Geometric-type Sobolev inequalities and applications to the regularity of minimizers

The purpose of this paper is twofold. We first prove a weighted Sobolev inequality and part of a weighted Morrey's inequality, where the weights are a power of the mean curvature of the level sets of the function appearing in the inequalities. Then, as main application of our inequalities, we establish new $L^q$ and $W^{1,q}$ estimates for semi-stable solutions of $-\Delta u=g(u)$ in a bounded domain $\Omega$ of $\mathbb{R}^n$. These estimates lead to an $L^{2n/(n-4)}(\Omega)$ bound for the extremal solution of $-\Delta u=\lambda f(u)$ when $n\geq 5$ and the domain is convex. We recall that extremal solutions are known to be bounded in convex domains if $n\leq 4$, and that their boundedness is expected ---but still unkwown--- for $n\leq 9$.Comment: 20 pages; 1 figur

Antisymmetry of solutions for some weighted elliptic problems

This article concerns the antisymmetry, uniqueness, and monotonicity properties of solutions to some elliptic functionals involving weights and a double well potential. In the one-dimensional case, we introduce the continuous odd rearrangement of an increasing function and we show that it decreases the energy functional when the weights satisfy a certain convexity-type hypothesis. This leads to the antisymmetry or oddness of increasing solutions (and not only of minimizers). We also prove a uniqueness result (which leads to antisymmetry) where a convexity-type condition by Berestycki and Nirenberg on the weights is improved to a monotonicity condition. In addition, we provide with a large class of problems where antisymmetry does not hold. Finally, some rather partial extensions in higher dimensions are also given

New methodology for known metabolite identification in metabonomics / metabolomics: topological metabolite identification carbon efficiency (tMICE)

A new, simple-to-implement and quantitative approach to assessing the confidence in NMR-based identification of known metabolites is introduced. The approach is based on a topological analysis of metabolite identification information available from NMR spectroscopy studies and is a development of the metabolite identification carbon efficiency (MICE) method. New topological metabolite identification indices are introduced, analysed and proposed for general use, including topological metabolite identification carbon efficiency (tMICE). Since known metabolite identification is one of the key bottlenecks in either NMR spectroscopy- or mass spectrometry-based metabonomics/metabolomics studies, and given the fact that there is no current consensus on how to assess metabolite identification confidence, it is hoped that these new approaches and the topological indices will find utility

Regularity of stable solutions of pp-Laplace equations through geometric Sobolev type inequalities

In this paper we prove a Sobolev and a Morrey type inequality involving the mean curvature and the tangential gradient with respect to the level sets of the function that appears in the inequalities. Then, as an application, we establish \textit{a priori} estimates for semi-stable solutions of $-\Delta_p u= g(u)$ in a smooth bounded domain $\Omega\subset \mathbb{R}^n$. In particular, we obtain new $L^r$ and $W^{1,r}$ bounds for the extremal solution $u^\star$ when the domain is strictly convex. More precisely, we prove that $u^\star\in L^\infty(\Omega)$ if $n\leq p+2$ and $u^\star\in L^{\frac{np}{n-p-2}}(\Omega)\cap W^{1,p}_0(\Omega)$ if $n>p+2$.Comment: 26 page

Relação entre status social subjetivo e saúde percebida entre mulheres imigrantes latino-americanas

