Weighted approval voting

To allow society to treat unequal alternatives distinctly we propose a natural extension of Approval Voting by relaxing the assumption of neutrality. According to this extension, every alternative receives ex-ante a non-negative and finite weight. These weights may differ across alternatives. Given the voting decisions of every individual (individuals are allowed to vote for, or approve of, as many alternatives as they wish to), society elects all alternatives for which the product of total number of votes times exogenous weight is maximal. Our main result is an axiomatic characterization of this voting procedure.

Weighted Hardy spaces for the unit disc: approximation properties

In this paper we study basic properties of the weighted Hardy space for the unit disc with the weight function satisfying Muckenhoupt's (Aq) condition, and study related approximation problems (expansion, moment and interpolation) with respect to two incomplete systems of holomorphic functions in this space.

Scenario-based assessment of future land use change on butterfly species distributions

Species distribution models (SDMs) are increasingly used to predict environmentally induced range shifts of habitats of plant and animal species. Consequently SDMs are valuable tools for scientifically based conservation decisions. The aims of this paper are (1) to identify important drivers of butterfly species persistence or extinction, and (2) to analyse the responses of endangered butterfly species of dry grasslands and wetlands to likely future landscape changes in Switzerland. Future land use was represented by four scenarios describing: (1) ongoing land use changes as observed at the end of the last century; (2) a liberalisation of the agricultural markets; (3) a slightly lowered agricultural production; and (4) a strongly lowered agricultural production. Two model approaches have been applied. The first (logistic regression with principal components) explains what environmental variables have significant impact on species presence (and absence). The second (predictive SDM) is used to project species distribution under current and likely future land uses. The results of the explanatory analyses reveal that four principal components related to urbanisation, abandonment of open land and intensive agricultural practices as well as two climate parameters are primary drivers of species occurrence (decline). The scenario analyses show that lowered agricultural production is likely to favour dry grassland species due to an increase of non-intensively used land, open canopy forests, and overgrown areas. In the liberalisation scenario dry grassland species show a decrease in abundance due to a strong increase of forested patches. Wetland butterfly species would decrease under all four scenarios as their habitats become overgrown

Risk prediction of prevalent diabetes in a Swiss population using a weighted genetic score--the CoLaus Study.

AIMS/HYPOTHESIS: Several susceptibility genes for type 2 diabetes have been discovered recently. Individually, these genes increase the disease risk only minimally. The goals of the present study were to determine, at the population level, the risk of diabetes in individuals who carry risk alleles within several susceptibility genes for the disease and the added value of this genetic information over the clinical predictors. METHODS: We constructed an additive genetic score using the most replicated single-nucleotide polymorphisms (SNPs) within 15 type 2 diabetes-susceptibility genes, weighting each SNP with its reported effect. We tested this score in the extensively phenotyped population-based cross-sectional CoLaus Study in Lausanne, Switzerland (n = 5,360), involving 356 diabetic individuals. RESULTS: The clinical predictors of prevalent diabetes were age, BMI, family history of diabetes, WHR, and triacylglycerol/HDL-cholesterol ratio. After adjustment for these variables, the risk of diabetes was 2.7 (95% CI 1.8-4.0, p = 0.000006) for individuals with a genetic score within the top quintile, compared with the bottom quintile. Adding the genetic score to the clinical covariates improved the area under the receiver operating characteristic curve slightly (from 0.86 to 0.87), yet significantly (p = 0.002). BMI was similar in these two extreme quintiles. CONCLUSIONS/INTERPRETATION: In this population, a simple weighted 15 SNP-based genetic score provides additional information over clinical predictors of prevalent diabetes. At this stage, however, the clinical benefit of this genetic information is limited.

Weighted limits in simplicial homotopy theory

We extend the theory of Quillen adjunctions by combining ideas of homotopical algebra and of enriched category theory. Our results describe how the formulas for homotopy colimits of Bousfield and Kan arise from general formulas describing the derived functor of the weighted colimit functor.

Dividends and weighted values in games with externalities

We consider cooperative environments with externalities (games in partition function form) and provide a recursive definition of dividends for each coalition and any partition of the players it belongs to. We show that with this definition and equal sharing of these dividends the averaged sum of dividends for each player, over all the coalitions that contain the player, coincides with the corresponding average value of the player. We then construct weighted Shapley values by departing from equal division of dividends and finally, for each such value, provide a bidding mechanism implementing it.

Device-specific weighted T-score for two quantitative ultrasounds: operational propositions for the management of osteoporosis for 65 years and older women in Switzerland.

