911 resultados para Penrose limit and pp-wave background
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In an increasingly multilingual world, English language has kept a marked predominance as a global language. In many countries, English is the primary choice for foreign language learning. There is a long history of research in English language learning. The same applies for research in reading. A main interest since the 1970s has been the reading strategy defined as inferencing or guessing the meaning of unknown words from context. Inferencing has ben widely researched, however, the results and conclusions seem to be mixed. While some agree that inferencing is a useful strategy, others doubt its usefulness. Nevertheless, most of the research seem to agree that the cultural background affects comprehension and inferencing. While most of these studies have been done with texts and contexts created by the researches, little has been done using natural prose. The present study will attempt to further clarify the process of inferencing and the effects of the text’s cultural context and the linguistic background of the reader using a text that has not been created by the researcher. The participants of the study are 40 international students from Turku, Finland. Their linguistic background was obtained through a questionnaire and proved to be diverse. Think aloud protocols were performed to investigate their inferencing process and find connections between their inferences, comments, the text, and their linguistic background. The results show that: some inferences were made based on the participants’ world knowledge, experience, other languages, and English language knowledge; other inferences and comments were made based on the text, its use of language and vocabulary, and few cues provided by the author. The results from the present study and previous research seem to show that: 1) linguistic background is a source of information for inferencing but is not a major source; 2) the cultural context of the text affected the inferences made by the participants according to their closeness or distance from it.
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In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.
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This thesis focuses on experimental and numerical studies of the hydrodynamic interaction between two vessels in close proximity in waves. In the model tests, two identical box-like models with round corners were used. Regular waves with the same wave steepness and different wave frequencies were generated. Six degrees of freedom body motions and wave elevations between bodies were measured in a head sea condition. Three initial gap widths were examined. In the numerical computations, a panel-free method based seakeeping program, MAPS0, and a panel method based program, WAMIT, were used for the prediction of body motions and wave elevations. The computed body motions and wave elevations were compared with experimental data.
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This dissertation investigates the connection between spectral analysis and frame theory. When considering the spectral properties of a frame, we present a few novel results relating to the spectral decomposition. We first show that scalable frames have the property that the inner product of the scaling coefficients and the eigenvectors must equal the inverse eigenvalues. From this, we prove a similar result when an approximate scaling is obtained. We then focus on the optimization problems inherent to the scalable frames by first showing that there is an equivalence between scaling a frame and optimization problems with a non-restrictive objective function. Various objective functions are considered, and an analysis of the solution type is presented. For linear objectives, we can encourage sparse scalings, and with barrier objective functions, we force dense solutions. We further consider frames in high dimensions, and derive various solution techniques. From here, we restrict ourselves to various frame classes, to add more specificity to the results. Using frames generated from distributions allows for the placement of probabilistic bounds on scalability. For discrete distributions (Bernoulli and Rademacher), we bound the probability of encountering an ONB, and for continuous symmetric distributions (Uniform and Gaussian), we show that symmetry is retained in the transformed domain. We also prove several hyperplane-separation results. With the theory developed, we discuss graph applications of the scalability framework. We make a connection with graph conditioning, and show the in-feasibility of the problem in the general case. After a modification, we show that any complete graph can be conditioned. We then present a modification of standard PCA (robust PCA) developed by Cand\`es, and give some background into Electron Energy-Loss Spectroscopy (EELS). We design a novel scheme for the processing of EELS through robust PCA and least-squares regression, and test this scheme on biological samples. Finally, we take the idea of robust PCA and apply the technique of kernel PCA to perform robust manifold learning. We derive the problem and present an algorithm for its solution. There is also discussion of the differences with RPCA that make theoretical guarantees difficult.
