Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof

In this paper, we present a new unified approach and an elementary proof of a very general theorem on the existence of a semicontinuous or continuous utility function representing a preference relation. A simple and interesting new proof of the famous Debreu Gap Lemma is given. In addition, we prove a new Gap Lemma for the rational numbers and derive some consequences. We also prove a theorem which characterizes the existence of upper semicontinuous utility functions on a preordered topological space which need not be second countable. This is a generalization of the classical theorem of Rader which only gives sufficient conditions for the existence of an upper semicontinuous utility function for second countable topological spaces. (C) 2002 Elsevier Science B.V. All rights reserved.

The non-existence of a utility function and the structure of non-representable preference relations

In this paper we investigate the structure of non-representable preference relations. While there is a vast literature on different kinds of preference relations that can be represented by a real-valued utility function, very little is known or understood about preference relations that cannot be represented by a real-valued utility function. There has been no systematic analysis of the non-representation problem. In this paper we give a complete description of non-representable preference relations which are total preorders or chains. We introduce and study the properties of four classes of non-representable chains: long chains, planar chains, Aronszajn-like chains and Souslin chains. In the main theorem of the paper we prove that a chain is non-representable if and only it is a long chain, a planar chain, an Aronszajn-like chain or a Souslin chain. (C) 2002 Published by Elsevier Science B.V.

On the importance function in splitting simulation

The splitting method is a simulation technique for the estimation of very small probabilities. In this technique, the sample paths are split into multiple copies, at various stages in the simulation. Of vital importance to the efficiency of the method is the Importance Function (IF). This function governs the placement of the thresholds or surfaces at which the paths are split. We derive a characterisation of the optimal IF and show that for multi-dimensional models the natural choice for the IF is usually not optimal. We also show how nearly optimal splitting surfaces can be derived or simulated using reverse time analysis. Our numerical experiments illustrate that by using the optimal IF, one can obtain a significant improvement in simulation efficiency.

Investigation of electrical conductivity as a function of dopant-ion radius in the systems Zr0.75Ce0.08M0.17O1.92 (M=Nd, Sm, Gd, Dy, Ho, Y, Er, Yb, Sc)

Electrical conductivity versus dopant ionic radius studies in zirconia- and ceria-based, solid oxide fuel cell (SOFC) electrolyte systems have shown that oxygen-ion conductivity is highest when the host and dopant ions are similar in size [J. Am. Ceram. Soc. 48 (1965) 286; Solid State Ionics 37 (1989) 67; Solid State Ionics 5 (1981) 547]. Under these conditions, it is thought that the conduction paths within the crystal lattice become less distorted [Solid State Ionics 8 (1983) 201]. In this study, binary ZrO2-M2O3 unit cells were expanded, via the partial substitution of Ce+4 for Zr+4 into the lattice, in an attempt to identify new, ternary, zirconia/ceria-based electrolyte systems with enhanced electrical conductivity. The compositions Zr0.75Ce0.08M0.17O1.92 (M = Nd, Sm, Gd, Dy, Ho, Y, Yb, Sc) were prepared using traditional solid state techniques. Bulk phase characterisation and precise lattice parameter measurements were performed with X-ray diffraction techniques. Four-probe DC conductivity measurements between 400 and 900 degreesC showed that the dopant-ion radius influenced electrical conductivity. The conductivity versus dopant-ion radius trends previously observed in zirconia-based, binary systems are clearly apparent in the ternary systems investigated in this study. The addition of ceria was found to have a negative influence on the electrical conductivity over the temperature range 400-900 degreesC. It is suggested that distortion of the oxygen-ion conduction path by the presence of the larger M+3 and Ce+4 species (relative to Zr+4) is the reason for the decreasing electrical conductivity as a function of increasing dopant size and ceria addition, respectively. (C) 2002 Elsevier Science B.V. All rights reserved.

