Mapification of n-dimensional abstract polytopes and hypertopes

The n-dimensional abstract polytopes and hypertopes, particularly the regular ones, have gained great popularity over recent years. The main focus of research has been their symmetries and regularity. The planification of a polyhedron helps its spatial construction, yet it destroys symmetries. No “planification” of n-dimensional polytopes do exist, however it is possible to make a “mapification” of an n-dimensional polytope; in other words it is possible to construct a restrictedly-marked map representation of an abstract polytope on some surface that describes its combinatorial structures as well as all of its symmetries. There are infinitely many ways to do this, yet there is one that is more natural that describes reflections on the sides of (n-1)-simplices (flags or n-flags) with reflections on the sides of n-gons. The restrictedly-marked map representation of an abstract polytope is a cellular embedding of the flag graph of a polytope. We illustrate this construction with the 4-cube, a regular 4-polytope with automorphism group of size 384. This paper pays a tribute to Lynne James’ last work on map representations.publishe

Classification of regular maps of negative prime Euler characteristic

We give a classification of all regular maps on nonorientable surfaces with a negative odd prime Euler characteristic (equivalently, on nonorientable surfaces of genus where is an odd prime). A consequence of our classification is that there are no regular maps on nonorientable surfaces of genus where is a prime such that (mod ) and

Tipos de clones e perfis de resistência antimicrobiana de Staphylococcus aureus resistentes à meticilina isolados de hospitais no sul do Brasil

In the present study were evaluated the DNA macrorestriction profile and SCCmec types for nine multi-resistant MRSA selected. Also antimicrobial susceptibility testing by disk diffusion method was evaluated for 68 MRSA isolates against 12 antimicrobial agents. The isolates were recovered from blood culture collected from hospitalized patients in three hospitals of Porto Alegre, Brazil. PFGE and PCR for mecA and SCCmec I, II, III, IV types genes were done on selected nine isolates with susceptibility only to vancomycin, teicoplanin and linezolid. Two clone profiles, with five subtypes, were demonstrated among multi-resistant MRSA analyzed. Eight isolates showed harbor SCCmec type III and one isolate was not typeable. The knowledge of SCCmec type, clone and antimicrobial profiles among S. aureus is essential mainly to prevention and control of dissemination of the antimicrobial resistance.No presente estudo foram avaliados o perfil de macrorrestrição do DNA e tipos de SCCmec para nove MRSA multirresistentes selecionados. Além disso, susceptibilidade a 12 agentes antimicrobianos pelo teste de disco-difusão foi avaliada para 68 isolados de MRSA. Os isolados foram obtidos de hemoculturas de pacientes hospitalizados de três hospitais de Porto Alegre, Brasil. PFGE e PCR para detecção do gene mecA e para os tipos genéticos SCCmec I, II, III e IV foram realizados em nove isolados selecionados que apresentaram susceptibilidade somente a vancomicina, teicoplanina e linezolida. Dois perfis clonais, com cinco subtipos, foram demonstrados entre os isolados analisados. Oito isolados apresentaram SCCmec tipo III e um isolado não foi caracterizado quanto ao tipo de SCCmec. O conhecimento do tipo de SCCmec bem como dos perfis clonais e de susceptibilidade aos antimicrobianos entre isolados de S. aureus é essencial, principalmente, para a prevenção e controle da disseminação da resistência antimicrobiana

Packing of R3 by crosses

The existence of tilings of R^n by crosses, a cluster of unit cubes comprising a central one and 2n arms, has been studied by several authors. We have completely solved the problem for R^2, characterizing the crosses which lattice tile R^2, as well as determining the maximum packing density for the crosses which do not lattice tile the plane. In this paper we motivate a similar approach to study lattice packings of R^3 by crosses.The existence of tilings of Rn by crosses, a cluster of unit cubes comprising a central one and 2n arms, has been studied by several authors. We have completely solved the problem for R2 characterizing the crosses which lattice tile R2 as well as determining the maximum packing density for the crosses which do not lattice tile the plane. In this paper we motivate a similar approach to study lattice packings of R3 by crosses.publishe

Toxoplasma-IgM and IgG-avidity in single samples from areas with a high infection rate can determine the risk of mother-to-child transmission

Anti-Toxoplasma IgG-avidity was determined in 168 serum samples from IgG- and IgM-positive pregnant women at various times during pregnancy, in order to evaluate the predictive value for risk of mother-to-child transmission in a single sample, taking the limitations of conventional serology into account. The neonatal IgM was considered the serologic marker of transmission. Fluorometric tests for IgG, IgM (immunocapture) and IgG-avidity were performed. Fifty-one of the 128 pregnant women tested gave birth in the hospital and neonatal IgM was obtained. The results showed 32 (62.75%) pregnant women having high avidity, IgM indexes between 0.6 and 2.4, and no infected newborn. Nineteen (37.25%) had low or inconclusive avidity, IgM indexes between 0.6 and 11.9, and five infected newborns and one stillbirth. In two infected newborns and the stillbirth maternal IgM indexes were low and in one infected newborn the only maternal parameter that suggested fetal risk was IgG-avidity. In the present study, IgG-avidity performed in single samples from positive IgM pregnant women helped to determine the risk of transmission at any time during pregnancy, especially when the indexes of the two tests were analysed with respect to gestational age. This model may be less expensive in developing countries where there is a high prevalence of infection than the follow-up of susceptible mothers until childbirth with monthly serology, and it creates a new perspective for the diagnosis of congenital toxoplasmosis.A avidez de IgG anti-Toxoplasma foi realizada em 168 amostras IgG e IgM positivas de gestantes, coletadas em qualquer período da gestação, para avaliar o valor preditivo do risco de transmissão materno-fetal em amostra única, considerando as limitações da sorologia convencional. A IgM neonatal foi considerada o marcador sorológico de transmissão. Testes fluorométricos foram realizados para IgG, IgM (imunocaptura) e avidez de IgG. Cinqüenta e uma das 128 gestantes testadas tiveram os partos realizados na instituição e a IgM neonatal foi obtida. Os resultados mostraram 32 (62.75%) gestantes com avidez alta, índices de IgM entre 0,6 e 2,4 e nenhum recém-nascido infectado. Dezenove (37.25%) tiveram avidez baixa ou inconclusiva, índices de IgM entre 0,6 e 11,9, cinco recém-nascidos infectados e um natimorto. Em dois recém-nascidos infectados e no natimorto, os índices maternos de IgM foram baixos e em um recém-nascido infectado, o único parâmetro materno que sugeriu risco para o feto foi a avidez de IgG. No presente estudo, a avidez de IgG realizada em amostras isoladas de gestantes IgM positivas auxiliou a determinar o risco de transmissão durante toda a gestação, especialmente quando os índices dos dois testes foram analisados em relação à idade gestacional. Este modelo pode ser menos oneroso para países em desenvolvimento com alta prevalência da infecção e cria nova perspectiva para o diagnóstico da toxoplasmose congênita