We prove that, given a finitely generated subgroup H of a free group F, the following questions are decidable: is H closed (dense) in F for the pro-(met)abelian topology? Is the closure of H in F for the pro-(met)abelian topology finitely generated? We show also that if the latter question has a positive answer, then we can effectively construct a basis for the closure, and the closure has decidable membership problem in any case. Moreover, it is decidable whether H is closed for the pro-$\mathbf {V}$ topology when $\mathbf {V}$ is an equational pseudovariety of finite groups, such as the pseudovariety $\mathbf {S}_k$ of all finite solvable groups with derived length $\leq k$. We also connect the pro-abelian topology with the topologies defined by abelian groups of bounded exponent.

The complex algebra of an inverse semigroup with finitely many idempotents in each $\mathcal D$-class is stably finite by a result of Munn. This can be proved fairly easily using $C^{*}$-algebras for inverse semigroups satisfying this condition that have a Hausdorff universal groupoid, or more generally for direct limits of inverse semigroups satisfying this condition and having Hausdorff universal groupoids. It is not difficult to see that a finitely presented inverse semigroup with a non-Hausdorff universal groupoid cannot be a direct limit of inverse semigroups with Hausdorff universal groupoids. We construct here countably many nonisomorphic finitely presented inverse semigroups with finitely many idempotents in each $\mathcal D$-class and non-Hausdorff universal groupoids. At this time, there is not a clear $C^{*}$-algebraic technique to prove these inverse semigroups have stably finite complex algebras.

Litter size reduction can induce early overnourishment, being an attractive experimental model to study short- and long-term consequences of childhood obesity. Epidemiological data indicate sex differences regarding cardiometabolic disorders and hypertrophic cardiomyopathy. The present study aimed to describe biometric, nutritional and cardiovascular changes related to neonatal overweight promoted by litter size reduction in young and adult Wistar rats of both sexes. Litter adjustment to eight or four pups/mother (1:1 male-to-female ratio) gave, respectively, control and overweight groups. Body mass, food intake, haemodynamic and echocardiographic parameters and cardiorespiratory capacity were evaluated at postnatal days 30 and 150. Diminished litters were correlated with higher body mass and weight gain (12 %) during lactation, validating the experimental model of neonatal overweight. Soon after weaning male (16 %) and female (25 %) offspring of these litters presented a lower food intake than their respective control, without differences in body mass. Adult males from reduced litters presented higher abdominal circumference (7 %), systolic blood pressure (10 %), interventricular septum thickness (15 %) and relative wall thickness (15 %) compared with their respective control. Rats' performance on the maximal effort ergometer test was not affected by neonatal overweight. Data suggest the occurrence of catch-down growth and hypophagia in male and female rats submitted to neonatal overweight. However, only male rats presented haemodynamic and cardiac structural changes. These findings are crucial to personalised/gender medicine.

Non-exercise physical activity (NEPA) and/or non-exercise activity thermogenesis (NEAT) reductions may occur from diet and/or exercise-induced negative energy balance interventions, resulting in less-than-expected weight loss. This systematic review describes the effects of prescribed diet and/or physical activity (PA)/exercise on NEPA and/or NEAT in adults. Studies were identified from PubMed, web-of-knowledge, Embase, SPORTDiscus, ERIC and PsycINFO searches up to 1 March 2017. Eligibility criteria included randomised controlled trials (RCT), randomised trials (RT) and non-randomised trials (NRT); objective measures of PA and energy expenditure; data on NEPA, NEAT and spontaneous PA; ≥10 healthy male/female aged>18 years; and ≥7 d length. The trial is registered at PROSPERO-2017-CRD42017052635. In all, thirty-six articles (RCT-10, RT-9, NRT-17) with a total of seventy intervention arms (diet, exercise, combined diet/exercise), with a total of 1561 participants, were included. Compensation was observed in twenty-six out of seventy intervention arms (fifteen studies out of thirty-six reporting declines in NEAT (eight), NEPA (four) or both (three)) representing 63, 27 and 23 % of diet-only, combined diet/exercise, and exercise-only intervention arms, respectively. Weight loss observed in participants who decreased NEAT was double the weight loss found in those who did not compensate, suggesting that the energy imbalance degree may lead to energy conservation. Although these findings do not support the hypothesis that prescribed diet and/or exercise results in decreased NEAT and NEPA in healthy adults, the underpowered trial design and the lack of state-of-the-art methods may limit these conclusions. Future studies should explore the impact of weight-loss magnitude, energetic restriction degree, exercise dose and participant characteristics on NEAT and/or NEPA.

Studies were conducted to identify and characterize different accessions of itchgrass. Seeds were collected in the counties of Aramina, Campinas, Dumont, Igarapava, Jaboticabal, and Ribeirão Preto, all in the state of São Paulo, Brazil. Accessions were characterized based on dimensions of their stomata, stomatal index (SI), and length and width of their seed (caryopses and husk). Chromosome number and length also were determined, and accessions were further differentiated using molecular markers (polymerase chain reaction [PCR]). Itchgrass from Ribeirão Preto had much longer and narrower seeds than those from the other locations, and their husks were longer as well. Accessions had similar SIs, both on the abaxial and adaxial leaf surfaces. Stomata from Campinas and Igarapava accessions were longer and wider, whereas those from Dumont and Ribeirão Preto were similar and smaller than all others. The accession from Ribeirão Preto is diploid (2n = 20); the rest are polyploid, with the total length of chromosomes smaller than all others. These differences were confirmed by molecular differentiation (PCR).

