On solutions of linear ordinary differential equations in their coefficient field

AbstractWe describe a rational algorithm for finding the denominator of any solution of a linear ordinary differential equation in its coefficient field. As a consequence, there is now a rational algorithm for finding all such solutions when the coefficients can be built up from the rational functions by finitely many algebraic and primitive adjunctions. This also eliminates one of the computational bottlenecks in algorithms that either factor or search for Liouvillian solutions of such equations with Liouvillian coefficients

Integral D-Finite Functions

We propose a differential analog of the notion of integral closure of algebraic function fields. We present an algorithm for computing the integral closure of the algebra defined by a linear differential operator. Our algorithm is a direct analog of van Hoeij's algorithm for computing integral bases of algebraic function fields

The Lazy Hermite Reduction

The Hermite reduction is a symbolic integration technique that reduces algebraic functions to integrands having only simple affine poles [1,2,8] . While it is very effective in the case of simple radical extensions, its use in more general algebraic extensions requires the precomputation of an integral basis, which makes the reduction impractical for either multiple algebraic extensions or complicated ground fields. In this paper, we show that the Hermite reduction can be performed without a priori computation of either a primitive element or integral basis, computing the smallest order necessary for a particular integrand along the way

On solutions of Linear Ordinary Difference Equations in their Coefficient Field

We extend the notion of monomial extensions of differential fields, i.e. simp- le transcendental extensions in which the polynomials are closed under differentiation, to difference fields. The structure of such extensions provides an algebraic framework for solving generalized linear difference equations with coefficients in such fields. We then describe algorithms for finding the denominator of any solution of those equations in an important subclass of monomial extensions that includes transcendental indefinite sums and products. This reduces the general problem of finding the solutions of such equations in their coefficient fields to bounding their degrees. In the base case, this yields in particular a new algorithm for computing the rational solutions of q-difference equations with polynomial coefficients

Linear algebra for skew-polynomial matrices

We describe an algorithm for transforming skew-polynomial matrices over an Ore domain in row-reduced form, and show that this algorithm can be used to perform the standard calculations of linear algebra on such matrices (ranks, kernels, linear dependences, inhomogeneous solving). The main application of our algorithm is to desingularize recurrences and to compute the rational solutions of a large class of linear functional systems. It also turns out to be efficient when applied to ordinary commutative matrix polynomials

Recommendations of Neuroendocrinology Department from Brazilian Society of Endocrinology and Metabolism for diagnosis and treatment of acromegaly in Brazil

A acromegalia é uma doença associada à elevada morbidade e à redução da expectativa de vida. Em virtude do seu caráter insidioso e do seu não reconhecimento, o diagnóstico é frequentemente realizado com atraso, o que, associado às complicações relacionadas ao excesso do GH/IGF-I, determina elevada morbimortalidade. No entanto, um diagnóstico precoce e um tratamento efetivo minimizam a morbidade e normalizam a taxa de mortalidade. Nesta publicação, o objetivo do Departamento de Neuroendocrinologia da Sociedade Brasileira de Endocrinologia e Metabologia é divulgar quando suspeitar clinicamente da acromegalia e como diagnosticá-la. Além disso, discute-se a maneira mais eficaz e segura de realizar o tratamento da acromegalia, enfatizando que este deve ser realizado em centros de referência. Assim, com base em dados publicados em periódicos de nível científico reconhecido e na experiência dos autores, são apresentadas as recomendações para o diagnóstico e tratamento da doença.Acromegaly is a disease associated with increased morbidity and reduced life expectancy. Because of its insidious character and its non-recognition, the diagnosis is often made with delay, which, along with the complications related to GH/IGF-I excess, determines high morbidity and mortality. However, an early diagnosis and an effective treatment reduce the morbidity and normalize the mortality rate. In this publication, the goal of Neuroendocrinology Department from Brazilian Society of Endocrinology and Metabolism is to disclose which clinical set should arouse the suspicious of acromegaly and how to diagnose it. Furthermore, we discuss the most effective and safe approach to perform the treatment of acromegaly, emphasizing that it must be carried out in reference centers. Therefore, based on data published in journals with recognized scientific level and authors' experience, recommendations are presented for diagnosis and treatment of the disease

Educational inequalities in obesity: a multilevel analysis of survey data from cities in Latin America

Abstract Using newly harmonised individual-level data on health and socio-economic environments in Latin American cities (from the Salud Urbana en América Latina (SALURBAL) study), we assessed the association between obesity and education levels and explored potential effect modification of this association by city-level socio-economic development. Design This cross-sectional study used survey data collected between 2002 and 2017. Absolute and relative educational inequalities in obesity (BMI ≥ 30 kg/m2, derived from measured weight and height) were calculated first. Then, a two-level mixed-effects logistic regression was run to test for effect modification of the education–obesity association by city-level socio-economic development. All analyses were stratified by sex. Setting: One hundred seventy-six Latin American cities within eight countries (Brazil, Chile, Colombia, Costa Rica, El Salvador, Guatemala, Mexico and Peru). Results: Among women, 25 % were living with obesity and obesity was negatively associated with educational level (higher education–lower obesity) and this pattern was consistent across city-level socio-economic development. Among men, 18 % were living with obesity and there was a positive association between education and obesity (higher education–higher obesity) for men living in cities with lower levels of development, whereas for those living in cities with higher levels of development, the pattern was inverted and university education was protective of obesity. Conclusions: Among women, education was protective of obesity regardless, whereas among men, it was only protective in cities with higher levels of development. These divergent results suggest the need for sex- and city-specific interventions to reduce obesity prevalence and inequalities

Acquisition of uropygial gland microbiome by hoopoe nestlings

Mutualistic symbioses between animals and bacteria depend on acquisition of appropriate symbionts while avoiding exploitation by non-beneficial microbes. The mode of acquisition of symbionts would determine, not only the probability of encountering but also evolutionary outcomes of mutualistic counterparts. The microbiome inhabiting the uropygial gland of the European hoopoe (Upupa epops) includes a variety of bacterial strains, some of them providing antimicrobial benefits. Here, the mode of acquisition and stability of this microbiome is analyzed by means of Automated rRNA Intergenic Spacer Analysis and two different experiments. The first experiment impeded mothers’ access to their glands, thus avoiding direct transmission of microorganisms from female to offspring secretions. The second experiment explored the stability of the microbiomes by inoculating glands with secretions from alien nests. The first experiment provoked a reduction in similarity of microbiomes of mother and nestlings. Interestingly, some bacterial strains were more often detected when females had not access to their glands, suggesting antagonistic effects among bacteria from different sources. The second experiment caused an increase in richness of the microbiome of receivers in terms of prevalence of Operational Taxonomic Units (OTUs) that reduced differences in microbiomes of donors and receivers. That occurred because OTUs that were present in donors but not in receivers incorporated to the microbiome of the latter, which provoked that cross-inoculated nestlings got similar final microbiomes that included the most prevalent OTUs. The results are therefore consistent with a central role of vertical transmission in bacterial acquisition by nestling hoopoes and support the idea that the typical composition of the hoopoe gland microbiome is reached by the incorporation of some bacteria during the nestling period. This scenario suggests the existence of a coevolved core microbiome composed by a mix of specialized vertically transmitted strains and facultative symbionts able to coexist with them. The implications of this mixed mode of transmission for the evolution of the mutualism are discussedMinisterio de Ciencia e Innovación (España)Junta de Andalucí