The World Health Organization (WHO) criteria for the diagnosis of osteoporosis are mainly applicable for dual X-ray absorptiometry (DXA) measurements at the spine and hip levels. There is a growing demand for cheaper devices, free of ionizing radiation such as promising quantitative ultrasound (QUS). In common with many other countries, QUS measurements are increasingly used in Switzerland without adequate clinical guidelines. The T-score approach developed for DXA cannot be applied to QUS, although well-conducted prospective studies have shown that ultrasound could be a valuable predictor of fracture risk. As a consequence, an expert committee named the Swiss Quality Assurance Project (SQAP, for which the main mission is the establishment of quality assurance procedures for DXA and QUS in Switzerland) was mandated by the Swiss Association Against Osteoporosis (ASCO) in 2000 to propose operational clinical recommendations for the use of QUS in the management of osteoporosis for two QUS devices sold in Switzerland. Device-specific weighted "T-score" based on the risk of osteoporotic hip fractures as well as on the prediction of DXA osteoporosis at the hip, according to the WHO definition of osteoporosis, were calculated for the Achilles (Lunar, General Electric, Madison, Wis.) and Sahara (Hologic, Waltham, Mass.) ultrasound devices. Several studies (totaling a few thousand subjects) were used to calculate age-adjusted odd ratios (OR) and area under the receiver operating curve (AUC) for the prediction of osteoporotic fracture (taking into account a weighting score depending on the design of the study involved in the calculation). The ORs were 2.4 (1.9-3.2) and AUC 0.72 (0.66-0.77), respectively, for the Achilles, and 2.3 (1.7-3.1) and 0.75 (0.68-0.82), respectively, for the Sahara device. To translate risk estimates into thresholds for clinical application, 90% sensitivity was used to define low fracture and low osteoporosis risk, and a specificity of 80% was used to define subjects as being at high risk of fracture or having osteoporosis at the hip. From the combination of the fracture model with the hip DXA osteoporotic model, we found a T-score threshold of -1.2 and -2.5 for the stiffness (Achilles) determining, respectively, the low- and high-risk subjects. Similarly, we found a T-score at -1.0 and -2.2 for the QUI index (Sahara). Then a screening strategy combining QUS, DXA, and clinical factors for the identification of women needing treatment was proposed. The application of this approach will help to minimize the inappropriate use of QUS from which the whole field currently suffers.

Alveolar echinococcosis of the liver: Diffusion-weighted MRI findings and potential role in lesion characterisation

PURPOSE: To report the diffusion-weighted MRI findings in alveolar echinococcosis (AE) of the liver and evaluate the potential role of apparent diffusion coefficients (ADCs) in the characterisation of lesions. MATERIALS AND METHODS: We retrospectively included 22 patients with 63 AE liver lesions (≥1cm), examined with 3-T liver MRI, including a free-breathing diffusion-weighted single-shot echo-planar imaging sequence (b-values=50, 300 and 600s/mm(2)). Two radiologists jointly assessed the following lesion features: size, location, presence of cystic and/or solid components (according to Kodama's classification system), relative contrast enhancement, and calcifications (on CT). The ADCtotal, ADCmin and ADCmax were measured in each lesion and the surrounding liver parenchyma. RESULTS: Three type 1, 19 type 2, 17 type 3, three type 4 and 21 type 5 lesions were identified. The mean (±SD) ADCtotal, ADCmin and ADCmax for all lesions were 1.73±0.50, 0.76±0.38 and 2.63±0.76×10(-3)mm(2)/s, respectively. The mean ADCtotal for type 1, type 2, type 3, type 4 and type 5 lesions were 1.97±1.01, 1.76±0.53, 1.73±0.41, 1.15±0.42 and 1.76±0.44×10(-3)mm(2)/s, respectively. No significant differences were found between the five lesion types, except for type 4 (p=0.0363). There was a significant correlation between the presence of a solid component and low ADCmin (r=0.39, p=0.0016), whereas an inverse correlation was found between the relative contrast enhancement and ADCtotal (r=-0.34, p=0.0072). CONCLUSION: The ADCs of AE lesions are relatively low compared to other cystic liver lesions, which may help in the differential diagnosis. Although ADCs are of little use to distinguish between the five lesion types, their low value reflects the underlying solid component.

Are two tax rates better than one?

Abstract: Should two–band income taxes be progressive given a general income distribution? We provide a negative answer under utilitarian and max-min welfare functions. While this result clarifies some ambiguities in the literature, it does not rule out progressive taxes in general. If we maximize total or weighted utility of the poor, as often intended by the society, progressive taxes can be justified, especially when the ‘rich’ are very rich. Under these objectives we obtain new necessary conditions for progressive taxes, which only depend on aggregate features of income distributions. The validity of these conditions is examined using plausible income distributions.

