Differentiable positive definite kernels on two-point homogeneous spaces

In this work we study continuous kernels on compact two-point homogeneous spaces which are positive definite and zonal (isotropic). Such kernels were characterized by R. Gangolli some forty years ago and are very useful for solving scattered data interpolation problems on the spaces. In the case the space is the d-dimensional unit sphere, J. Ziegel showed in 2013 that the radial part of a continuous positive definite and zonal kernel is continuously differentiable up to order ⌊(d−1)/2⌋ in the interior of its domain. The main issue here is to obtain a similar result for all the other compact two-point homogeneous spaces.CNPq (grant 141908/2015-7)FAPESP (grant 2014/00277-5

Cycling as the Best Sub-8-Hour Performance Predictor in Full Distance Triathlon

For any triathlon distance (short, Olympic, half-distance and full-distance), competitors spend more time cycling than swimming or running, but running has emerged as the discipline with the greatest influence on overall performance at the Olympic distance. However, there is a lack of evidence on which discipline has the greatest influence on performance in the overall full-distance triathlon (3.8 km swimming/180 km cycling/42.195 km running), especially for the fastest performing athletes of all time. The total race times of 51 fastest triathletes (sub-8-hour) were studied, while for the split times, a sample of 44 participants was considered. The discipline that seemed to better predict total race time was cycling (coefficient = 0.828; < 0.001), followed by running (coefficient = 0.726; < 0.001) and swimming (coefficient = 0.476; < 0.001). Furthermore, cycling was the discipline with the highest performance improvement over the years, whereas running had a slightly decrease. In conclusion, cycling seems to be the discipline with greater influence in final result for the full-distance triathlon

CRESCIMENTO E ACUMULO DE NUTRIENTES EM MUDAS DE ACEROLEIRAS EM FUNÇÃO DA APLICAÇÃO DE DIFERENTES DOSES DE NITROGÊNIO E POTÁSSIO

Com o objetivo de estudar o efeito de doses de nitrogênio (N) e potássio (K) no crescimento e acúmulo de nutrientes na parte aérea de mudas de aceroleira (Malpighia emarginata D.C), instalou-se um experimento em casa de vegetação na Universidade Federal de São João Del Rei-UFSJ em Sete Lagoas, MG, utilizando-se mudas oriundas do processo de estaquia. Utilizou-se o esquema fatorial 4 x 4, em delineamento de blocos casualizados, com três repetições e três plantas por parcela. Os fatores consistiram de quatro doses de N (0, 200, 400 e 600 mg dm-3) e quatro doses de K (0, 100, 200 e 300 mg dm-3). Aos 110 dias após o transplantio, as mudas foram avaliadas quanto ao comprimento de parte aérea e raiz, diâmetro do caule, número de folhas e Índice de Qualidade de Dickson, posteriormente foram colhidas, secas em estufa a 65 °C para a obtenção da matéria seca da parte aérea, raiz e total, sendo trituradas para a determinação da concentração de nutrientes. Foram determinadas as quantidades acumuladas de N, P, K, Ca, Mg, S, B, Cu, Zn, Fe e Mn na matéria seca da parte aérea. As doses isoladas de N e K influenciaram as variáveis de crescimento e aumentaram as quantidades acumuladas de P, K e Zn, sendo as quantidades acumuladas dos demais nutrientes afetadas apenas pelo N. O acúmulo dos nutrientes nas mudas seguiu a ordem decrescente N>Ca>Mg>P>S>K>Mn>B>Zn>Fe

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Universality and orthogonality in reproducing Kernel Hilbert spaces

