FREE GROUP ALGEBRAS IN DIVISION RINGS

Let k be an algebraically closed field of characteristic zero and let L be an algebraic function field over k. Let sigma : L -> L be a k-automorphism of infinite order, and let D be the skew field of fractions of the skew polynomial ring L[t; sigma]. We show that D contains the group algebra kF of the free group F of rank 2.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

A SURVEY ON FREE OBJECTS IN DIVISION RINGS AND IN DIVISION RINGS WITH AN INVOLUTION

Let D be a division ring with center k, and let D-dagger be its multiplicative group. We investigate the existence of free groups in D-dagger, and free algebras and free group algebras in D. We also go through the case when D has an involution * and consider the existence of free symmetric and unitary pairs in D-dagger.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

Extended regimens of the contraceptive vaginal ring versus hormonal oral contraceptives: effects on lipid metabolism

Background: Combined oral contraceptives used in an extended regimen have been studied because of their potential benefits; however, there have been few publications on extended regimens of contraceptive vaginal rings. The aim of this study was to assess the effects of these two extended regimens on the lipid metabolism of women using these contraceptive methods during 1 year. Study Design: This prospective study enrolled 150 women: 75 used a vaginal contraceptive ring (11.7 mg etonogestrel and 2.7 mg ethinyl estradiol), and 75 used oral contraceptives (30 mcg ethinyl estradiol and 150 mg desogestrel). Both groups used their respective method for 84 days followed by a 7-day pause during I year. At baseline and every 3 months during the study period, blood was collected to assess total cholesterol, high-density lipoprotein cholesterol, low-density lipoprotein cholesterol, triglycerides and apolipoprotein (apo) A-I and B. The analysis of variance test was used to analyze differences in the results of these exams over time. Results: A total of 62 vaginal ring and 61 oral contraceptive users completed the study. There were no significant differences in the discontinuation rate, mean total cholesterol and fraction levels, apo B concentration or apo A-I/apo B ratio. Vaginal ring users had significantly higher apo A-I levels than oral contraceptive users. Conclusion: Despite the vaginal route of administration, the steroids released by the ring had the same effects on the lipid metabolism and lipoprotein levels typically seen with ethinyl estradiol given either by oral or parenteral routes. (C) 2012 Elsevier Inc. All rights reserved.

Non-substituted B-ring flavonoids and an indole alkaloid from Piper aleyreanum (Piperaceae)

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq)

Limiting the influence of friction on the split Hopkinson pressure bar tests by using a ring specimen

The deformation of a ring under axial compression is analyzed in order to estimate a favorable ring specimen geometry capable of limiting the influence of friction on the stress-strain curve obtained from SHPB tests. The analysis shows that the use of a ring specimen with a large inner diameter and a small radial thickness offers some advantages comparing with the traditional disk sample. In particular, it can improve the reliability of the test results for ductile materials in the presence of friction. Based on the deformation analysis of a ductile ring under compression, a correction coefficient is proposed to relate the actual material stress strain curve with the reading from the SHPB. It is shown using finite element simulation that the proposed correction can be used for a wide range of conventional ductile materials. Experimental results with steel alloys indicate that the correction procedure is an effective technique for an accurate measurement of the dynamic material strength response. (C) 2012 Elsevier Ltd. All rights reserved.

The COP9 signalosome counteracts the accumulation of cullin SCF ubiquitin E3 RING ligases during fungal development

Defects in the COP9 signalosome (CSN) impair multicellular development, including embryonic plant or animal death or a block in sexual development of the fungus Aspergillus nidulans. CSN deneddylates cullin-RING ligases (CRLs), which are activated by covalent linkage to ubiquitin-like NEDD8. Deneddylation allows CRL disassembly for subsequent reassembly. An attractive hypothesis is a consecutive order of CRLs for development, which demands repeated cycles of neddylation and deneddylation for reassembling CRLs. Interruption of these cycles could explain developmental blocks caused by csn mutations. This predicts an accumulation of neddylated CRLs exhibiting developmental functions when CSN is dysfunctional. We tested this hypothesis in A. nidulans, which tolerates reduced levels of neddylation for growth. We show that only genes for CRL subunits or neddylation are essential, whereas CSN is primarily required for development. We used functional tagged NEDD8, recruiting all three fungal cullins. Cullins are associated with the CSN1/CsnA subunit when deneddylation is defective. Two CRLs were identified which are specifically involved in differentiation and accumulate during the developmental block. This suggests that an active CSN complex is required to counteract the accumulation of specific CRLs during development.

Solar-Terrestrial Signal Record in Tree Ring Width Time Series from Brazil

This work investigates the behavior of the sunspot number and Southern Oscillation Index (SOI) signal recorded in the tree ring time series for three different locations in Brazil: Humaita in Amaznia State, Porto Ferreira in So Paulo State, and Passo Fundo in Rio Grande do Sul State, using wavelet and cross-wavelet analysis techniques. The wavelet spectra of tree ring time series showed signs of 11 and 22 years, possibly related to the solar activity, and periods of 2-8 years, possibly related to El Nio events. The cross-wavelet spectra for all tree ring time series from Brazil present a significant response to the 11-year solar cycle in the time interval between 1921 to after 1981. These tree ring time series still have a response to the second harmonic of the solar cycle (5.5 years), but in different time intervals. The cross-wavelet maps also showed that the relationship between the SOI x tree ring time series is more intense, for oscillation in the range of 4-8 years.

