of the sets of its extreme and smooth points. We also show that an extreme point of P(3H) remains extreme as considered as an element of L(3H). Finally we make a few remarks about the geometry of the unit ball of the predual of P(3H) and give a characterization of its smooth points.

Exoplanets or Dynamic Atmospheres? The Radial Velocity and Line Shape Variations of 51 Pegasi and tau Bootis

The stars 51 Pegasi and tau Bootis show radial velocity variations that have been interpreted as resulting from companions with roughly Jovian mass and orbital periods of a few days. Gray and Gray & Hatzes reported that the radial velocity signal of 51 Peg is synchronous with variations in the shape of the line lambda 6253 Fe I; thus, they argue that the velocity signal arises not from a companion of planetary mass but from dynamic processes in the atmosphere of the star, possibly nonradial pulsations. Here we seek confirming evidence for line shape or strength variations in both 51 Peg and tau Boo, using R = 50,000 observations taken with the Advanced Fiber Optic Echelle. Because of our relatively low spectral resolution, we compare our observations with Gray's line bisector data by fitting observed line profiles to an expansion in terms of orthogonal (Hermite) functions. To obtain an accurate comparison, we model the emergent line profiles from rotating and pulsating stars, taking the instrumental point-spread function into account. We describe this modeling process in detail. We find no evidence for line profile or strength variations at the radial velocity period in either 51 Peg or in tau Boo. For 51 Peg, our upper limit for line shape variations with 4.23 day periodicity is small enough to exclude with 10 sigma confidence the bisector curvature signal reported by Gray & Hatzes; the bisector span and relative line depth signals reported by Gray are also not seen, but in this case with marginal (2 sigma ) confidence. We cannot, however, exclude pulsations as the source of 51 Peg's radial velocity variation because our models imply that line shape variations associated with pulsations should be much smaller than those computed by Gray & Hatzes; these smaller signals are below the detection limits both for Gray & Hatzes's data and for our own. tau Boo's large radial velocity amplitude and v sin i make it easier to test for pulsations in this star. Again we find no evidence for periodic line shape changes, at a level that rules out pulsations as the source of the radial velocity variability. We conclude that the planet hypothesis remains the most likely explanation for the existing data.

Accuracy of LightCycler® SeptiFast for the detection and identification of pathogens in the blood of patients with suspected sepsis: a systematic review protocol

Background: There is growing interest in the potential utility of molecular diagnostics in improving the detection of life-threatening infection (sepsis). LightCycler® SeptiFast is a multipathogen probebased real-time PCR system targeting DNA sequences of bacteria and fungi present in blood samples within a few hours. We report here the protocol of the first systematic review of published clinical diagnostic accuracy studies of this technology when compared with blood culture in the setting of suspected sepsis. Methods/design: Data sources: the Cochrane Database of Systematic Reviews, the Database of Abstracts of Reviews of Effects (DARE), the Health Technology Assessment Database (HTA), the NHS Economic Evaluation Database (NHSEED), The Cochrane Library, MEDLINE, EMBASE, ISI Web of Science, BIOSIS Previews, MEDION and the Aggressive Research Intelligence Facility Database (ARIF). Study selection: diagnostic accuracy studies that compare the real-time PCR technology with standard culture results performed on a patient's blood sample during the management of sepsis. Data extraction: three reviewers, working independently, will determine the level of evidence, methodological quality and a standard data set relating to demographics and diagnostic accuracy metrics for each study. Statistical analysis/data synthesis: heterogeneity of studies will be investigated using a coupled forest plot of sensitivity and specificity and a scatter plot in Receiver Operator Characteristic (ROC) space. Bivariate model method will be used to estimate summary sensitivity and specificity. The authors will investigate reporting biases using funnel plots based on effective sample size and regression tests of asymmetry. Subgroup analyses are planned for adults, children and infection setting (hospital vs community) if sufficient data are uncovered. Dissemination: Recommendations will be made to the Department of Health (as part of an open-access HTA report) as to whether the real-time PCR technology has sufficient clinical diagnostic accuracy potential to move forward to efficacy testing during the provision of routine clinical care.

