Decompositions of spaces of measures

Let M be the Banach space of sigma-additive complex-valued measures on an abstract measurable space. We prove that any closed, with respect to absolute continuity norm-closed, linear subspace L of M is complemented and describe the unique complement, projection onto L along which has norm 1. Using this fact we prove a decomposition theorem, which includes the Jordan decomposition theorem, the generalized Radon-Nikodym theorem and the decomposition of measures into decaying and non-decaying components as particular cases. We also prove an analog of the Jessen-Wintner purity theorem for our decompositions.

Decay measures on locally compact abelian topological groups

Source: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS Volume: 131 Pages: 1257-1273 Part: Part 6 Published: 2001 Times Cited: 5 References: 23 Citation MapCitation Map beta Abstract: We show that the Banach space M of regular sigma-additive finite Borel complex-valued measures on a non-discrete locally compact Hausdorff topological Abelian group is the direct sum of two linear closed subspaces M-D and M-ND, where M-D is the set of measures mu is an element of M whose Fourier transform vanishes at infinity and M-ND is the set of measures mu is an element of M such that nu is not an element of MD for any nu is an element of M \ {0} absolutely continuous with respect to the variation \mu\. For any corresponding decomposition mu = mu(D) + mu(ND) (mu(D) is an element of M-D and mu(ND) is an element of M-ND) there exist a Borel set A = A(mu) such that mu(D) is the restriction of mu to A, therefore the measures mu(D) and mu(ND) are singular with respect to each other. The measures mu(D) and mu(ND) are real if mu is real and positive if mu is positive. In the case of singular continuous measures we have a refinement of Jordan's decomposition theorem. We provide series of examples of different behaviour of convolutions of measures from M-D and M-ND.

Improved reliability in diagnosing faults using multivariate statistics

This paper analyses multivariate statistical techniques for identifying and isolating abnormal process behaviour. These techniques include contribution charts and variable reconstructions that relate to the application of principal component analysis (PCA). The analysis reveals firstly that contribution charts produce variable contributions which are linearly dependent and may lead to an incorrect diagnosis, if the number of principal components retained is close to the number of recorded process variables. The analysis secondly yields that variable reconstruction affects the geometry of the PCA decomposition. The paper further introduces an improved variable reconstruction method for identifying multiple sensor and process faults and for isolating their influence upon the recorded process variables. It is shown that this can accommodate the effect of reconstruction, i.e. changes in the covariance matrix of the sensor readings and correctly re-defining the PCA-based monitoring statistics and their confidence limits. (c) 2006 Elsevier Ltd. All rights reserved.

Reliability and Validity of the Child Health QuestionnairePF-50 for European Children with Cerebral Palsy

Objective: To evaluate the psychometric performance of the Child Health Questionnaire (CHQ) in children with cerebral palsy (CP).
Method: 818 parents of children with CP, aged 8–12 from nine regions of Europe completed the CHQ (parent form 50 items). Functional abilities were classified using the five-level Gross Motor Function Classification Scheme (Levels I–III as ambulant; Level IV–V as nonambulant CP).
Results: Ceiling effects were observed for a number of subscales and summary scores across all Gross Motor Function Classification System levels, whilst floor effects occurred only in the physical functioning scale (Level V CP). Reliability was satisfactory overall. Confirmatory factor analysis (CFA) revealed a seven-factor structure for the total sample of children with CP but with different factor structures for ambulant and nonambulant children.
Conclusion: The CHQ has limited applicability in children with CP, although with judicious use of certain domains for ambulant and nonambulant children can provide useful and comparable data about child health status for descriptive purposes.

