Regular subalgebras and nilpotent orbits of real graded Lie algebras

For a semisimple Lie algebra over the complex numbers, Dynkin (1952) developed an algorithm to classify the regular semisimple subalgebras, up to conjugacy by the inner automorphism group. For a graded semisimple Lie algebra over the complex numbers, Vinberg (1979) showed that a classification of a certain type of regular subalgebras (called carrier algebras) yields a classification of the nilpotent orbits in a homogeneous component of that Lie algebra. Here we consider these problems for (graded) semisimple Lie algebras over the real numbers. First, we describe an algorithm to classify the regular semisimple subalgebras of a real semisimple Lie algebra. This also yields an algorithm for listing, up to conjugacy, the carrier algebras in a real graded semisimple real algebra. We then discuss what needs to be done to obtain a classification of the nilpotent orbits from that; such classifications have applications in differential geometry and theoretical physics. Our algorithms are implemented in the language of the computer algebra system GAP, using our package CoReLG; we report on example computations

Computing generators of the unit group of an integral abelian group ring

We describe an algorithm for obtaining generators of the unit group of the integral group ring ZG of a finite abelian group G. We used our implementation in Magma of this algorithm to compute the unit groups of ZG for G of order up to 110. In particular for those cases we obtained the index of the group of Hoechsmann units in the full unit group. At the end of the paper we describe an algorithm for the more general problem of finding generators of an arithmetic group corresponding to a diagonalizable algebraic group

Computational problems in algebra: units in group rings and subalgebras of real simple Lie algebras

In the first part of the thesis I produce and implement an algorithm for obtaining generators of the unit group of the integral group ring ZG of finite abelian group G. We use our implementation in MAGMA of this algorithm to compute the unit group of ZG for G of order up to 110. In the second part of the thesis I show how to construct multiplication tables of the semisimple real Lie algebras. Next I give an algorithm, based on the work of Sugiura, to find all Cartan subalgebra of such a Lie algebra. Finally I show algorithms for finding semisimple subalgebras of a given semisimple real Lie algebra

Clinical Value Of Serum Levels Of 11-Oxygenated Metabolites Of Testosterone In Women With Polycystic Ovary Syndrome

Context/objective: Recent data suggested that 11-oxygenated androgens may be the preponderant circulating androgens in women with PCOS. However, the pathophysiological significance of these hormones remains unclear. The aim of this study was to evaluate the relationships between serum 11-OH testosterone (11-OHT) and 11-Keto testosterone (11-KetoT) and clinical and biochemical hyperandrogenism, as well as the metabolic parameters, in women with PCOS. Subjects: One hundred and twenty-three women with PCOS, diagnosed according to the Rotterdam criteria, and 38 healthy controls. Design: The main classic and 11-oxygenated androgens were measured by LC-MS/MS and direct equilibrium dialysis. Insulin sensitivity was assessed by hyperinsulinemic euglycemic clamp. Results: Serum 11-oxygenated androgens were higher in women with PCOS than in controls. Elevated levels of 11-OHT and 11-KetoT were found in 28.5% and 30.1% of PCOS women, respectively, whereas free testosterone (FT) was increased in 61.0% of them. Serum 11-oxygenated androgens showed a limited performance in recognizing women with classically-defined hyperandrogenism. Unlike FT, 11-oxygenated androgens did not show significant relationships with anthropometric and metabolic parameters, except for a direct association with insulin sensitivity. In multivariable analysis, 11-OHT and 11-KetoT, directly, and FT, inversely, remained significant independent predictors of insulin sensitivity. Conclusions: Serum levels of 11-oxygenated androgens are higher in women with PCOS than in controls. However, these hormones show a poor performance in recognizing women with hyperandrogenism, as currently defined. The relationships of these androgens with insulin sensitivity strongly differ from that of FT, suggesting a different role of classic and 11-oxygenated androgens in the pathophysiology of PCOS

Insulin-Mediated Substrate Use in Women With Different Phenotypes of {PCOS}: the Role of Androgens

Context: Few studies have explored in vivo insulin action on substrate use in women with PCOS. In particular, no data are available in women with different PCOS phenotypes.Objective: The aim of the study was to evaluate insulin action on glucose (Gox) and lipid (Lox) oxidation, nonoxidative glucose metabolism (Gnonox), and serum free fatty acids (FFAs) in different PCOS phenotypes.Methods: Participants included 187 nondiabetic women with PCOS diagnosed according to the Rotterdam criteria. Data from a historical sample of 20 healthy women were used as reference values. Whole-body substrate use data were obtained by the hyperinsulinemic euglycemic clamp associated with indirect calorimetry. Serum androgens were assessed by liquid chromatography-mass spectrometry and equilibrium dialysis.Results: During hyperinsulinemia, the increase of Gox (Delta Gox), Gnonox, as well as the suppression of Lox (Delta Lox) and serum FFA (Delta% FFA) were altered in each PCOS phenotype. Moreover, Gnonox and Delta% FFA were lower in women with the classic phenotype than in those with the ovulatory or the normoandrogenic phenotypes, and Delta Gox was lower in women with the classic than in those with the ovulatory phenotype. In multivariable analysis fat mass and free testosterone were independent predictors of Delta Gox, Gnonox, and Delta% FFA, whereas only fat mass predicted Delta Lox.Conclusion: In women with PCOS, regardless of phenotype, insulin-mediated substrate use is impaired. This phenomenon is greater in individuals with the classic phenotype. Free testosterone plays an independent role in insulin action abnormalities in glucose and lipid metabolism

Switching Between Biological Treatments in Psoriatic Arthritis: A Review of the Evidence

Psoriatic arthritis (PsA) is a chronic inflammatory arthropathy. Therapy with anti-tumor necrosis factor (TNF)-α agents represents the first therapeutic choice for moderate and severe forms; however, PsA patients can experience anti-TNFα failure, lack of efficacy, or adverse events. Several evidences exist on the effectiveness of switching among different TNFα inhibitors, and we reviewed the published data on the effectiveness of anti-TNFα first-, second- and third-line. Most of the studies report that the main reason for switching to a second anti-TNFα agent is represented by lack of efficacy (primary or secondary) and, more rarely, adverse events. Switchers receiving their second anti-TNFα agent have considerably poorer responses compared with non-switchers. Survival of anti-TNFα treatment appears to be superior in PsA patients when compared with rheumatoid arthritis patients. Switching from anti-TNF agents to ustekinumab or secukinumab or apremilast can represent a valid alternative therapeutic strategy