Peripheral Sterile Corneal Ring Infiltrate After Riboflavin-UVA Collagen Cross-Linking in Keratoconus

Purpose: To present 7 cases of peripheral sterile corneal infiltrates that occurred after corneal cross-linking (CXL) for progressive keratectasia. Methods: Seven patients who had their progressive keratoconus documented underwent corneal deepithelization and subsequently CXL, which was performed with the application of 0.1% riboflavin with 20% dextran, and exposure to UVA light (370 nm, 2.9-3.1 mW/cm(2)) for 30 minutes. Results: Nearly a week after the procedure, the patients presented with peripheral stromal infiltrates. The ring-like infiltrates were superficial and were present at the 9.0-mm zone. Sterile infiltration was diagnosed. Patients were treated with topical corticosteroids, and complete resolution was achieved after a few weeks of treatment. Conclusions: We hypothesize that the phototoxic effect on the corneal stroma may be the main mechanism that triggers these infiltrates. Alternatively, alterations in antigenicity that occur in native proteins after CXL could result in patients recognizing the proteins as nonself and mounting immune responses.

Mechanisms of ring chromosome formation, ring instability and clinical consequences

Background The breakpoints and mechanisms of ring chromosome formation were studied and mapped in 14 patients. Methods Several techniques were performed such as genome-wide array, MLPA (Multiplex Ligation-Dependent Probe Amplification) and FISH (Fluorescent in situ Hybridization). Results The ring chromosomes of patients I to XIV were determined to be, respectively: r(3)(p26.1q29), r(4)(p16.3q35.2), r(10)(p15.3q26.2), r(10)(p15.3q26.13), r(13)(p13q31.1), r(13)(p13q34), r(14)(p13q32.33), r(15)(p13q26.2), r(18)(p11.32q22.2), r(18)(p11.32q21.33), r(18)(p11.21q23), r(22)(p13q13.33), r(22)(p13q13.2), and r(22)(p13q13.2). These rings were found to have been formed by different mechanisms, such as: breaks in both chromosome arms followed by end-to-end reunion (patients IV, VIII, IX, XI, XIII and XIV); a break in one chromosome arm followed by fusion with the subtelomeric region of the other (patients I and II); a break in one chromosome arm followed by fusion with the opposite telomeric region (patients III and X); fusion of two subtelomeric regions (patient VII); and telomere-telomere fusion (patient XII). Thus, the r(14) and one r(22) can be considered complete rings, since there was no loss of relevant genetic material. Two patients (V and VI) with r(13) showed duplication along with terminal deletion of 13q, one of them proved to be inverted, a mechanism known as inv-dup-del. Ring instability was detected by ring loss and secondary aberrations in all but three patients, who presented stable ring chromosomes (II, XIII and XIV). Conclusions We concluded that the clinical phenotype of patients with ring chromosomes may be related with different factors, including gene haploinsufficiency, gene duplications and ring instability. Epigenetic factors due to the circular architecture of ring chromosomes must also be considered, since even complete ring chromosomes can result in phenotypic alterations, as observed in our patients with complete r(14) and r(22).

A Galactic ring of minimum stellar density near the solar orbit radius

We analyse the secular effects of a long-lived Galactic spiral structure on the stellar orbits with mean radii close to the corotation resonance. By test-particle simulations and different spiral potential models with parameters constrained on observations, we verified the formation of a minimum with amplitude ∼30–40 per cent of the background disc stellar density at corotation. Such a minimum is formed by the secular angular momentum transfer between stars and the spiral density wave on both sides of corotation. We demonstrate that the secular loss (gain) of angular momentum and decrease (increase) of mean orbital radius of stars just inside (outside) corotation can counterbalance the opposite trend of exchange of angular momentum shown by stars orbiting the librational points L4/5 at the corotation circle. Such secular processes actually allow steady spiral waves to promote radial migration across corotation. We propose some pieces of observational evidence for the minimum stellar density in the Galactic disc, such as its direct relation to the minimum in the observed rotation curve of the Galaxy at the radius r ∼ 9 kpc (for R0 = 7.5 kpc), as well as its association with a minimum in the distribution of Galactic radii of a sample of open clusters older than 1Gyr. The closeness of the solar orbit adius to the corotation resonance implies that the solar orbit lies inside a ring of minimum surface density (stellar + gas). This also implies a correction to larger values for the estimated total mass of the Galactic disc, and consequently, a greater contribution of the disc componente to the inner rotation curve of the Galaxy.

Nonlocal asymmetric exclusion process on a ring and conformal invariance

We present a one-dimensional nonlocal hopping model with exclusion on a ring. The model is related to the Raise and Peel growth model. A nonnegative parameter u controls the ratio of the local backwards and nonlocal forwards hopping rates. The phase diagram, and consequently the values of the current, depend on u and the density of particles. In the special case of half-lling and u = 1 the system is conformal invariant and an exact value of the current for any size L of the system is conjectured and checked for large lattice sizes in Monte Carlo simulations. For u > 1 the current has a non-analytic dependence on the density when the latter approaches the half-lling value.