How Porosity and Permeability Vary Spatially With Grain Size, Sorting, Cement Volume, and Mineral Dissolution In Fluvial Triassic Sandstones: The Value of Geostatistics and Local Regression

Although it is well known that sandstone porosity and permeability are controlled by a range of parameters such as grain size and sorting, amount, type, and location of diagenetic cements, extent and type of compaction, and the generation of intergranular and intragranular secondary porosity, it is less constrained how these controlling parameters link up in rock volumes (within and between beds) and how they spatially interact to determine porosity and permeability. To address these unknowns, this study examined Triassic fluvial sandstone outcrops from the UK using field logging, probe permeametry of 200 points, and sampling at 100 points on a gridded rock surface. These field observations were supplemented by laser particle-size analysis, thin-section point-count analysis of primary and diagenetic mineralogy, quantitiative XRD mineral analysis, and SEM/EDAX analysis of all 100 samples. These data were analyzed using global regression, variography, kriging, conditional simulation, and geographically weighted regression to examine the spatial relationships between porosity and permeability and their potential controls. The results of bivariate analysis (global regression) of the entire outcrop dataset indicate only a weak correlation between both permeability porosity and their diagenetic and depositional controls and provide very limited information on the role of primary textural structures such as grain size and sorting. Subdividing the dataset further by bedding unit revealed details of more local controls on porosity and permeability. An alternative geostatistical approach combined with a local modelling technique (geographically weighted regression; GWR) subsequently was used to examine the spatial variability of porosity and permeability and their controls. The use of GWR does not require prior knowledge of divisions between bedding units, but the results from GWR broadly concur with results of regression analysis by bedding unit and provide much greater clarity of how porosity and permeability and their controls vary laterally and vertically. The close relationship between depositional lithofacies in each bed, diagenesis, and permeability, porosity demonstrates that each influences the other, and in turn how understanding of reservoir properties is enhanced by integration of paleoenvironmental reconstruction, stratigraphy, mineralogy, and geostatistics.

Polynomial Functions and the Riesz Interpolation Property

Building on a proof by D. Handelman of a generalisation of an example due to L. Fuchs, we show that the space of real-valued polynomials on a non-empty set X of reals has the Riesz Interpolation Property if and only if X is bounded.

Serum eosinophil cationic protein (ECP):reference values in healthy nonatopic children

BACKGROUND: Although serum ECP concentrations have been reported in normal children, there are currently no published upper cutoff reference limits for serum ECP in normal, nonatopic, nonasthmatic children aged 1-15 years.
METHODS: We recruited 123 nonatopic, nonasthmatic normal children attending the Royal Belfast Hospital for Sick Children for elective surgery and measured serum ECP concentrations. The effects of age and exposure to environmental tobacco smoke (ETS) on the upper reference limits were studied by multiple regression and fractional polynomials.
RESULTS: The median serum ECP concentration was 6.5 microg/l and the 95th and 97.5 th percentiles were 18.8 and 19.9 microg/l. The median and 95th percentile did not vary with age. Exposure to ETS was not associated with altered serum ECP concentrations (P = 0.14).
CONCLUSIONS: The 95th and 97.5 th percentiles for serum ECP for normal, nonatopic, nonasthmatic children (aged 1-15 years) were 19 and 20 microg/l, respectively. Age and exposure to parental ETS did not significantly alter serum ECP concentrations or the normal upper reference limits. Our data provide cutoff upper reference limits for normal children for use of serum ECP in a clinical or research setting.
PMID: 10604557 [PubMed - indexed for MEDLINE]