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A method for systematically tracking swells across oceanic basins is developed by taking advantage of high-quality data from space-borne altimeters and wave model output. The evolution of swells is observed over large distances based on 202 swell events with periods ranging from 12 to 18 s. An empirical attenuation rate of swell energy of about 4 × 10−7 m−1 is estimated using these observations, and the nonbreaking energy dissipation rates of swells far away from their generating areas are also estimated using a point source model. The resulting acceptance range of nonbreaking dissipation rates is −2.5 to 5.0 × 10−7 m−1, which corresponds to a dissipation e-folding scales of at least 2000 km for steep swells, to almost infinite for small-amplitude swells. These resulting rates are consistent with previous studies using in-situ and synthetic aperture radar (SAR) observations. The frequency dispersion and angular spreading effects during swell propagation are discussed by comparing the results with other studies, demonstrating that they are the two dominant processes for swell height attenuation, especially in the near field. The resulting dissipation rates from these observations can be used as a reference for ocean engineering and wave modeling, and for related studies such as air-sea and wind-wave-turbulence interactions.
Epidemiology and genetic architecture of blood pressure: a family based study of Generation Scotland
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Hypertension is a major risk factor for cardiovascular disease and mortality, and a growing global public health concern, with up to one-third of the world’s population affected. Despite the vast amount of evidence for the benefits of blood pressure (BP) lowering accumulated to date, elevated BP is still the leading risk factor for disease and disability worldwide. It is well established that hypertension and BP are common complex traits, where multiple genetic and environmental factors contribute to BP variation. Furthermore, family and twin studies confirmed the genetic component of BP, with a heritability estimate in the range of 30-50%. Contemporary genomic tools enabling the genotyping of millions of genetic variants across the human genome in an efficient, reliable, and cost-effective manner, has transformed hypertension genetics research. This is accompanied by the presence of international consortia that have offered unprecedentedly large sample sizes for genome-wide association studies (GWASs). While GWAS for hypertension and BP have identified more than 60 loci, variants in these loci are associated with modest effects on BP and in aggregate can explain less than 3% of the variance in BP. The aims of this thesis are to study the genetic and environmental factors that influence BP and hypertension traits in the Scottish population, by performing several genetic epidemiological analyses. In the first part of this thesis, it aims to study the burden of hypertension in the Scottish population, along with assessing the familial aggregation and heritialbity of BP and hypertension traits. In the second part, it aims to validate the association of common SNPs reported in the large GWAS and to estimate the variance explained by these variants. In this thesis, comprehensive genetic epidemiology analyses were performed on Generation Scotland: Scottish Family Health Study (GS:SFHS), one of the largest population-based family design studies. The availability of clinical, biological samples, self-reported information, and medical records for study participants has allowed several assessments to be performed to evaluate factors that influence BP variation in the Scottish population. Of the 20,753 subjects genotyped in the study, a total of 18,470 individuals (grouped into 7,025 extended families) passed the stringent quality control (QC) criteria and were available for all subsequent analysis. Based on the BP-lowering treatment exposure sources, subjects were further classified into two groups. First, subjects with both a self-reported medications (SRMs) history and electronic-prescription records (EPRs; n =12,347); second, all the subjects with at least one medication history source (n =18,470). In the first group, the analysis showed a good concordance between SRMs and EPRs (kappa =71%), indicating that SRMs can be used as a surrogate to assess the exposure to BP-lowering medication in GS:SFHS participants. Although both sources suffer from some limitations, SRMs can be considered the best available source to estimate the drug exposure history in those without EPRs. The prevalence of hypertension was 40.8% with higher prevalence in men (46.3%) compared to women (35.8%). The prevalence of awareness, treatment and controlled hypertension as defined by the study definition were 25.3%, 31.2%, and 54.3%, respectively. These findings are lower than similar reported studies in other populations, with the exception of controlled hypertension prevalence, which can be considered better than other populations. Odds of hypertension were higher in men, obese or overweight individuals, people with a parental history of hypertension, and those living in the most deprived area of Scotland. On the other hand, deprivation was associated with higher odds of treatment, awareness and controlled hypertension, suggesting that people living in the most deprived area may have been receiving better quality of care, or have higher comorbidity levels requiring greater engagement