Concentration analysis and cocompactness

Loss of compactness that occurs in may significant PDE settings can be expressed in a well-structured form of profile decomposition for sequences. Profile decompositions are formulated in relation to a triplet $(X,Y,D)$, where $X$ and $Y$ are Banach spaces, $X\hookrightarrow Y$, and $D$ is, typically, a set of surjective isometries on both $X$ and $Y$. A profile decomposition is a representation of a bounded sequence in $X$ as a sum of elementary concentrations of the form $g_kw$, $g_k\in D$, $w\in X$, and a remainder that vanishes in $Y$. A necessary requirement for $Y$ is, therefore, that any sequence in $X$ that develops no $D$-concentrations has a subsequence convergent in the norm of $Y$. An imbedding $X\hookrightarrow Y$ with this property is called $D$-cocompact, a property weaker than, but related to, compactness. We survey known cocompact imbeddings and their role in profile decompositions

Reference Distorted Prices

I show that when consumers (mis)perceive prices relative to reference prices, budgets turn out to be soft, prices tend to be lower and the average quality of goods sold decreases. These observations provide explanations for decentralized purchase decisions, for people being happy with a purchase even when they have paid their evaluation, and for why trade might affect high quality local firms 'unfairly'

Emotional intelligence buffers the effect of physiological arousal on dishonesty

We studied the emotional processes that allow people to balance two competing desires: benefitting from dishonesty and keeping a positive self-image. We recorded physiological arousal (skin conductance and heart rate) during a computer card game in which participants could cheat and fail to report a certain card when presented on the screen to avoid losing their money. We found that higher skin conductance corresponded to lower cheating rates. Importantly, emotional intelligence regulated this effect; participants with high emotional intelligence were less affected by their physiological reactions than those with low emotional intelligence. As a result, they were more likely to profit from dishonesty. However, no interaction emerged between heart rate and emotional intelligence. We suggest that the ability to manage and control emotions can allow people to overcome the tension between doing right or wrong and license them to bend the rules

Risk measures for direct real estate investments with non-normal or unknown return distributions

The volatility of returns is probably the most widely used risk measure for real estate. This is rather surprising since a number of studies have cast doubts on the view that volatility can capture the manifold risks attached to properties and corresponds to the risk attitude of investors. A central issue in this discussion is the statistical properties of real estate returns—in contrast to neoclassical capital market theory they are mostly non-normal and often unknown, which render many statistical measures useless. Based on a literature review and an analysis of data from Germany we provide evidence that volatility alone is inappropriate for measuring the risk of direct real estate. We use a unique data sample by IPD, which includes the total returns of 939 properties across different usage types (56% office, 20% retail, 8% others and 16% residential properties) from 1996 to 2009, the German IPD Index, and the German Property Index. The analysis of the distributional characteristics shows that German real estate returns in this period were not normally distributed and that a logistic distribution would have been a better fit. This is in line with most of the current literature on this subject and leads to the question which indicators are more appropriate to measure real estate risks. We suggest that a combination of quantitative and qualitative risk measures more adequately captures real estate risks and conforms better with investor attitudes to risk. Furthermore, we present criteria for the purpose of risk classification

Myocardial perfusion reserve compared with peripheral perfusion reserve: A [13N]ammonia PET study

INTRODUCTION: [13N]ammonia PET allows quantification of myocardial perfusion. The similarity between peripheral flow and myocardial perfusion is unclear. We compared perfusion flow in the myocardium with the upper limb during rest and adenosine stress [13N]ammonia PET to establish whether peripheral perfusion reserve (PPR) correlates with MPR. METHODS: [13N]ammonia myocardial perfusion PET-scans of 58 patients were evaluated (27 men, 31 women, age 64 ± 13 years) and were divided in four subgroups: patients with coronary artery disease (CAD, n = 15), cardiac syndrome X (SX, n = 14), idiopathic dilating cardiomyopathy (DCM, n = 16), and normal controls (NC, n = 13). Peripheral limb perfusion was measured in the muscular tissue of the proximal upper limb and quantified through a 2-tissue-compartment model and the PPR was calculated (stress/rest ratio). MPR was also calculated by a 2-tissue-compartment model. The PPR results were compared with the MPR findings. RESULTS: Mean myocardial perfusion increased significantly in all groups as evidenced by the MPR (CAD 1.99 ± 0.47; SX 1.39 ± 0.31; DCM 1.72 ± 0.69; NC 2.91 ± 0.78). Mean peripheral perfusion also increased but not significantly and accompanied with great variations within and between groups (mean PPR: CAD 1.30 ± 0.79; SX 1.36 ± 0.71; DCM 1.60 ± 1.22; NC 1.27 ± 0.63). The mean difference between PPR and MPR for all subpopulations varied widely. No significant correlations in flow reserve were found between peripheral and myocardial microcirculatory beds in any of the groups (Total group: r = -0.07, SEE = 0.70, CAD: r = 0.14, SEE = 0.48, SX: r = 0.17, SEE = 0.30, DCM: r = -0.11, SEE = 0.71, NC: r = -0.19, SEE = 0.80). CONCLUSION: No correlations between myocardial and peripheral perfusion (reserve) were found in different patient populations in the same PET session. This suggests a functional difference between peripheral and myocardial flow in the response to intravenously administered adenosine stress

