Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

Laboratorial training of examiners for using a visual caries detection system in epidemiological surveys

Background: In epidemiological surveys, a good reliability among the examiners regarding the caries detection method is essential. However, training and calibrating those examiners is an arduous task because it involves several patients who are examined many times. To facilitate this step, we aimed to propose a laboratory methodology to simulate the examinations performed to detect caries lesions using the International Caries Detection and Assessment System (ICDAS) in epidemiological surveys. Methods: A benchmark examiner conducted all training sessions. A total of 67 exfoliated primary teeth, varying from sound to extensive cavitated, were set in seven arch models to simulate complete mouths in primary dentition. Sixteen examiners (graduate students) evaluated all surfaces of the teeth under illumination using buccal mirrors and ball-ended probe in two occasions, using only coronal primary caries scores of the ICDAS. As reference standard, two different examiners assessed the proximal surfaces by direct visual inspection, classifying them in sound, with non-cavitated or with cavitated lesions. After, teeth were sectioned in the bucco-lingual direction, and the examiners assessed the sections in stereomicroscope, classifying the occlusal and smooth surfaces according to lesion depth. Inter-examiner reproducibility was evaluated using weighted kappa. Sensitivities and specificities were calculated at two thresholds: all lesions and advanced lesions (cavitated lesions in proximal surfaces and lesions reaching the dentine in occlusal and smooth surfaces). Conclusion: The methodology purposed for training and calibration of several examiners designated for epidemiological surveys of dental caries in preschool children using the ICDAS is feasible, permitting the assessment of reliability and accuracy of the examiners previously to the survey´s development.

Cross-cultural adaptation and psychometric properties of the Brazilian version of the scale of oral health outcomes for 5-year-old children (SOHO-5)

Abstract Background Most of the instruments available to measure the oral health-related quality of life (OHRQoL) in paediatric populations focus on older children, whereas parental reports are used for very young children. The scale of oral health outcomes for 5-year-old children (SOHO-5) assesses the OHRQoL of very young children through self-reports and parental proxy reports. We aimed to cross-culturally adapt the SOHO-5 to the Brazilian Portuguese language and to assess its reliability and validity. Findings We tested the quality of the cross-cultural adaptation in 2 pilot studies with 40 children aged 5–6 years and their parents. The measurement was tested for reliability and validity on 193 children that attended the paediatric dental screening program at the University of São Paulo. The children were also clinically examined for dental caries. The internal consistency was demonstrated by a Cronbach's alpha coefficient of 0.90 for the children’s self-reports and 0.77 for the parental proxy reports. The test-retest reliability results, which were based on repeated administrations on 159 children, were excellent; the intraclass correlation coefficient was 0.98 for parental and 0.92 for child reports. In general, the construct validity was satisfactory and demonstrated consistent and strong associations between the SOHO-5 and different subjective global ratings of oral health, perceived dental treatment need and overall well-being in both the parental and children’s versions (p < 0.001). The SOHO-5 was also able to clearly discriminate between children with and without a history of dental caries (mean scores: 5.8 and 1.1, respectively; p < 0.001). Conclusion The present study demonstrated that the SOHO-5 exhibits satisfactory psychometric properties and is applicable to 5- to 6-year-old children in Brazil.