Search results for " inequality."

Reciprocal lower bound on modulus of curve families in metric surfaces

2019

We prove that any metric space $X$ homeomorphic to $\mathbb{R}^2$ with locally finite Hausdorff 2-measure satisfies a reciprocal lower bound on modulus of curve families associated to a quadrilateral. More precisely, let $Q \subset X$ be a topological quadrilateral with boundary edges (in cyclic order) denoted by $\zeta_1, \zeta_2, \zeta_3, \zeta_4$ and let $\Gamma(\zeta_i, \zeta_j; Q)$ denote the family of curves in $Q$ connecting $\zeta_i$ and $\zeta_j$; then $\text{mod} \Gamma(\zeta_1, \zeta_3; Q) \text{mod} \Gamma(\zeta_2, \zeta_4; Q) \geq 1/\kappa$ for $\kappa = 2000^2\cdot (4/\pi)^2$. This answers a question concerning minimal hypotheses under which a metric space admits a quasiconfor…

Accessible parts of boundary for simply connected domains

2018

For a bounded simply connected domain $\Omega\subset\mathbb{R}^2$, any point $z\in\Omega$ and any $0<\alpha<1$, we give a lower bound for the $\alpha$-dimensional Hausdorff content of the set of points in the boundary of $\Omega$ which can be joined to $z$ by a John curve with a suitable John constant depending only on $\alpha$, in terms of the distance of $z$ to $\partial\Omega$. In fact this set in the boundary contains the intersection $\partial\Omega_z\cap\partial\Omega$ of the boundary of a John sub-domain $\Omega_z$ of $\Omega$, centered at $z$, with the boundary of $\Omega$. This may be understood as a quantitative version of a result of Makarov. This estimate is then applied to obta…

No evidence that economic inequality moderates the effect of income on generosity

2019

A landmark study published in PNAS [Côté S, House J, Willer R (2015) Proc Natl Acad Sci USA 112:15838–15843] showed that higher income individuals are less generous than poorer individuals only if they reside in a US state with comparatively large economic inequality. This finding might serve to reconcile inconsistent findings on the effect of social class on generosity by highlighting the moderating role of economic inequality. On the basis of the importance of replicating a major finding before readily accepting it as evidence, we analyzed the effect of the interaction between income and inequality on generosity in three large representative datasets. We analyzed the donating behavior of…

Reply to Côté and Willer: New replication attempts provide no evidence that inequality moderates the effect of income on generosity

2020

Cote et al. (1) provided evidence that economic inequality moderates the effect of income on generosity. In their study, individuals with higher household income were less generous in a dictator game than poorer individuals only if they resided in a US state with comparatively large economic inequality. We questioned this finding because we did not find any evidence for the postulated moderation effect of economic inequality across three studies (ref. 2; for similar replication failures see ref. 3). However, our studies were conceptual rather than direct replications as we used different measures of generosity (charitable donations, behavior in a trust game, and volunteering) and also inclu…

Genetic variability at neutral markers, quantitative trait loci and trait in a subdivided population under selection

2003

Abstract Genetic variability in a subdivided population under stabilizing and diversifying selection was investigated at three levels: neutral markers, QTL coding for a trait, and the trait itself. A quantitative model with additive effects was used to link genotypes to phenotypes. No physical linkage was introduced. Using an analytical approach, we compared the diversity within deme (HS) and the differentiation (FST) at the QTL with the genetic variance within deme (VW) and the differentiation (QST) for the trait. The difference between FST and QST was shown to depend on the relative amounts of covariance between QTL within and between demes. Simulations were used to study the effect of se…

Class II HLA interactions modulate genetic risk for multiple sclerosis

2015

Association studies have greatly refined the understanding of how variation within the human leukocyte antigen (HLA) genes influences risk of multiple sclerosis. However, the extent to which major effects are modulated by interactions is poorly characterized. We analyzed high-density SNP data on 17,465 cases and 30,385 controls from 11 cohorts of European ancestry, in combination with imputation of classical HLA alleles, to build a high-resolution map of HLA genetic risk and assess the evidence for interactions involving classical HLA alleles. Among new and previously identified class II risk alleles (HLA-DRB1*15:01, HLA-DRB1*13:03, HLA-DRB1*03:01, HLA-DRB1*08:01 and HLA-DQB1*03:02) and cla…

The isoperimetric inequality and the geodesic spheres. Some geometric consequences

1986

Social Geographical Patterns in Membership of the Established Church in Denmark

2019

The Church of Denmark was established in 1849 and is regarded as a pillar of traditional national identity. This status is being challenged by a steady decline in membership in recent decades. The Capital area is especially prone to low membership rates, and this regional pattern remains when the analysis controls for income and education. Furthermore, the local membership rate is also related to affiliation to the neighbourhood. Our detailed analysis is based on public register data on the individual level combined with geographical mapping information. Denmark is thereby divided into micro-aggregated areas in order to locate varying church membership rates. While some local variation can …

Exploratory spatial data analysis of the distribution of regional per capita GDP in Europe, 1980-1995

2000

The aim of this paper is to study the dynamics of European regional per capita product over time and space. This purpose is achieved by using the recently developed methods of Exploratory Spatial Data Analysis. Using a sample of European regions over the 1980-1995 period, we find strong evidence of global and local spatial autocorrelation in per capita GDP throughout the period. The detection of clusters of high and low per capita products during the period is an indication of the persistence of spatial disparities between European regions. This analysis is finally refined by the investigation of the spatial pattern of regional growth. Key words:exploratory spatial data analysis; distributi…

Frailty as a predictor of all-cause mortality in older men and women

2014

Aims To investigate the modifying effect of sex on the association between frailty and all-cause mortality, and to determine the effects of changes in frailty status on mortality. Methods This population-based study comprised 654 persons aged 76–100 years (mean age 82 ± 4.6 years). Frailty status was assessed at baseline in 2005, and reassessed in 2007 (n = 546) using the Cardiovascular Health Study criteria. Death dates were received from the official register until the end of 2009. The associations between frailty, changes in frailty and mortality were investigated using Cox regression models. Results At baseline, 93 (14%) participants were classified as frail, and 311 (48%) as pre-frail.…