Systematic review and meta-analysis of the diagnostic accuracy of ultrasonography for deep vein thrombosis

Background Ultrasound (US) has largely replaced contrast venography as the definitive diagnostic test for deep vein thrombosis (DVT). We aimed to derive a definitive estimate of the diagnostic accuracy of US for clinically suspected DVT and identify study-level factors that might predict accuracy. Methods We undertook a systematic review, meta-analysis and meta-regression of diagnostic cohort studies that compared US to contrast venography in patients with suspected DVT. We searched Medline, EMBASE, CINAHL, Web of Science, Cochrane Database of Systematic Reviews, Cochrane Controlled Trials Register, Database of Reviews of Effectiveness, the ACP Journal Club, and citation lists (1966 to April 2004). Random effects meta-analysis was used to derive pooled estimates of sensitivity and specificity. Random effects meta-regression was used to identify study-level covariates that predicted diagnostic performance. Results We identified 100 cohorts comparing US to venography in patients with suspected DVT. Overall sensitivity for proximal DVT (95% confidence interval) was 94.2% (93.2 to 95.0), for distal DVT was 63.5% (59.8 to 67.0), and specificity was 93.8% (93.1 to 94.4). Duplex US had pooled sensitivity of 96.5% (95.1 to 97.6) for proximal DVT, 71.2% (64.6 to 77.2) for distal DVT and specificity of 94.0% (92.8 to 95.1). Triplex US had pooled sensitivity of 96.4% (94.4 to 97.1%) for proximal DVT, 75.2% (67.7 to 81.6) for distal DVT and specificity of 94.3% (92.5 to 95.8). Compression US alone had pooled sensitivity of 93.8 % (92.0 to 95.3%) for proximal DVT, 56.8% (49.0 to 66.4) for distal DVT and specificity of 97.8% (97.0 to 98.4). Sensitivity was higher in more recently published studies and in cohorts with higher prevalence of DVT and more proximal DVT, and was lower in cohorts that reported interpretation by a radiologist. Specificity was higher in cohorts that excluded patients with previous DVT. No studies were identified that compared repeat US to venography in all patients. Repeat US appears to have a positive yield of 1.3%, with 89% of these being confirmed by venography. Conclusion Combined colour-doppler US techniques have optimal sensitivity, while compression US has optimal specificity for DVT. However, all estimates are subject to substantial unexplained heterogeneity. The role of repeat scanning is very uncertain and based upon limited data

Solitary waves in the Nonlinear Dirac Equation

In the present work, we consider the existence, stability, and dynamics of solitary waves in the nonlinear Dirac equation. We start by introducing the Soler model of self-interacting spinors, and discuss its localized waveforms in one, two, and three spatial dimensions and the equations they satisfy. We present the associated explicit solutions in one dimension and numerically obtain their analogues in higher dimensions. The stability is subsequently discussed from a theoretical perspective and then complemented with numerical computations. Finally, the dynamics of the solutions is explored and compared to its non-relativistic analogue, which is the nonlinear Schr{\"o}dinger equation. A few special topics are also explored, including the discrete variant of the nonlinear Dirac equation and its solitary wave properties, as well as the PT-symmetric variant of the model

Measurement of the residual stress tensor in a compact tension weld specimen

Neutron diffraction measurements have been performed to determine the full residual stress tensor along the expected crack path in an austenitic stainless steel (Esshete 1250) compact tension weld specimen. A destructive slitting method was then implemented on the same specimen to measure the stress intensity factor profile associated with the residual stress field as a function of crack length. Finally deformations of the cut surfaces were measured to determine a contour map of the residual stresses in the specimen prior to the cut. The distributions of transverse residual stress measured by the three techniques are in close agreement. A peak tensile stress in excess of 600 MPa was found to be associated with an electron beam weld used to attach an extension piece to the test sample, which had been extracted from a pipe manual metal arc butt weld. The neutron diffraction measurements show that exceptionally high residual stress triaxiality is present at crack depths likely to be used for creep crack growth testing and where a peak stress intensity factor of 35 MPa√m was measured (crack depth of 21 mm). The neutron diffraction measurements identified maximum values of shear stress in the order of 50 MPa and showed that the principal stress directions were aligned to within ~20° of the specimen orthogonal axes. Furthermore it was confirmed that measurement of strains by neutron diffraction in just the three specimen orthogonal directions would have been sufficient to provide a reasonably accurate characterisation of the stress state in welded CT specimens