Partial orders on transformation semigroups

In 1986, Kowol and Mitsch studied properties of the so-called 'natural partial order' less than or equal to on T(X), the total transformation semigroup defined on a set X. In particular, they determined when two total transformations are related under this order, and they described the minimal and maximal elements of (T(X), less than or equal to). In this paper, we extend that work to the semigroup P(X) of all partial transformations of X, compare less than or equal to with another 'natural' partial order on P(X), characterise the meet and join of these two orders, and determine the minimal and maximal elements of P(X) with respect to each order.Centro de Matemática da Universidade do Minho.Fundação para a Ciência e a Tecnologia (FCT)

The ideal structure of nilpotent-generated transformation semigroups

In1987 Sullivan determined the elements of the semigroup N (X ) generated by all nilpotent partial transformations of an infinite set X ; later in 1997 he studied subsemigroups of N (X ) defined by restricting the index of the nilpotents and the cardinality of the set. Here, we describe the ideals and the Green’s relations on such semigroups, like Reynolds and Sullivan did in 1985 for the semigroup generated by all idempotent total transformations of X . We then use this information to describe the congruences on certain Rees factor semigroups and to construct families of congruence-free semigroups with interesting algebraic properties. We also study analogous questions for X finite and for one-to-one partial transformations.Fundação para a Ciência e a Tecnologia (FCT)Centro de Matemática da Universidade do Minh

F–semigroups

A semigroup S is called F- semigroup if there exists a group-congruence ρ on S such that every ρ-class contains a greatest element with respect to the natural partial order ≤S of S (see [8]). This generalizes the concept of F-inverse semigroups introduced by V. Wagner [12] and investigated in [7]. Five different characterizations of general F-semigroups S are given: by means of residuals, by special principal anticones, by properties of the set of idempotents, by the maximal elements in (S,≤S) and finally, an axiomatic one using an additional unary operation. Also F-semigroups in special classes are considered; in particular, inflations of semigroups and strong semilattices of monoids are studied

Mitochondrial targeting adaptation of the hominoid-specific glutamate dehydrogenase driven by positive Darwinian selection

Many new gene copies emerged by gene duplication in hominoids, but little is known with respect to their functional evolution. Glutamate dehydrogenase (GLUD) is an enzyme central to the glutamate and energy metabolism of the cell. In addition to the single, GLUD-encoding gene present in all mammals (GLUD1), humans and apes acquired a second GLUD gene (GLUD2) through retroduplication of GLUD1, which codes for an enzyme with unique, potentially brain-adapted properties. Here we show that whereas the GLUD1 parental protein localizes to mitochondria and the cytoplasm, GLUD2 is specifically targeted to mitochondria. Using evolutionary analysis and resurrected ancestral protein variants, we demonstrate that the enhanced mitochondrial targeting specificity of GLUD2 is due to a single positively selected glutamic acid-to-lysine substitution, which was fixed in the N-terminal mitochondrial targeting sequence (MTS) of GLUD2 soon after the duplication event in the hominoid ancestor ~18–25 million years ago. This MTS substitution arose in parallel with two crucial adaptive amino acid changes in the enzyme and likely contributed to the functional adaptation of GLUD2 to the glutamate metabolism of the hominoid brain and other tissues. We suggest that rapid, selectively driven subcellular adaptation, as exemplified by GLUD2, represents a common route underlying the emergence of new gene functions

F-regular semigroups

A semigroup S is called F-regular if S is regular and if there exists a group congruence rho on S such that every rho-class contains a greatest element with respect to the natural partial order of S (see [K.S. Nambooripad, Proc. Edinburgh Math. Soc. 23 (1980) 249-260]). These semigroups were investigated in [C.C. Edwards, Semigroup Forum 19 (1980) 331-345] where a description similar to the F-inverse case (see [R. McFadden, L. O'Carroll, Proc. London Math. Soc. 22 (1971) 652-666]) is given. Further characterizations of F-regular semigroups, including an axiomatic one, are provided. The main objective is to give a new representation of such semigroups by means of Szendrei triples (see [M. Szendrei, Acta Sci. Math. 51 (1987) 229-249]). The particular case of F-regular semigroups S satisfying the identity (xy)* = y*x*, where x* epsilon S denotes the greatest element of the rho-class containing x epsilon S, is considered. Also the F-inversive semigroups, for which this identity holds, are characterized. (C) 2004 Elsevier Inc. All rights reserved.Fundação para a Ciência e a Tecnologia (FCT) - POCTI

The Transcriptomic Response of the Murine Thyroid Gland to Iodide Overload and the Role of the Nrf2 Antioxidant System.

