Automorphism Groups of Generalized (Binary) Icosahedral, Tetrahedral and Octahedral Groups

Let G be any of the (binary) icosahedral, generalized octahedral (tetrahedral) groups or their quotients by the center. We calculate the automorphism group Aut(G).

The group inverse of a product

In this paper, we characterize the existence and give an expression of the group inverse of a product of two regular elements by means of a ring unit.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

Cellular decomposition of quaternionic spherical space forms

We obtain an explicit cellular decomposition of the quaternionic spherical space forms, manifolds of positive constant curvature that are factors of an odd sphere by a free orthogonal action of a generalized quaternionic group. The cellular structure gives and explicit description of the associated cellular chain complex of modules over the integral group ring of the fundamental group. As an application we compute the Whitehead torsion of these spaces for any representation of the fundamental group. © 2012 Springer Science+Business Media B.V.

Sobre os grupos de Gottlieb

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

Group strategy-proof social choice functions with binary ranges and arbitrary domains: characterization results

We define different concepts of group strategy-proofness for social choice functions. We discuss the connections between the defined concepts under different assumptions on their domains of definition. We characterize the social choice functions that satisfy each one of them and whose ranges consist of two alternatives, in terms of two types of basic properties.

Generalized linear mixed models for the genetic evaluation of binary reproductive traits: a simulation study

The objective of this study was to evaluate the use of probit and logit link functions for the genetic evaluation of early pregnancy using simulated data. The following simulation/analysis structures were constructed: logit/logit, logit/probit, probit/logit, and probit/probit. The percentages of precocious females were 5, 10, 15, 20, 25 and 30% and were adjusted based on a change in the mean of the latent variable. The parametric heritability (h²) was 0.40. Simulation and genetic evaluation were implemented in the R software. Heritability estimates (ĥ²) were compared with h² using the mean squared error. Pearson correlations between predicted and true breeding values and the percentage of coincidence between true and predicted ranking, considering the 10% of bulls with the highest breeding values (TOP10) were calculated. The mean ĥ² values were under- and overestimated for all percentages of precocious females when logit/probit and probit/logit models used. In addition, the mean squared errors of these models were high when compared with those obtained with the probit/probit and logit/logit models. Considering ĥ², probit/probit and logit/logit were also superior to logit/probit and probit/logit, providing values close to the parametric heritability. Logit/probit and probit/logit presented low Pearson correlations, whereas the correlations obtained with probit/probit and logit/logit ranged from moderate to high. With respect to the TOP10 bulls, logit/probit and probit/logit presented much lower percentages than probit/probit and logit/logit. The genetic parameter estimates and predictions of breeding values of the animals obtained with the logit/logit and probit/probit models were similar. In contrast, the results obtained with probit/logit and logit/probit were not satisfactory. There is need to compare the estimation and prediction ability of logit and probit link functions.

Oral prednisolone induced acute generalized exanthematous pustulosis due to corticosteroids of group A confirmed by epicutaneous testing and lymphocyte transformation tests

BACKGROUND: Acute generalized exanthematous pustulosis (AGEP) is a rare cutaneous eruption which is often provoked by drugs. CASE REPORT: We report 2 cases of AGEP which showed rapidly spreading pustular eruptions accompanied by malaise, fever and neutrophilia after the administration of systemic prednisolone (corticosteroid of group A, hydrocortisone type). The histological examination showing neutrophilic subcorneal spongiform pustules was consistent with the diagnosis of AGEP. In both cases the rash cleared within a week upon treatment with topical steroids (corticosteroid of group D1, betamethasonedipropionate type and corticosteroid of group D2, hydrocortisone-17-butyrate type). Three months after recovery, the sensitization to corticosteroids of group A was confirmed by epicutaneous testing and positive lymphocyte transformation tests. CONCLUSION: These cases show that systemic corticosteroids can induce AGEP and demonstrate that epicutaneous testing and lymphocyte transformation tests may be helpful in identifying the causative drug. Our data support previous reports indicating an important role for drug-specific T cells in inducing neutrophil inflammation in this disease.