Intestinal mucositis is an important toxic side effect of 5-fluorouracil (5-FU) treatment. Saccharomyces boulardii is known to protect from intestinal injury via an effect on the gastrointestinal microbiota. The objective of the present study was to evaluate the effect of S. boulardii on intestinal mucositis induced by 5-FU in a murine model. Mice were divided into saline, saline (control)+5-FU or 5-FU+S. boulardii (16 × 109 colony-forming units/kg) treatment groups, and the jejunum and ileum were removed after killing of mice for the evaluation of histopathology, myeloperoxidase (MPO) activity, and non-protein sulfhydryl group (mainly reduced glutathione; GSH), nitrite and cytokine concentrations. To determine gastric emptying, phenol red was administered orally, mice were killed 20 min after administration, and the absorbance of samples collected from the mice was measured by spectrophotometry. Intestinal permeability was measured by the urinary excretion rate of lactulose and mannitol following oral administration. S. boulardii significantly reversed the histopathological changes in intestinal mucositis induced by 5-FU and reduced the inflammatory parameters: neutrophil infiltration (control 1·73 (sem 0·37) ultrastructural MPO (UMPO)/mg, 5-FU 7·37 (sem 1·77) UMPO/mg and 5-FU+S. boulardii 4·15 (sem 0·73) UMPO/mg); nitrite concentration (control 37·00 (sem 2·39) μm, 5-FU 59·04 (sem 11·41) μm and 5-FU+S. boulardii 37·90 (sem 5·78) μm); GSH concentration (control 477·60 (sem 25·25) μg/mg, 5-FU 270·90 (sem 38·50) μg/mg and 5-FU+S. boulardii 514·00 (sem 38·64) μg/mg). Treatment with S. Boulardii significantly reduced the concentrations of TNF-α and IL-1β by 48·92 and 32·21 % in the jejunum and 38·92 and 61·79 % in the ileum. In addition, S. boulardii decreased the concentrations of chemokine (C–X–C motif) ligand 1 by 5-fold in the jejunum and 3-fold in the ileum. Interestingly, S. boulardii reduced the delay in gastric emptying (control 25·21 (sem 2·55) %, 5-FU 54·91 (sem 3·43) % and 5-FU+S. boulardii 31·38 (sem 2·80) %) and induced the recovery of intestinal permeability (lactulose:mannitol ratio: control 0·52 (sem 0·03), 5-FU 1·38 (sem 0·24) and 5-FU+S. boulardii 0·62 (sem 0·03)). In conclusion, S. boulardii reduces the inflammation and dysfunction of the gastrointestinal tract in intestinal mucositis induced by 5-FU.

The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.

Some new concepts are introduced, in particular that of a unique factorization semilattice. Necessary and sufficient conditions are given for two principal ideals of the semilattice of idempotents of a free inverse monoid FIM(X) to be isomorphic and some properties of the Munn semigroup of E[FIM(X)] are obtained. Some results on the embedding of semilattices in E[FIM(X)] are also obtained.

We revisit the problem of deciding whether a finitely generated subgroup H is a free factor of a given free group F. Known algorithms solve this problem in time polynomial in the sum of the lengths of the generators of H and exponential in the rank of F. We show that the latter dependency can be made exponential in the rank difference rank(F) - rank(H), which often makes a significant change.

We provide alternative proofs and algorithms for results proved by Sénizergues on rational and recognizable free group languages. We consider two different approaches to the basic problem of deciding recognizability for rational free group languages following two fully independent paths: the symmetrification method (using techniques inspired by the study of inverse automata and inverse monoids) and the right stabilizer method (a general approach generalizable to other classes of groups). Several different algorithmic characterizations of recognizability are obtained, as well as other decidability results.

The structure of an inverse monoid can be determined by the complete set of Schützenberger graphs of a presentation. Necessary and sufficient conditions for a collection of inverse X-graphs to be the complete set of Schützenberger graphs of some inverse monoid presentation are established and decidability results are obtained. Conditions for a single inverse X-graph to be a Schu¨tzenberger graph for some presentation are also obtained, and both problems are restricted to the case of Clifford monoids and E-unitary inverse monoids. Decidability and undecidability results are obtained for the case of finite graphs. It is also proved that the problem of embedding a finite inverse X-graph in the Cayley graph of a group is undecidable.

Normal-convex embeddings are introduced for inverse semigroups, generalizing the group-theoretic concept, due to Papakyriakopoulos [4]. It is shown that every E-unitary inverse semigroup admits a normal-convex embedding into a semidirect product of a semilattice by a group, a stronger version of a result by O'Carroll [3]. A general embedding result for inverse semigroups is also obtained.

Some decidability results for presentations in the variety of Clifford monoids are obtained. These results are applied in the solution of the E-unitary problem for presentations in the variety of inverse monoids.

This note discusses primeness for semigroup rings of semigroups satisfying a certain condition, weaker than the u.p. property. These semigroups include free products of semigroups, semigroups presented by a single relator and at least three generators, and free inverse semigroups of infinite rank.