with doctors. These findings highlight the need for further work to improve hypertension management in Scotland. The family design of GS:SFHS has allowed family-based analysis to be performed to assess the familial aggregation and heritability of BP and hypertension traits. The familial correlation of BP traits ranged from 0.07 to 0.20, and from 0.18 to 0.34 for parent-offspring pairs and sibling pairs, respectively. A higher correlation of BP traits was observed among first-degree relatives than other types of relative pairs. A variance-component model that was adjusted for sex, body mass index (BMI), age, and age-squared was used to estimate heritability of BP traits, which ranged from 24% to 32% with pulse pressure (PP) having the lowest estimates. The genetic correlation between BP traits showed a high correlation between systolic (SBP), diastolic (DBP) and mean arterial pressure (MAP) (G: 81% to 94%), but lower correlations with PP (G: 22% to 78%). The sibling recurrence risk ratio (λS) for hypertension and treatment were calculated as 1.60 and 2.04 respectively. These findings confirm the genetic components of BP traits in GS:SFHS, and justify further work to investigate genetic determinants of BP. Genetic variants reported in the recent large GWAS of BP traits were selected for genotyping in GS:SFHS using a custom designed TaqMan® OpenArray®. The genotyping plate included 44 single nucleotide polymorphisms (SNPs) that have been previously reported to be associated with BP or hypertension at genome-wide significance level. A linear mixed model that is adjusted for age, age-squared, sex, and BMI was used to test for the association between the genetic variants and BP traits. Of the 43 variants that passed the QC, 11 variants showed statistically significant association with at least one BP trait. The phenotypic variance explained by these variant for the four BP traits were 1.4%, 1.5%, 1.6%, and 0.8% for SBP, DBP, MAP, and PP, respectively. The association of genetic risk score (GRS) that were constructed from selected variants has showed a positive association with BP level and hypertension prevalence, with an average effect of one mmHg increase with each 0.80 unit increases in the GRS across the different BP traits. The impact of BP-lowering medication on the genetic association study for BP traits has been established, with typical practice of adding a fixed value (i.e. 15/10 mmHg) to the measured BP values to adjust for BP treatment. Using the subset of participants with the two treatment exposure sources (i.e. SRMs and EPRs), the influence of using either source to justify the addition of fixed values in SNP association signal was analysed. BP phenotypes derived from EPRs were considered the true phenotypes, and those derived from SRMs were considered less accurate, with some phenotypic noise. Comparing SNPs association signals between the four BP traits in the two model derived from the different adjustments showed that MAP was the least impacted by the phenotypic noise. This was suggested by identifying the same overlapped significant SNPs for the two models in the case of MAP, while other BP traits had some discrepancy between the two sources
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International audience
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Chronic kidney disease (CKD) is associated with increased cardiovascular risk in comparison with the general population. This can be observed even in the early stages of CKD, and rises in proportion to the degree of renal impairment. Not only is cardiovascular disease (CVD) more prevalent in CKD, but its nature differs too, with an excess of morbidity and mortality associated with congestive cardiac failure, arrhythmia and sudden death, as well as the accelerated atherosclerosis which is also observed. Conventional cardiovascular risk factors such as hypertension, dyslipidaemia, obesity, glycaemia and smoking, are highly prevalent amongst patients with CKD, although in many of these examples the interaction between risk factor and disease differs from that which exists in normal renal function. Nevertheless, the extent of CVD cannot be fully explained by these conventional risk factors, and non-conventional factors specific to CKD are now recognised to contribute to the burden of CVD. Oxidative stress is a state characterised by excessive production of reactive oxygen species (ROS) and other radical species, a reduction in the capacity of antioxidant systems, and disturbance in normal redox homeostasis with depletion of protective vascular signalling molecules such as nitric oxide (NO). This results in oxidative damage to macromolecules such as lipids, proteins and DNA which can alter their functionality. Moreover, many enzymes are sensitive to redox regulation such that oxidative modification to cysteine thiol groups results in activation of signalling cascades which result in adverse cardiovascular effects such as vascular and endothelial dysfunction. Endothelial dysfunction and oxidative stress are present in association with many conventional cardiovascular risk factors, and can be observed even prior to the development of overt, clinical, vascular pathology, suggesting that these phenomena represent the earliest stages of CVD. In the presence of CKD, there is increased ROS production due to upregulated NADPH oxidase (NOX), increase in a circulating asymmetric dimethylarginine (ADMA), uncoupling of endothelial nitric oxide synthase (eNOS) as well as other mechanisms. There is also depletion