Impact of malocclusion and orthognathic reconstruction surgery on resonance and articulatory function: an examination of variability in five cases

Articulatory patterns and nasal resonance were assessed before and 6 months after orthognathic reconstruction surgery in five patients with dentofacial deformities. Perceptual and physiological assessments showed disorders of nasality and articulatory function preoperatively, two patients being hyponasal, and one hypernasal. Four patients had mild articulatory deficits, and four had reduced maximal lip or tongue pressures. Operation resulted in different patterns of change. Nasality deteriorated in three patients and articulatory precision and intelligibility improved in only one patient and showed no change in the other four. Operation improved interlabial pressures in three patients, while its impact on tongue pressures varied, being improved in one case, deteriorating in one, and remaining unchanged in the other three. The variability in the results highlights the need for routine assessment of speech and resonance before and after orthognathic reconstruction. (C) 2002 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Science Ltd. All rights reserved.

The role of Doppler left ventricular filling indexes and Doppler tissue echocardiography in the assessment of cardiac involvement in hereditary hemochromatosis

Although cardiac dysfunction in hereditary hemochromatosis (HHC) can be evaluated by conventional echocardiography, findings are often not specific. To test the hypothesis that the assessment of (1) conventional Doppler left ventricular filling indexes and (2) intrinsic elastic properties of the myocardium by Doppler tissue echocardiography can both enhance the accuracy of echocardiographic diagnosis of cardiac involvement in HHC, a group of 18 patients with HHC (mean age 50+/-7 years) and 22 age-matched healthy subjects were studied. The following indexes were characteristic for HHC: (1) the duration of atrial reversal measured from pulmonary venous flow (ms) was longer(118+/-20 vs 90+/-16; P

Guideline-discordant care in acute myocardial infarction: predictors and outcomes

Objectives: To determine (i) factors which predict whether patients hospitalised with acute myocardial infarction (AMI) receive care discordant with recommendations of clinical practice guidelines; and (ii) whether such discordant care results in worse outcomes compared with receiving guideline-concordant care. Design: Retrospective cohort study. Setting: Two community general hospitals. Participants: 607 consecutive patients admitted with AMI between July 1997 and December 2000. Main outcome measures: Clinical predictors of discordant care; crude and risk-adjusted rates of inhospital mortality and reinfarction, and mean length of hospital stay. Results: At least one treatment recommendation for AMI was applicable for 602 of the 607 patients. Of these patients, 411(68%) received concordant care, and 191 (32%) discordant care. Positive predictors at presentation of discordant care were age > 65 years (odds ratio [OR], 2.5; 95% Cl, 1.7-3.6), silent infarction (OR, 2.7; 95% Cl, 1.6-4.6), anterior infarction (OR, 2.5; 95% Cl, 1.7-3.8), a history of heart failure (OR, 6.3; 95% Cl, 3.7-10.7), chronic atrial fibrillation (OR, 3.2; 95% Cl, 1.5-6.4); and heart rate greater than or equal to 100 beats/min (OR, 2.1; 95% Cl, 1.4-3.1). Death occurred in 12.0% (23/191) of discordant-care patients versus 4.6% (19/411) of concordant-care patients (adjusted OR, 2.42; 95% Cl, 1.22-4.82). Mortality was inversely related to the level of guideline concordance (P = 0.03). Reinfarction rates also tended to be higher in the discordant-care group (4.2% v 1.7%; adjusted OR, 2.5; 95% Cl, 0.90-7.1). Conclusions: Certain clinical features at presentation predict a higher likelihood of guideline-discordant care in patients presenting with AMI Such care appears to increase the risk of inhospital death.

A monolithic smoothing-gap algorithm for contact-impact based on the signed distance function

A new algorithm has been developed for smoothing the surfaces in finite element formulations of contact-impact. A key feature of this method is that the smoothing is done implicitly by constructing smooth signed distance functions for the bodies. These functions are then employed for the computation of the gap and other variables needed for implementation of contact-impact. The smoothed signed distance functions are constructed by a moving least-squares approximation with a polynomial basis. Results show that when nodes are placed on a surface, the surface can be reproduced with an error of about one per cent or less with either a quadratic or a linear basis. With a quadratic basis, the method exactly reproduces a circle or a sphere even for coarse meshes. Results are presented for contact problems involving the contact of circular bodies. Copyright (C) 2002 John Wiley Sons, Ltd.