Thermo-solvatochromism in binary mixtures of water and ionic liquids: on the relative importance of solvophobic interactions

The thermo-solvatochromism of 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), has been studied in mixtures of water, W, with ionic liquids, ILs, in the temperature range of 10 to 60 degrees C, where feasible. The objectives of the study were to test the applicability of a recently introduced solvation model, and to assess the relative importance of solute-solvent solvophobic interactions. The ILs were 1-allyl-3-alkylimidazolium chlorides, where the alkyl groups are methyl, 1-butyl, and 1-hexyl, respectively. The equilibrium constants for the interaction of W and the ILs were calculated from density data; they were found to be linearly dependent on N(C), the number of carbon atoms of the alkyl group; van't Hoff equation (log K versus 1/T) applied satisfactorily. Plots of the empirical solvent polarities, E(T) (MePMBr(2)) in kcal mol(-1), versus the mole fraction of water in the binary mixture, chi(w), showed non-linear, i.e., non-ideal behavior. The dependence of E(T) (MePMBr(2)) on chi(w), has been conveniently quantified in terms of solvation by W, IL, and the ""complex"" solvent IL-W. The non-ideal behavior is due to preferential solvation by the IL and, more efficiently, by IL-W. The deviation from linearity increases as a function of increasing N(C) of the IL, and is stronger than that observed for solvation of MePMBr(2) by aqueous 1-propanol, a solvent whose lipophilicity is 12.8 to 52.1 times larger than those of the ILs investigated. The dependence on N(C) is attributed to solute-solvent solvophobic interactions, whose relative contribution to solvation are presumably greater than that in mixtures of water and 1-propanol.

Detection of Herpesviruses and Periodontal Pathogens in Subgingival Plaque of Patients With Chronic Periodontitis, Generalized Aggressive Periodontitis, or Gingivitis

Background: Herpesviruses may be related to the etiology of aggressive periodontitis (AgP) and chronic periodontitis (CP) by triggering periodontal destruction or by increasing the risk for bacterial infection. This case-control study evaluated the presence of herpes simplex virus type 1 (HSV-1), Epstein-Barr virus type 1 (EBV-1), human cytomegalovirus (HCMV), Aggregatibacter actinomycetemcomitans (previously Actinobacillus actinomycetemcomitans), Porphyromonas gingivalis, Prevotella intermedia, and Tannerella forsythia (previously T. forsythensis) in patients with generalized AgP (AgP group), CP (CP group), or gingivitis (G group) and in healthy individuals (C group). Methods: Subgingival plaque samples were collected with paper points from 30 patients in each group. The nested polymerase chain reaction (PCR) method was used to detect HSV-1, EBV-1, and HCMV. Bacteria were identified by 16S rRNA-based PCR. Results: HSV-1, HCMV, and EBV-1 were detected in 86.7%, 46.7%, and 33.3% of the AgP group, respectively; in 40.0%, 50.0%, and 46.7% of the CP group, respectively; in 53.3%, 40.0%, and 20.0% of the G group, respectively; and in 20.0%, 56.7%, and 0.0% of the C group, respectively. A. actinomycetemcomitans was detected significantly more often in the AgP group compared to the other groups (P<0.005). P. gingivalis and T. forsythia were identified more frequently in AgP and CP groups, and AgP, CP, and G groups had higher frequencies of P. intermedia compared to the C group. Conclusion: In Brazilian patients, HSV-1 and EBV-1, rather than HCMV, were more frequently associated with CP and AgP. J Periodontol 2008;79:2313-2321.

Estimating Income Inequality in China Using Grouped Data and the Generalized Beta Distribution

There are two main types of data sources of income distributions in China: household survey data and grouped data. Household survey data are typically available for isolated years and individual provinces. In comparison, aggregate or grouped data are typically available more frequently and usually have national coverage. In principle, grouped data allow investigation of the change of inequality over longer, continuous periods of time, and the identification of patterns of inequality across broader regions. Nevertheless, a major limitation of grouped data is that only mean (average) income and income shares of quintile or decile groups of the population are reported. Directly using grouped data reported in this format is equivalent to assuming that all individuals in a quintile or decile group have the same income. This potentially distorts the estimate of inequality within each region. The aim of this paper is to apply an improved econometric method designed to use grouped data to study income inequality in China. A generalized beta distribution is employed to model income inequality in China at various levels and periods of time. The generalized beta distribution is more general and flexible than the lognormal distribution that has been used in past research, and also relaxes the assumption of a uniform distribution of income within quintile and decile groups of populations. The paper studies the nature and extent of inequality in rural and urban China over the period 1978 to 2002. Income inequality in the whole of China is then modeled using a mixture of province-specific distributions. The estimated results are used to study the trends in national inequality, and to discuss the empirical findings in the light of economic reforms, regional policies, and globalization of the Chinese economy.