in exogenous antioxidants such as ascorbic acid and tocopherol, and a reduction in activity of endogenous antioxidant systems regulated by the master gene regulator Nrf-2. In previous studies, circulating markers of oxidative stress have been shown to be increased in CKD, together with a reduction in endothelial function in a stepwise fashion relating to the severity of renal impairment. Not only is CVD linked to oxidative stress, but the progression of CKD itself is also in part dependent on redox sensitive mechanisms. For example, administration of the ROS scavenger tempol attenuates renal injury and reduces renal fibrosis seen on biopsy in a mouse model of CKD, whilst conversely, supplementation with the NOS inhibitor L-NAME causes proteinuria and renal impairment. Previous human studies examining the effect of antioxidant administration on vascular and renal function have been conflicting however. The work contained in this thesis therefore examines the effect of antioxidant administration on vascular and endothelial function in CKD. Firstly, 30 patients with CKD stages 3 – 5, and 20 matched hypertensive controls were recruited. Participants with CKD had lower ascorbic acid, higher TAP and ADMA, together with higher augmentation index and pulse wave velocity. There was no difference in baseline flow mediated dilatation (FMD) between groups. Intravenous ascorbic acid increased TAP and O2-, and reduced central BP and augmentation index in both groups, and lowered ADMA in the CKD group only. No effect on FMD was observed. The effects of ascorbic acid on kidney function was then investigated, however this was hindered by the inherent drawbacks of existing methods of non-invasively measuring kidney function. Arterial spin labelling MRI is an emerging imaging technique which allows measurement of renal perfusion without administration of an exogenous contrast agent. The technique relies upon application of an inversion pulse to blood within the vasculature proximal to the kidneys, which magnetically labels protons allowing measurement upon transit to the kidney. At the outset of this project local experience using ASL MRI was limited and there ensued a prolonged pre-clinical phase of testing with the aim of optimising imaging strategy. A study was then designed to investigate the repeatability of ASL MRI in a group of 12 healthy volunteers with normal renal function. The measured T1 longitudinal relaxation times and ASL MRI perfusion values were in keeping with those found in the literature; T1 time was 1376 ms in the cortex and 1491 ms in the whole kidney ROI, whilst perfusion was 321 mL/min/100g in the cortex, and 228 mL/min/100g in the whole kidney ROI. There was good reproducibility demonstrated on Bland Altman analysis, with a CVws was 9.2% for cortical perfusion and 7.1% for whole kidney perfusion. Subsequently, in a study of 17 patients with CKD and 24 healthy volunteers, the effects of ascorbic acid on renal perfusion was investigated. Although no change in renal perfusion was found following ascorbic acid, it was found that ASL MRI demonstrated significant differences between those with normal renal function and participants with CKD stages 3 – 5, with increased cortical and whole kidney T1, and reduced cortical and whole kidney perfusion. Interestingly, absolute perfusion showed a weak but significant correlation with progression of kidney disease over the preceding year. Ascorbic acid was therefore shown to have a significant effect on vascular biology both in CKD and in those with normal renal function, and to reduce ADMA only in patients with CKD. ASL MRI has shown promise as a non-invasive investigation of renal function and as a biomarker to identify individuals at high risk of progressive renal impairment.
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The sea state of the Beaufort and Chukchi seas is controlled by the wind forcing and the amount of ice-free water available to generate surface waves. Clear trends in the annual duration of the open water season and in the extent of the seasonal sea ice minimum suggest that the sea state should be increasing, independent of changes in the wind forcing. Wave model hindcasts from four selected years spanning recent conditions are consistent with this expectation. In particular, larger waves are more common in years with less summer sea ice and/or a longer open water season, and peak wave periods are generally longer. The increase in wave energy may affect both the coastal zones and the remaining summer ice pack, as well as delay the autumn ice-edge advance. However, trends in the amount of wave energy impinging on the ice-edge are inconclusive, and the associated processes, especially in the autumn period of new ice formation, have yet to be well-described by in situ observations. There is an implicit trend and evidence for increasing wave energy along the coast of northern Alaska, and this coastal signal is corroborated by satellite altimeter estimates of wave energy.
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The French research EMACOP project aims at characterising wave power nearby onshore structures. This paper presents the application of the non-hydrostatic wave-flow model SWASH to wave propagation and transformation on two hot spots in Brittany. The numerical simulations were performed for dominant wave conditions and three tide levels. The results of wave simulations allow us to characterise wave energy resources and define Wave Energy Converters (WEC)'s promising positions on both sites.