Influence of left ventricular size and hemodynamics on the systolic longitudinal myocardial Doppler velocity response to stress

Background Systolic myocardial Doppler velocity accurately identifies coronary artery disease. However, these velocities may be affected by age, hemodynamic responses to stress, and left ventricular cavity size. We sought to examine the influences of these variables on myocardial velocity during dobutamine stress in patients with normal wall motion. Methods One hundred seventy-nine consecutive patients with normal dobutamine echocardiograms were studied. Color myocardial tissue Doppler data were obtained at rest and peak stress, and peak systolic myocardial velocity (PSV) was measured in all basal and midventricular segments. Velocities at rest and peak stress were compared with left ventricular diastolic and systolic volumes, blood pressure, heart rate, and age by Pearson correlation and interdecile analysis by use of analysis of variance. Results The only clinical variable correlating with velocity was age; PSV showed only mild correlation with age at rest (r(2) = 0.01, P = .001) and peak stress (r(2) = 0.02, P = .001), but the normal peak velocity was significantly different between the extremes of age (<44 years and >74 years). There was very weak correlation of PSV with systolic and diastolic blood pressure (r(2) < 0.01), heart rate (r(2) < 0.01), systemic vascular resistance (r(2) = 0.08), and left ventricular volumes (r(2) < 0.01). Conclusions Peak systolic velocity during dobutamine stress is relatively independent of hemodynamic factors and left ventricular cavity size. The extremes of age may influence peak systolic Doppler velocities. These results suggest that peak systolic velocity may be a robust quantitative measure during dobutamine echocardiography across most patient subgroups.

Vascular dysfunction and heart failure: Epiphenomenon or etiologic agent?

Endothelial function plays a key role in the local regulation of vascular tone. Alterations in endothelial function may result in impaired release of endothelium-derived relaxing factors or increased release of endothelium-derived contracting factors. Heart failure may impair endothelial function by means of reduced synthesis and release of nitric oxide (NO) or by increased degradation of NO and increased production of endothelin-1. Endothelial dysfunction may worsen heart function by means of peripheral effects, causing increased afterload and central effects such as myocardial ischemia and inducible nitric oxide synthase (iNOS)-induced detrimental effects. Evidence from clinical studies has suggested that there is a correlation between decreased endothelial function and increasing severity of congestive heart failure (CHF). Treatments that improve heart function may also improve endothelial dysfunction. The relationship between endothelial dysfunction and heart failure may be masked by the stage of endothelial dysfunction, the location of vessels being tested, and the state of endothelial-dependent vasodilatation response.

Automated regional myocardial displacement for facilitating the interpretation of dobutamine echocardiography

Quantification of stress echocardiography may overcome the training requirements and subjective nature of visual wall motion score (WMS) assessment, but quantitative approaches may be difficult to apply and require significant time for image processing. The integral of long-axis myocardial velocity is displacement, which may be represented as a color map over the left ventricular myocardium. This study was designed to explore the feasibility and accuracy of measuring long-axis myocardial displacement, derived from tissue Doppler, for the detection of coronary artery disease (CAD) during dobutamine stress echocardiography (DBE). One hundred thirty patients underwent standard DBE, including 30 patients at low risk of CAD, 30 patients with normal coronary angiography (both groups studied to define normal ranges of displacement), and 70 patients who underwent coronary angiography in whom the accuracy of normal ranges was tested. Regional myocardial displacement was obtained by analysis of color tissue Doppler apical images acquired at peak stress. Displacement was compared with WMS, and with the presence of CAD by angiography. The analysis time was 3.2 +/- 1.5 minutes per patient. Segmental displacement was correlated with wall motion (normal 7.4 +/- 3.2 mm, ischemia 5.8 +/- 4.2 mm, viability 4.6 +/- 3.0 mm, scar 4.5 +/- 3.5 mm, p <0.001). Reversal of normal base-apex displacement was an insensitive (19%) but specific (90%) marker of CAD. The sum of displacements within each vascular territory had a sensitivity and specificity of 89% and 79%, respectively, for prediction of significant CAD, compared with 86% and 78%, respectively, for WMS (p = NS). The displacements in the basal segments had a sensitivity and specificity of 83% and 78%, respectively (p = NS). Regional myocardial displacement during DBE is feasible and offers a fast and accurate method for the diagnosis of CAD. (C),2002 by Excerpta Medica, Inc.

