A multidimensional solution to additive homological equations

In this paper we prove that for a finite-dimensional real normed space $V$, every bounded mean zero function $f\in L_\infty([0,1];V)$ can be written in the form $f = g\circ T - g$ for some $g\in L_\infty([0,1];V)$ and some ergodic invertible measure preserving transformation $T$ of $[0,1]$. Our method moreover allows us to choose $g$, for any given $\varepsilon>0$, to be such that $\|g\|_\infty\leq (S_V+\varepsilon)\|f\|_\infty$, where $S_V$ is the Steinitz constant corresponding to $V$

A multidimensional solution to additive homological equations

In this paper we prove that for a finite-dimensional real normed space $V$, every bounded mean zero function $f\in L_\infty([0,1];V)$ can be written in the form $f = g\circ T - g$ for some $g\in L_\infty([0,1];V)$ and some ergodic invertible measure preserving transformation $T$ of $[0,1]$. Our method moreover allows us to choose $g$, for any given $\varepsilon>0$, to be such that $\|g\|_\infty\leq (S_V+\varepsilon)\|f\|_\infty$, where $S_V$ is the Steinitz constant corresponding to $V$

A solution to the multidimensional additive homological equation

We prove that, for a finite-dimensional real normed space V, every bounded mean zero function f ∈ L∞([0, 1]; V) can be written in the form f = g ◦ T − g for some g ∈ L∞([0, 1]; V) and some ergodic invertible measure preserving transformation T of [0, 1]. Our method moreover allows us to choose g, for any given ε > 0, to be such that ∥g∥∞ ⩽ (SV + ε)∥f∥∞, where SV is the Steinitz constant corresponding to V

Predictors of Enhancing Human Physical Attractiveness: Data from 93 Countries

People across the world and throughout history have gone to great lengths to enhance their physical appearance. Evolutionary psychologists and ethologists have largely attempted to explain this phenomenon via mating preferences and strategies. Here, we test one of the most popular evolutionary hypotheses for beauty-enhancing behaviors, drawn from mating market and parasite stress perspectives, in a large cross-cultural sample. We also test hypotheses drawn from other influential and non-mutually exclusive theoretical frameworks, from biosocial role theory to a cultural media perspective. Survey data from 93,158 human participants across 93 countries provide evidence that behaviors such as applying makeup or using other cosmetics, hair grooming, clothing style, caring for body hygiene, and exercising or following a specific diet for the specific purpose of improving ones physical attractiveness, are universal. Indeed, 99% of participants reported spending \u3e10 min a day performing beauty-enhancing behaviors. The results largely support evolutionary hypotheses: more time was spent enhancing beauty by women (almost 4 h a day, on average) than by men (3.6 h a day), by the youngest participants (and contrary to predictions, also the oldest), by those with a relatively more severe history of infectious diseases, and by participants currently dating compared to those in established relationships. The strongest predictor of attractiveness-enhancing behaviors was social media usage. Other predictors, in order of effect size, included adhering to traditional gender roles, residing in countries with less gender equality, considering oneself as highly attractive or, conversely, highly unattractive, TV watching time, higher socioeconomic status, right-wing political beliefs, a lower level of education, and personal individualistic attitudes. This study provides novel insight into universal beauty-enhancing behaviors by unifying evolutionary theory with several other complementary perspectives

Exposure to Coxiella burnetii and risk of non-Hodgkin lymphoma: a retrospective population-based analysis in the Netherlands

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Exposure to Coxiella burnetii and risk of non-Hodgkin lymphoma : a retrospective population-based analysis in the Netherlands

Background: An association between Coxiella burnetii and non-Hodgkin lymphoma has been suggested. After a large Q fever epidemic in the Netherlands (2007–10), we postulated that the incidence of non-Hodgkin lymphoma would be increased during and after the epidemic in areas with a high endemicity of Q fever compared with those with low endemicity. Methods: We did a retrospective population-based analysis and calculated relative risks (RRs) of non-Hodgkin lymphoma during 1-year periods before, during, and after the Q fever epidemic, for areas with intermediate and high endemicity of Q fever compared with low endemic areas. We also calculated the RR of non-Hodgkin lymphoma in people with chronic Q fever compared with the general population. Findings: Between Jan 1, 2002, and Dec 31, 2013, 48 760 cases of non-Hodgkin lymphoma were diagnosed. The incidence of non-Hodgkin lymphoma ranged from 21·4 per 100 000 per year in 2002 to 26·7 per 100 000 per year in 2010. A significant association with non-Hodgkin lymphoma was noted in 2009 for areas with a high endemicity of Q fever compared with low endemic areas (RR 1·16, 95% CI 1·02–1·33; p=0·029); no further associations were noted in any other year or for areas with intermediate Q fever endemicity. Among 439 individuals with chronic Q fever, five developed non-Hodgkin lymphoma, yielding a crude absolute risk of 301·0 cases per 100 000 per year (RR 4·99, 95% CI 2·07–11·98; p=0·0003) compared with the general population in the Netherlands. Interpretation: These findings do not support the hypothesis that Q fever has a relevant causal role in the development of non-Hodgkin lymphoma. Several limitations, inherent to the design of this study, might lead to both underestimation and overestimation of the studied association. Funding: Foundation Q-support and Institut Mérieux