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Natural stone has been a popular and reliable building material throughout history appearing in many historic monuments and in more recent buildings. Research into the intrinsic properties of specific stones is important because it gives us a greater understanding of the factors that limit and act on them. This can help prevent serious problems from occurring in our buildings bringing both esthetic benefits and financial savings. To this end, the main objective of this research has been to study the influence of the fabric and the mineral composition of two types of sandstone on their durability. The first is a red continental sandstone from the Buntsandstein Age called “Molinaza Roja”, which is quarried in Montoro (Cordoba). The second is quarried in Ronda (Malaga) and is sold under the trade name of “Arenisca Ronda”. It is a light pink-whitish calcarenite deposited during the Late Tortonian to Late Messinian. We characterized their petrological and petrophysical properties by studying their rock fabrics, porous systems and mechanical properties. In order to obtain a complete vision of the behavior of their rock fabrics, we also carried out two decay tests, the salt crystallization and the freeze–thaw tests. We then measured the effects on the textures of the altered samples during and after the decay tests and we evaluated the changes in the porous system. By comparing the results between intact and altered samples, we found that Arenisca Ronda is less durable because it has a high quantity of expandable clays (smectites) and a high percentage of pores in the 0.1–1 μm range, in which the pressure produced by salt crystallization is strongest. In Molinaza Roja the decay agents caused significant sanding due to loss of cohesion between the clasts, especially during the salt crystallization test. In both stones, the anisotropies (oriented textures) have an important role in their hydric and dynamic behavior and also affect their mechanical properties (especially in the compression resistance). No changes in color were detected.
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The activity of Fuego volcano during the 1999 - 2013 eruptive episode is studied through field, remote sensing and observatory records. Mapping of the deposits allows quantifying the erupted volumes and areas affected by the largest eruptions during this period. A wide range of volcanic processes results in a diversity of products and associated deposits, including minor airfall tephra, rockfall avalanches, lava flows, and pyroclastic flows. The activity can be characterized by long term, low level background activity, and sporadic larger explosive eruptions. Although the background activity erupts lava and ash at a low rate (~ 0.1 m3/s), the persistence of such activity over time results in a significant contribution (~ 30%) to the eruption budget during the studied period. Larger eruptions produced the majority of the volume of products during the studied period, mainly during three large events (May 21, 1999, June 29, 2003, and September 13, 2012), mostly in the form of pyroclastic flows. A total volume of ~ 1.4 x 108 m3 was estimated from the mapped deposits and the estimated background eruption rate. Posterior remobilization of pyroclastic flow material by stream erosion in the highly confined Barranca channels leads to lahar generation, either by normal rainfall, or by extreme rainfall events. A reassessment of the types of products and volumes erupted during the decade of 1970's allows comparing the activity happening since 1999 with the older activity, and suggests that many of the eruptive phenomena at Fuego may have similar mechanisms, despite the differences in scale between. The deposits of large pyroclastic flows erupted during the 1970's are remarkably similar in appearance to the deposit of pyroclastic flows from the 1999 - 2013 period, despite their much larger volume; this is also the case for prehistoric eruptions. Radiocarbon dating of pyroclastic flow deposits suggests that Fuego has produced large eruptions many times during the last ~ 2 ka, including larger eruptions during the last 500 years, which has important hazard implications. A survey was conducted among the local residents living near to the volcano, about their expectations of possible future crises. The results show that people are aware of the risk they could face in case of a large eruption, and therefore they are willing to evacuate in such case. However, their decision to evacuate may also be influenced by the conditions in which the evacuation could take place. If the evacuation represents a potential loss of their livelihood or property they will be more hesitant to leave their villages during a large eruption. The prospect of facing hardship conditions during the evacuation and in the shelters may further cause reluctance to evacuate. A short discussion on some of the issues regarding risk assessment and management through an early warning system is presented in the last chapter.