Comparing population distributions from bin-aggregated sample data: an application to historical height data from France

This paper develops a methodology to estimate the entire population distributions from bin-aggregated sample data. We do this through the estimation of the parameters of mixtures of distributions that allow for maximal parametric flexibility. The statistical approach we develop enables comparisons of the full distributions of height data from potential army conscripts across France's 88 departments for most of the nineteenth century. These comparisons are made by testing for differences-of-means stochastic dominance. Corrections for possible measurement errors are also devised by taking advantage of the richness of the data sets. Our methodology is of interest to researchers working on historical as well as contemporary bin-aggregated or histogram-type data, something that is still widely done since much of the information that is publicly available is in that form, often due to restrictions due to political sensitivity and/or confidentiality concerns.

T1-weighted MRI as a substitute to CT for refocusing planning in MR-guided focused ultrasound.

Precise focusing is essential for transcranial MRI-guided focused ultrasound (TcMRgFUS) to minimize collateral damage to non-diseased tissues and to achieve temperatures capable of inducing coagulative necrosis at acceptable power deposition levels. CT is usually used for this refocusing but requires a separate study (CT) ahead of the TcMRgFUS procedure. The goal of this study was to determine whether MRI using an appropriate sequence would be a viable alternative to CT for planning ultrasound refocusing in TcMRgFUS. We tested three MRI pulse sequences (3D T1 weighted 3D volume interpolated breath hold examination (VIBE), proton density weighted 3D sampling perfection with applications optimized contrasts using different flip angle evolution and 3D true fast imaging with steady state precision T2-weighted imaging) on patients who have already had a CT scan performed. We made detailed measurements of the calvarial structure based on the MRI data and compared those so-called 'virtual CT' to detailed measurements of the calvarial structure based on the CT data, used as a reference standard. We then loaded both standard and virtual CT in a TcMRgFUS device and compared the calculated phase correction values, as well as the temperature elevation in a phantom. A series of Bland-Altman measurement agreement analyses showed T1 3D VIBE as the optimal MRI sequence, with respect to minimizing the measurement discrepancy between the MRI derived total skull thickness measurement and the CT derived total skull thickness measurement (mean measurement discrepancy: 0.025; 95% CL (-0.22-0.27); p = 0.825). The T1-weighted sequence was also optimal in estimating skull CT density and skull layer thickness. The mean difference between the phase shifts calculated with the standard CT and the virtual CT reconstructed from the T1 dataset was 0.08 ± 1.2 rad on patients and 0.1 ± 0.9 rad on phantom. Compared to the real CT, the MR-based correction showed a 1 °C drop on the maximum temperature elevation in the phantom (7% relative drop). Without any correction, the maximum temperature was down 6 °C (43% relative drop). We have developed an approach that allows for a reconstruction of a virtual CT dataset from MRI to perform phase correction in TcMRgFUS.

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Investigation of field and diffusion time dependence of the diffusion-weighted signal at ultrahigh magnetic fields.

Over the last decade, there has been a significant increase in the number of high-magnetic-field MRI magnets. However, the exact effect of a high magnetic field strength (B0 ) on diffusion-weighted MR signals is not yet fully understood. The goal of this study was to investigate the influence of different high magnetic field strengths (9.4 T and 14.1 T) and diffusion times (9, 11, 13, 15, 17 and 24 ms) on the diffusion-weighted signal in rat brain white matter. At a short diffusion time (9 ms), fractional anisotropy values were found to be lower at 14.1 T than at 9.4 T, but this difference disappeared at longer diffusion times. A simple two-pool model was used to explain these findings. The model describes the white matter as a first hindered compartment (often associated with the extra-axonal space), characterized by a faster orthogonal diffusion and a lower fractional anisotropy, and a second restricted compartment (often associated with the intra-axonal space), characterized by a slower orthogonal diffusion (i.e. orthogonal to the axon direction) and a higher fractional anisotropy. Apparent T2 relaxation time measurements of the hindered and restricted pools were performed. The shortening of the pseudo-T2 value from the restricted compartment with B0 is likely to be more pronounced than the apparent T2 changes in the hindered compartment. This study suggests that the observed differences in diffusion tensor imaging parameters between the two magnetic field strengths at short diffusion time may be related to differences in the apparent T2 values between the pools. Copyright © 2013 John Wiley & Sons, Ltd.

On the existence of hysteresis in the Kuramoto model with bimodal frequency distributions

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.