Family caregiver views on patient-centred care at the end of life

Aim: The purpose of this study was to evaluate the patient-centredness of community palliative care from the perspective of family members who were responsible for the care of a terminally ill family member. Method: A survey questionnaire was mailed to families of a deceased family member who had been designated as palliative and had received formal home care services in the central west region of the Province of Ontario, Canada. Respondents reported on service use in the last four weeks of life; the Client-Centred Care Questionnaire (CCCQ) was used to evaluate the extent to which care was patient-centred. The accessibility instrument was used to assess respondent perception of access to care. Descriptive and inferential statistics were used for data analyses. Results: Of the 243 potential participants, 111 (46.0%) family caregivers completed the survey questionnaire. On average, respondents reported that they used five different services during the last four weeks of the care recipient's life. When asked about programme accessibility, care was also perceived as largely accessible and responsive to patients' changing needs (M=4.3 (SD=1.04)]. Most respondents also reported that they knew what service provider to contact if they experienced any problems concerning the care of their family member. However, this service provider was not consistent among respondents. Most respondents were relatively positive about the patient-centred care they received. There were however considerable differences between some items on the CCCQ. Respondents tended to provide more negative ratings concerning practical arrangement and the organization of care: who was coming, how often and when. They also rated more negatively the observation that service providers were quick to say something was possible when it was not the case. Bivariate analyses found no significant differences in CCCQ or accessibility domain scores by caregiver age, care recipient age, income, education and caregiver sex. Conclusions: Patient-centred care represents a service attribute that should be recognized as an important outcome to assess the quality of service delivery. This study demonstrates how this attribute can be evaluated in the provision of care. © 2011 The Authors. Scandinavian Journal of Caring Sciences © 2011 Nordic College of Caring Science.

An Examination of Transformation Techniques to Investigate and Interpret Multivariate Geochemical Data Analysis: Tellus Case Study

This research aims to use the multivariate geochemical dataset, generated by the Tellus project, to investigate the appropriate use of transformation methods to maintain the integrity of geochemical data and inherent constrained behaviour in multivariate relationships. The widely used normal score transform is compared with the use of a stepwise conditional transform technique. The Tellus Project, managed by GSNI and funded by the Department of Enterprise Trade and Development and the EU’s Building Sustainable Prosperity Fund, involves the most comprehensive geological mapping project ever undertaken in Northern Ireland. Previous study has demonstrated spatial variability in the Tellus data but geostatistical analysis and interpretation of the datasets requires use of an appropriate methodology that reproduces the inherently complex multivariate relations. Previous investigation of the Tellus geochemical data has included use of Gaussian-based techniques. However, earth science variables are rarely Gaussian, hence transformation of data is integral to the approach. The multivariate geochemical dataset generated by the Tellus project provides an opportunity to investigate the appropriate use of transformation methods, as required for Gaussian-based geostatistical analysis. In particular, the stepwise conditional transform is investigated and developed for the geochemical datasets obtained as part of the Tellus project. The transform is applied to four variables in a bivariate nested fashion due to the limited availability of data. Simulation of these transformed variables is then carried out, along with a corresponding back transformation to original units. Results show that the stepwise transform is successful in reproducing both univariate statistics and the complex bivariate relations exhibited by the data. Greater fidelity to multivariate relationships will improve uncertainty models, which are required for consequent geological, environmental and economic inferences.

Sliding window two-thermocouple sensor characterization for variable flow environments

A two-thermocouple sensor characterization method for use in variable flow applications is proposed. Previous offline methods for constant velocity flow are extended using sliding data windows and polynomials to accommodate variable velocity. Analysis of Monte-Carlo simulation studies confirms that the unbiased and consistent parameter estimator outperforms alternatives in the literature and has the added advantage of not requiring a priori knowledge of the time constant ratio of thermocouples. Experimental results from a test rig are also presented. © 2008 The Institute of Measurement and Control.

Integrating Multiple Point Statistics with Aerial Geophysical Data to assist Groundwater Flow Models

The process of accounting for heterogeneity has made significant advances in statistical research, primarily in the framework of stochastic analysis and the development of multiple-point statistics (MPS). Among MPS techniques, the direct sampling (DS) method is tested to determine its ability to delineate heterogeneity from aerial magnetics data in a regional sandstone aquifer intruded by low-permeability volcanic dykes in Northern Ireland, UK. The use of two two-dimensional bivariate training images aids in creating spatial probability distributions of heterogeneities of hydrogeological interest, despite relatively ‘noisy’ magnetics data (i.e. including hydrogeologically irrelevant urban noise and regional geologic effects). These distributions are incorporated into a hierarchy system where previously published density function and upscaling methods are applied to derive regional distributions of equivalent hydraulic conductivity tensor K. Several K models, as determined by several stochastic realisations of MPS dyke locations, are computed within groundwater flow models and evaluated by comparing modelled heads with field observations. Results show a significant improvement in model calibration when compared to a simplistic homogeneous and isotropic aquifer model that does not account for the dyke occurrence evidenced by airborne magnetic data. The best model is obtained when normal and reverse polarity dykes are computed separately within MPS simulations and when a probability threshold of 0.7 is applied. The presented stochastic approach also provides improvement when compared to a previously published deterministic anisotropic model based on the unprocessed (i.e. noisy) airborne magnetics. This demonstrates the potential of coupling MPS to airborne geophysical data for regional groundwater modelling.