Thyroid follicular cells have physiologically high levels of reactive oxygen species because oxidation of iodide is essential for the iodination of thyroglobulin (Tg) during thyroid hormone synthesis. Thyroid follicles (the functional units of the thyroid) also utilize incompletely understood autoregulatory mechanisms to defend against exposure to excess iodide. To date, no transcriptomic studies have investigated these phenomena in vivo. Nuclear erythroid factor 2 like 2 (Nrf2 or Nfe2l2) is a transcription factor that regulates the expression of numerous antioxidant and other cytoprotective genes. We showed previously that the Nrf2 pathway regulates the antioxidant defense of follicular cells, as well as Tg transcription and Tg iodination. We, thus, hypothesized that Nrf2 might be involved in the transcriptional response to iodide overload. C57BL6/J wild-type (WT) or Nrf2 knockout (KO) male mice were administered regular water or water supplemented with 0.05% sodium iodide for seven days. RNA from their thyroids was prepared for next-generation RNA sequencing (RNA-Seq). Gene expression changes were assessed and pathway analyses were performed on the sets of differentially expressed genes. Analysis of differentially expressed messenger RNAs (mRNAs) indicated that iodide overload upregulates inflammatory-, immune-, fibrosis- and oxidative stress-related pathways, including the Nrf2 pathway. Nrf2 KO mice showed a more pronounced inflammatory-autoimmune transcriptional response to iodide than WT mice. Compared to previously published datasets, the response patterns observed in WT mice had strong similarities with the patterns typical of Graves' disease and papillary thyroid carcinoma (PTC). Long non-coding RNAs (lncRNAs) and microRNAs (miRNAs) also responded to iodide overload, with the latter targeting mRNAs that participate mainly in inflammation pathways. Iodide overload induces the Nrf2 cytoprotective response and upregulates inflammatory, immune, and fibrosis pathways similar to autoimmune hyperthyroidism (Graves' disease) and PTC

Heaviness, health and happiness: a cross-sectional study of 163 066 UK Biobank participants

<b>Background</b><p></p> Obesity is known to increase the risk of many diseases and reduce overall quality of life. This study examines the relationship with self-reported health (SRH) and happiness.<p></p> <b>Methods</b> <p></p>We conducted a cross-sectional study of the 163 066 UK Biobank participants who completed the happiness rating. The association between adiposity and SRH and happiness was examined using logistic regression. SRH was defined as good (excellent, good), or poor (fair, poor). Self-reported happiness was defined as happy (extremely, very, moderately) or unhappy (moderately, very, extremely). <p></p> <b>Results</b> <p></p>Poor health was reported by 44 457 (27.3%) participants. The adjusted ORs for poor health were 3.86, 2.92, 2.60 and 6.41 for the highest, compared with lowest, deciles of Body Mass Index, waist circumference, waist to hip ratio and body fat percent, respectively. The associations were stronger in men (p<0.001). Overall, 7511 (4.6%) participants felt unhappy, and only class III obese participants were more likely to feel unhappy (adjusted OR 1.33, 95% CI 1.15 to 1.53, p<0.001) but the associations differed by sex (p<0.001). Among women, there was a significant association between unhappiness and all levels of obesity. By contrast, only class III obese men had significantly increased risk and overweight and class I obese men were less likely to be unhappy. <p></p> <b>Conclusions</b><p></p>Obesity impacts adversely on happiness as well as health, but the association with unhappiness disappeared after adjustment for self-reported health, indicating this may be mediated by health. Compared with obese men, obese women are less likely to report poor health, but more likely to feel unhappy. <p></p&gt

Exact Solutions of the Klein-Gordon Equation in the Presence of a Dyon, Magnetic Flux and Scalar Potential in the Specetime of Gravitational Defects

In this paper we analyse the relativistic quantum motion of a charged spin-0 particle in the presence of a dyon, Aharonov-Bohm magnetic field and scalar potential, in the spacetimes produced by an idealized cosmic string and global monopole. In order to develop this analysis, we assume that the dyon and the Aharonov-Bohm magnetic field are superposed to both gravitational defects. Two distinct configurations for the scalar potential, $S(r)$, are considered: $i)$ the potential proportional to the inverse of the radial distance, i.e., $S\propto1/r$, and $ii)$ the potential proportional to this distance, i.e., $S\propto r$. For both cases the center of the potentials coincide with the dyon's position. In the case of the cosmic string the Aharonov-Bohm magnetic field is considered along the defect, and for the global monopole this magnetic field pierces the defect. The energy spectra are computed for both cases and explicitly shown their dependence on the electrostatic and scalar coupling constants. Also we analyse scattering states of the Klein-Gordon equations, and show how the phase shifts depend on the geometry of the spacetime and on the coupling constants parameter.Comment: To be published in CQG. Minor comments adde

Severe feed restriction increases permeability of mammary gland cell tight junctions and reduces ethanol stability of milk.

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