OBJECTIVE: to explore the relationship between socioeconomic status and subjective social status and explain how subjective social status predicts health in immigrant women. METHODS: cross-sectional study based on data from 371 Latin American women (16-65 years old) from a total of 7,056 registered immigrants accesse through community parthers between 2009-2010. Socioeconomic status was measured through education, income and occupation; subjective social status was measured using the MacArthur Scale, and perceived health, using a Likert scale. RESULTS: a weak correlation between socioeconomic and subjective social status was found. In the bivariate analysis, a significantly higher prevalence of negative perceived health in women with no education, low income, undocumented employment was observed. In the multivariate analysis, higher odds of prevalence of negative perceptions of health in the lower levels of the MacArthur scale were observed. No significant differences with the rest of the variables were found. CONCLUSIONS: the study suggests that subjective social status was a better predictor of health status than the socioeconomic status measurements. Therefore, the use of this measurement may be relevant to the study of health inequalities, particularly in socially disadvantaged groups such as immigrants.OBJETIVO: explorar la relación entre el estatus socioeconómico y el estatus social subjetivo y explicar en qué medida el estatus social subjetivo predice la salud en mujeres inmigrantes. MÉTODOS: estudio transversal. Observaciones basadas en 371 latinoamericanas (16-65 años) de un total de 7.056 empadronadas, captadas a través de asociaciones entre 2009-2010. El estatus socioeconómico se midió a través de educación, ingresos y ocupación; el estatus social subjetivo usando la Escala MacArthur; y la salud percibida mediante una escala de likert. RESULTADOS: se encontró una correlación débil entre el estatus socioeconómico y el social subjetivo. En el análisis bivariante se observó significativamente una prevalencia mayor de salud percibida negativa en las mujeres sin estudios, con ingresos bajos, desempleadas e indocumentadas. En el análisis multivariante, se observaron Odds de prevalencia de salud percibida negativa más elevadas en los niveles de la escala MacArthur más bajos. No se observaron diferencias significativas con el resto de las variables. CONCLUSIONES: el estudio sugiere que el estatus social subjetivo es un predictor mejor del estado de salud que las medidas del estatus socioeconómico. Por tanto, el uso de esta medida puede ser relevante para el estudio de las desigualdades en salud, particularmente en los grupos en desventaja social como los inmigrantes.OBJETIVO: explorar a relação entre nível socieconômico e status social subjetivo e explicar como o status social subjetivo prediz a saúde em mulheres imigrantes. MÉTODOS: estudo transversal com observações baseadas em 371 mulheres latino-americanas (16-65 anos) de um total de 7.056 registradas, recrutadas por meio de parcerias entre os anos 2009 e 2010. O nível socioeconômico foi mensurado por meio de escolaridade, renda e profissão; o status social subjetivo foi mensurado utilizando-se a Escala MacArthur, e a saúde percebida, usando-se uma escala tipo Likert. RESULTADOS: encontrou-se fraca correlação entre o nível socioeconômico e o status social subjetivo. Na análise bivariada, observou-se prevalência significativamente mais alta de saúde percebida negativamente em mulheres sem escolaridade, baixa renda, desempregadas e com emprego informal. Na análise multivariada, observaram-se maiores chances de prevalência de saúde percebida negativamente, nos níveis mais baixos da escala MacArthur. Não foram encontradas diferenças significativas nas demais variáveis. CONCLUSÕES: o estudo sugere que o status social subjetivo foi um melhor preditor de status de saúde do que as mensurações de status econômico. Portanto, o uso dessa medida pode ser relevante para o estudo das desigualdades em saúde, particularmente nos grupos em desvantagem social, como os imigrantes

Associated factors of non-recurrence stroke among stroke patients in Thailand

Stroke is a silent killer. Preventing the recurrence of strokes is therefore essential. This study investigated i) the level of health literacy to prevent the recurrence of stroke, ii) factors associated with not having a stroke, and iii) Associations between health literacy and recurrence of stroke. This cross-sectional analytical research was conducted with 240 samples. Multiple logistic regression was performed to describe the factors and associations recurrence stroke. The results showed that the majority of the samples had a problematic level of health literacy to prevent recurrence stroke (52.08%), and 35.84% had recurrence stroke. Factor: Not drinking alcohol was 6.11 times more than drinking (adj. OR=6.11, 95% CI: 4.88 to 10.04). There was no recurrence of stroke with statistical significance at the 0.05 level. High understanding skill 4.43 times (adj. OR=4.43, 95% CI=3.44 to 5.58), and high apply skill 3.67 times (adj. OR=3.67, 95% CI=2.44 to 8.18) than low and moderate levels. Statistically significant at the 0.05 level. Per findings, health literacy should be actively promoted to prevent stroke recurrence

The future of metabolomics in ELIXIR.

Metabolomics, the youngest of the major omics technologies, is supported by an active community of researchers and infrastructure developers across Europe. To coordinate and focus efforts around infrastructure building for metabolomics within Europe, a workshop on the "Future of metabolomics in ELIXIR" was organised at Frankfurt Airport in Germany. This one-day strategic workshop involved representatives of ELIXIR Nodes, members of the PhenoMeNal consortium developing an e-infrastructure that supports workflow-based metabolomics analysis pipelines, and experts from the international metabolomics community. The workshop established metabolite identification as the critical area, where a maximal impact of computational metabolomics and data management on other fields could be achieved. In particular, the existing four ELIXIR Use Cases, where the metabolomics community - both industry and academia - would benefit most, and which could be exhaustively mapped onto the current five ELIXIR Platforms were discussed. This opinion article is a call for support for a new ELIXIR metabolomics Use Case, which aligns with and complements the existing and planned ELIXIR Platforms and Use Cases