Reliability of the input-output properties of the cortico-spinal pathway obtained from transcranial magnetic and electrical stimulation

The purpose of this experiment was to assess the test-retest reliability of input-output parameters of the cortico-spinal pathway derived from transcranial magnetic (TMS) and electrical (TES) stimulation at rest and during muscle contraction. Motor evoked potentials (MEPs) were recorded from the first dorsal interosseous muscle of eight individuals on three separate days. The intensity of TMS at rest was varied from 5% below threshold to the maximal output of the stimulator. During trials in which the muscle was active, TMS and TES intensities were selected that elicited MEPs of between 150 and 300 X at rest. MEPs were evoked while the participants exerted torques up to 50% of their maximum capacity. The relationship between MEP size and stimulus intensity at rest was sigmoidal (R-2 = 0.97). Intra-class correlation coefficients (ICC) ranged between 0.47 and 0.81 for the parameters of the sigmoid function. For the active trials, the slope and intercept of regression equations of MEP size on level of background contraction were obtained more reliably for TES (ICC = 0.63 and 0.78, respectively) than for TMS (ICC = 0.50 and 0.53, respectively), These results suggest that input-output parameters of the cortico-spinal pathway may be reliably obtained via transcranial stimulation during longitudinal investigations of cortico-spinal plasticity. (C) 2001 Elsevier Science B.V. All rights reserved.

Testing the reliability of the JEOL FEGSEM 6500F electron microprobe for quantitative major element analysis of glass shards from rhyolitic tephra.

Electronprobe microanalysis is now widely adopted in tephra studies as a technique for determining the major element geochemistry of individual glass shards. Accurate geochemical characterization is crucial for enabling robust tephra-based correlations; such information may also be used to link the tephra to a specific source and often to a particular eruption. In this article, we present major element analyses for rhyolitic natural glass standards analysed on three different microprobes and the new JEOL FEGSEM 6500F microprobe at Queen’s University Belfast. Despite the scatter in some elements, good comparability is demonstrated among data yielded from this new system, the previous Belfast JEOL-733 Superprobe, the JEOL-8200 Superprobe (Copenhagen) and the existing long-established microprobe facility in Edinburgh. Importantly, our results show that major elements analysed using different microprobes and variable operating conditions allow two high-silica glasses to be discriminated accurately.

Probabilistic classification of acute myocardial infarction from multiple cardiac markers

Logistic regression and Gaussian mixture model (GMM) classifiers have been trained to estimate the probability of acute myocardial infarction (AMI) in patients based upon the concentrations of a panel of cardiac markers. The panel consists of two new markers, fatty acid binding protein (FABP) and glycogen phosphorylase BB (GPBB), in addition to the traditional cardiac troponin I (cTnI), creatine kinase MB (CKMB) and myoglobin. The effect of using principal component analysis (PCA) and Fisher discriminant analysis (FDA) to preprocess the marker concentrations was also investigated. The need for classifiers to give an accurate estimate of the probability of AMI is argued and three categories of performance measure are described, namely discriminatory ability, sharpness, and reliability. Numerical performance measures for each category are given and applied. The optimum classifier, based solely upon the samples take on admission, was the logistic regression classifier using FDA preprocessing. This gave an accuracy of 0.85 (95% confidence interval: 0.78-0.91) and a normalised Brier score of 0.89. When samples at both admission and a further time, 1-6 h later, were included, the performance increased significantly, showing that logistic regression classifiers can indeed use the information from the five cardiac markers to accurately and reliably estimate the probability AMI. © Springer-Verlag London Limited 2008.

Surveying nursing students on their sources of stress: A validation study

This study tested the psychometric properties of a questionnaire that measured sources of distress and eustress, or good stress, in nursing students. The Transactional model of stress construes stress in these different ways and is frequently used to understand sources of stress, coping and stress responses. Limited research has attempted to measure sources of distress and eustress or sources that can potentially enhance performance and well-being. A volunteer sample of final year nursing students (n = 120) was surveyed in the United Kingdom in 2007. The questionnaire measured sources of stress and measures of psychological well-being were taken to test construct validity. This was tested through an exploratory factor analysis. This reduced the questionnaire from 49 to 29 items and suggested three factors: learning and teaching, placement related and course organization; second, it was analysed by testing the assumptions of the Transactional model, the model on which the questionnaire was based. In line with the assumptions of the model, measures of distress related to adverse well-being, and measures of eustress related to healthier well-being responses. The test–retest reliability estimate was 0.8. While certain programme issues were associated with distress, placement-related experiences were the most important source of eustress.