Use of cyclic variation of integrated backscatter to assess contractile reserve and myocardial viability in chronic ischemic left ventricular dysfunction

The detection of viable myocardium has important implications for management, but use of stress echocardiography to detect this is subjective and requires exposure to dobutamine. We investigated whether cyclic variation (CV) of integrated backscatter (IB) from the apical views could provide a resting study for detection of contractile reserve (CR) and prediction of myocardial viability in 27 patients with chronic ischemic left ventricular (LV) dysfunction. Repeat echocardiography was performed after 6.7 +/- 3.8 months of follow-up; 14 patients underwent revascularization and 13 were treated medically. Using a standardized dobutamine echocardiography (DbE) protocol, images from three apical views were acquired at 80-120 frames/sec at rest and during stress. CR was identified if improvement of wall motion was observed at low dose (5 or 10 mug/kg/min) DbE. Myocardial viability was characterized by improvement at follow-up echocardiography in patients with revascularization. CVIB at rest and low dose dobutamine were assessed in 194 segments with resting asynergy (severe hypokinesis or akinesis), of which 88 (45%) were in patients who underwent revascularization. Of these, CVIB could be measured in 190 (98%) segments at rest and 185 (95%) at low dose dobutamine. Sixty-two (33%) segments had CR during low dose DbE and 50 (57%) segments showed wall-motion recovery (myocardial viability) at follow-up echocardiography. Segments with CR had significantly higher CVIB at rest (P < 0.001) and low dose dobutamine (P = 0.005) than segments without CR. Using optimal thresholds of CVIB (> 8.2 dB) at rest, the accuracy of CVIB for detecting CR was 70%. Compared with nonviable segments, viable segments had significantly higher CVIB at rest (P < 0.001) and low dose dobutamine (P < 0.001). Using optimal thresholds of CVIB (> 5.3 dB) at rest, the accuracy of CVIB for detecting myocardial viability was 85%, which was higher than that in conventional DbE (62%, P < 0.01). Thus, assessment of CV.TB from the apical views is a feasible and accurate tool for detecting CR and predicting myocardial viability in chronic LV dysfunction.

A curious experiment: the paradigm switch from observation and speculation to experimentation, in the understanding of neuromuscular function and disease

The four-link chain of the motor unit represents the contemporary end-point of some two millennia of evolving knowledge in neuroscience. The paradigm shift in neuromuscular epistemology occurred in the mid-17th century. In 1666, the newly graduated Dutch doctor, Jan Swammerdam (1637-1680) published his former investigations of dissected nerve-muscle preparations. These experiments comprised the quantum leap from observation and speculation, to that of experimentation in the field of neuroanatomy and neurophysiology. In what he termed 'A Curious Experiment' he also described the phenomenon of intrinsic muscle excitability - I cannot observe that the muscle in the living animal ever absolutely ceases from all motion. Eighty years later (1752), von Haller demonstrated experimentally that irritability (contractility) was an intrinsic property of all muscular tissue; and distinguished between the sensibility of nerve impulses and the irritability of muscular contraction. This experimental progression from Swammerdam to von Haller culminated in 1850, when Claude Bernard's studies in experimental pharmacology confirmed that muscle was a functional unit, independent of any electrical innervation via its supplying nerve. This account comprises an audit of Swammerdam's work in the perspective of neuromuscular knowledge. (C) 2002 Elsevier Science B.V. All rights reserved.