Accuracy of LightCycler SeptiFast for the detection and identification of pathogens in the blood of patients with suspected sepsis: a systematic review and meta-analysis

Purpose: There is an urgent need to develop diagnostic tests to improve the detection of pathogens causing life-threatening infection (sepsis). SeptiFast is a CE-marked multi-pathogen real-time PCR system capable of detecting DNA sequences of bacteria and fungi present in blood samples within a few hours. We report here a systematic review and meta-analysis of diagnostic accuracy studies of SeptiFast in the setting of suspected sepsis.

Methods: A comprehensive search strategy was developed to identify studies that compared SeptiFast with blood culture in suspected sepsis. Methodological quality was assessed using QUADAS. Heterogeneity of studies was investigated using a coupled forest plot of sensitivity and specificity and a scatter plot in receiver operator characteristic space. Bivariate model method was used to estimate summary sensitivity and specificity.

Results: From 41 phase III diagnostic accuracy studies, summary sensitivity and specificity for SeptiFast compared with blood culture were 0.68 (95 % CI 0.63–0.73) and 0.86 (95 % CI 0.84–0.89) respectively. Study quality was judged to be variable with important deficiencies overall in design and reporting that could impact on derived diagnostic accuracy metrics.

Conclusions: SeptiFast appears to have higher specificity than sensitivity, but deficiencies in study quality are likely to render this body of work unreliable. Based on the evidence presented here, it remains difficult to make firm recommendations about the likely clinical utility of SeptiFast in the setting of suspected sepsis.

The British conservative party and Europe:The choosing of John Major

This article provides an empirical analysis of voting behaviour in the second ballot of the 1990 Conservative leadership contest that resulted in John Major becoming party leader and prime minister. Seven hypotheses of voting behaviour are generated from the extant literature relating voting to socio-economic variables (occupational and educational background), political variables (parliamentary experience, career status, age and electoral marginality) and ideological variables (drawn from survey data on MPs' positions on economic, European and moral issues). These hypotheses are tested using data on voting intentions gathered from published lists of MPs' declarations, interviews with each of the leadership campaign teams, and correspondence with MPs. Bivariate relationships are presented, followed by logistic regression analysis to isolate the unique impact that each variable had on voting. This shows that educational background, parliamentary experience and (especially) attitudes to Europe were the key factors determining voting. The importance of Europe in the contest is particularly instructive: the severe problems for Major's leadership which were caused by the issue can be attributed to, and understood in the context of, the 1990 contest in which he became leader.

Relationships between Religion and Two Forms of Homonegativity in Europe—A Multilevel Analysis of Effects of Believing, Belonging and Religious Practice

This paper examines relationships between religion and two forms of homonegativity
across 43 European countries using a bivariate response binary logistic multilevel model. The model analyzes effects of religious believing, belonging and practice on two response variables: a) a moral rejection of homosexuality as a practice and b) intolerance toward homosexuals as a group. The findings indicate that both forms of homonegativity are prevalent in Europe. Traditional doctrinal religious believing (belief in a personal God) is positively related to a moral rejection of homosexuality but to a much lesser extent associated with intolerance toward homosexuals as a group. Members of religious denominations are more likely than non-members to reject homosexuality as morally wrong and to reject homosexuals as neighbors. The analysis found significant differences between denominations that are likely context-dependent. Attendance at religious services is positively related to homonegativity in a majority of countries. The findings vary considerably across countries: Religion is more strongly related to homonegativity in Western than in Eastern Europe. In the post-soviet countries homonegativity appears to be largely a secular phenomenon. National contexts of high religiosity, high perceived government corruption, high income inequality and shortcomings in the implementation of gay rights in the countries’ legislations are statistically related to higher levels of both moralistic homonegativity and intolerance toward homosexuals as a group.