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Ulva rigida (UR) and Palmaria palmata (PP) were included in farmed Atlantic salmon diets at levels of 0-15% for 19 and 16 weeks, respectively. Quality and shelf-life parameters of salmon fillets stored in modified atmosphere packs (MAP) (60% N2 : 40% CO2) at 4ºC were compared to controls fed astaxanthin. Salmon fillets were enhanced with a yellow/orange colour. Proximate composition, pH and lipid oxidation were unaffected by dietary UR and PP. Salmon fed 5% UR and 5-15% PP did not influence sensory descriptors (texture, odour, oxidation flavour and overall acceptability) of cooked salmon fillets. Pig diets were supplemented with commercial wet- and spray-dried macroalgal (Laminaria digitata) polysaccharide extracts containing laminarin (L, 500 mg/kg feed) and fucoidan (F, 420 mg/kg feed) (L/F-WS, L/F-SD) for 3 weeks and quality and shelf-life parameters of fresh pork steaks (longissimus thoracis et lumborum) stored in MAP (80% O2 : 20% CO2) were examined. Level (450 or 900 mg L and F/kg feed) and duration (3 or 6 weeks) of dietary L/F-WS and mechanisms of antioxidant activities in pork were investigated. L/F-WS reduced (p < 0.05) lipid oxidation and lowered levels of saturated fatty acids in fresh pork after 3 weeks feeding. L/F-SD was added directly to mince pork (0.01 - 0.5%) and quality and shelf-life parameters of fresh pork patties stored in MAP (80% O2 : 20% CO2) were assessed. Direct addition of the L/F-SD increased levels of lipid oxidation and decreased surface redness (a* values) of fresh pork patties. Lipid oxidation was reduced in cooked patties due to the formation of Maillard reaction products. Cooked pork patties containing L/F-SD were subjected to an in vitro digestion and a cellular transwell model to confirm bioaccessibility and uptake of antioxidant compounds. In mechanistic studies, fucoidan demonstrated antiand pro-oxidant activities on muscle lipids and oxymyoglobin, respectively.
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BACKGROUND: Conceptualization of quality of care - in terms of what individuals, groups and organizations include in their meaning of quality, is an unexplored research area. It is important to understand how quality is conceptualised as a means to successfully implement improvement efforts and bridge potential disconnect in language about quality between system levels, professions, and clinical services. The aim is therefore to explore and compare conceptualization of quality among national bodies (macro level), senior hospital managers (meso level), and professional groups within clinical micro systems (micro level) in a cross-national study. METHODS: This cross-national multi-level case study combines analysis of national policy documents and regulations at the macro level with semi-structured interviews (383) and non-participant observation (803 hours) of key meetings and shadowing of staff at the meso and micro levels in ten purposively sampled European hospitals (England, the Netherlands, Portugal, Sweden, and Norway). Fieldwork at the meso and micro levels was undertaken over a 12-month period (2011-2012) and different types of micro systems were included (maternity, oncology, orthopaedics, elderly care, intensive care, and geriatrics). RESULTS: The three quality dimensions clinical effectiveness, patient safety, and patient experience were incorporated in macro level policies in all countries. Senior hospital managers adopted a similar conceptualization, but also included efficiency and costs in their conceptualization of quality. 'Quality' in the forms of measuring indicators and performance management were dominant among senior hospital managers (with clinical and non-clinical background). The differential emphasis on the three quality dimensions was strongly linked to professional roles, personal ideas, and beliefs at the micro level. Clinical effectiveness was dominant among physicians (evidence-based approach), while patient experience was dominant among nurses (patient-centered care, enough time to talk with patients). Conceptualization varied between micro systems depending on the type of services provided. CONCLUSION: The quality conceptualization differed across system levels (macro-meso-micro), among professional groups (nurses, doctors, managers), and between the studied micro systems in our ten sampled European hospitals. This entails a managerial alignment challenge translating macro level quality definitions into different local contexts.
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Numerical techniques such as the Boundary Element Method, Finite Element Method and Finite Difference Time Domain have been used widely to investigate plane and curved wave-front scattering by rough surfaces. For certain shapes of roughness elements (cylinders, semi-cylinders and ellipsoids) there are semi-analytical alternatives. Here, we present a theory for multiple scattering by cylinders on a hard surface to investigate effects due to different roughness shape, the effects of vacancies and variation of roughness element size on the excess attenuation due to a periodically rough surfaces.