Neste trabalho analisamos o papel das funções layout de um núcleo positivo definido K sobre um espaço topológico de Hausdor E com relação a duas propriedades específicas: a universalidade de K e a ortogonalidade no espaço de Hilbert de reprodução de K a partir de suportes disjuntos. As funções layout sempre existem mas podem não ser únicas. De uma maneira geral, a função layout e uma aplicação que transfere, convenientemente, informações do espaço E para um espaço com produto interno de dimensão alta, onde métodos lineares podem ser usados. Tanto a universalidade quanto a ortogonalidade pressupõem a continuidade do núcleo. O primeiro conceito exige que para cada compacto não vazio X de E, o conjunto de \"seções\" {K(., y) : y \'PERTENCE\' X} seja total no espaço de todas as funções contínuas com domínio X, munido da topologia da convergência uniforme. Um dos resultados principais do trabalho caracteriza a universalidade de um núcleo K através de uma propriedade de universalidade semelhante da função layout. A ortogonalidade a partir de suportes disjuntos almeja então a ortogonalidade de quaisquer duas funções do espaço de Hilbert de reprodução de K quando seus suportes não se intersectamWe analyze the role of feature maps of a positive denite kernel K acting on a Hausdorff topological space E in two specific properties: the universality of K and the orthogonality in the reproducing kernel Hilbert space of K from disjoint supports. Feature maps always exist but may not be unique. A feature map may be interpreted as a kernel based procedure that maps the data from the original input space E into a potentially higher dimensional \"feature space\" in which linear methods may then be used. Both properties, universality and orthogonality from disjoint supports, make sense under continuity of the kernel. Universality of K is equivalent to the fundamentality of {K(. ; y) : y \'IT BELONGS\' X} in the space of all continuous functions on X, with the topology of uniform convergence, for all nonempty compact subsets X of E. One of the main results in this work is a characterization of the universality of K from a similar concept for the feature map. Orthogonality from disjoint supports seeks the orthogonality of any two functions in the reproducing kernel Hilbert space of K when the functions have disjoint support

Positive definite kernels on two-point homogeneous spaces

Neste trabalho analisamos a positividade definida estrita de núcleos contínuos sobre um espaço compacto 2-homogêneo. R. Gangolli (1967) apresentou uma caracterização completa para os núcleos que são contínuos, isotrópicos e positivos definidos sobre um espaço compacto 2-homogêneo Md: a parte isotrópica do núcleo é uma série de Fourier uniformemente convergente, com coeficientes não negativos, em relação a certos polinômios de Jacobi atrelados a Md. Uma das contribuições de nosso trabalho é uma caracterização para a positividade definida estrita de tais núcleos, complementando a caracterização apresentada por Chen et al. (2003) no caso em que Md é uma esfera unitária de dimensão maior ou igual a 2. Outra contribuição do trabalho é uma extensão do resultado de Gangolli para núcleos sobre produtos cartesianos de espaços compactos 2-homogêneos, e a consequente caracterização para núcleos estritamente positivos definidos neste mesmo contexto. Por fim, a última contribuição do trabalho envolve a análise do grau de diferenciabilidade da parte isotrópica de um núcleo contínuo, isotrópico e positivo definido sobre Md e a aplicabilidade de tal análise em resultados envolvendo a positividade definida estrita.In this work we analyze the strict positive definiteness of continuous kernels on compact two-point homogeneous spaces Md. R. Gangolli (1967) presented a complete characterization for continuous, isotropic and positive definite kernels on Md: the isotropic part of the kernel is a uniformly convergent Fourier series of certain Jacobi polynomials associated to Md, with nonnegative coefficients. One of the contributions of our work is a characterization for the strict positive definiteness of such kernels, completing that one presented by Chen et al. (2003) in the case Md is the unit sphere of dimension at least 2. Another contribuition of this work is an extension of Gangolli\'s result for kernels on a product of compact two-point homogeneous spaces, and the subsequent characterization of strict positive definiteness in this same context. Finally, the last contribution in this work involves the analysis of the differentiability of the isotropic part of a continuous, isotropic and positive definite kernel on Md and the applicability of such analysis in results involving the strict positive definiteness

Núcleos positivos definidos em espaços 2-homogêneos

Tese (doutorado) - Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, Programa de Pós-Graduação em Matemática, São Carlos, 2016

Series expansions among weighted Lebesgue function spaces and applications to positive definite functions on compact two-point homogeneous spaces

Geodesically isotropic positive definite functions on compact two-point homogeneous spaces of dimension d have series representation as members of weighted Lebesgue spaces Lw 1 ([−1, 1]), where the weight w(x) = wα,β(x) = (1 − x)α(1 + x)β is the one related to the Jacobi orthogonal polynomials P(α,β)(x) in [−1, 1], and the exponents α and β are related to the dimension d. We derive some recurrence relations among the coefficients of the series representations under different exponents, and we apply them to prove inheritance of positive definiteness between dimensions. Additionally, we give bounds on the curvature at the origin of such positive definite functions with compact support, extending the existing solutions from d-dimensional spheres to compact two-point homogeneous spaces.Funding for open access charge: CRUE-Universitat Jaume