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The hyperelliptic Torelli group is the subgroup of the mapping class group consisting of elements that act trivially on the homology of the surface and that also commute with some fixed hyperelliptic involution. Putman and the authors proved that this group is generated by Dehn twists about separating curves fixed by the hyperelliptic involution. In this paper, we introduce an algorithmic approach to factoring a wide class of elements of the hyperelliptic Torelli group into such Dehn twists, and apply our methods to several basic types of elements. As one consequence, we answer an old question of Dennis Johnson. [ABSTRACT FROM PUBLISHER]

Statistical methods are usually applied in examining diet–disease associations, whereas factor analysis is commonly used for dietary pattern recognition. Recently, machine learning (ML) has been also proposed as an alternative technique in health classification. In this work, the predictive accuracy of statistical v. ML methodologies as regards the association of dietary patterns on CVD risk was tested. During 2001–2002, 3042 men and women (45 (sd 14) years) were enrolled in the ATTICA study. In 2011–2012, the 10-year CVD follow-up was performed among 2020 participants. Item Response Theory was applied to create a metric of combined 10-year cardiometabolic risk, the ‘Cardiometabolic Health Score’, that incorporated incidence of CVD, diabetes, hypertension and hypercholesterolaemia. Factor analysis was performed to extract dietary patterns, on the basis of either foods or nutrients consumed; linear regression analysis was used to assess their association with the cardiometabolic score. Two ML techniques (k-nearest-neighbor’s algorithm and random-forests decision tree) were applied to evaluate participants’ health based on dietary information. Factor analysis revealed five and three factors from foods and nutrients, respectively, explaining 54 and 65 % of the total variation in intake. Nutrient and food pattern regression models showed similar accuracy in correctly classifying an individual according to the cardiometabolic risk (R 2=9·6 % and R 2=8·3 %, respectively). ML techniques were superior compared with linear regression in correct classification of the individuals according to the Health Score (accuracy approximately 38 v. 6 %, respectively), whereas the two ML methods showed equal classification ability. Conclusively, ML methods could be a valuable tool in the field of nutritional epidemiology, leading to more accurate disease-risk evaluation. [ABSTRACT FROM AUTHOR]

CHD is becoming an increasing priority worldwide, as it is one of the main causes of death in low- and middle-income countries lately. This study aims to evaluate the association between beverage consumption patterns and the risk of CHD among Mexican adult population. We performed a cross-sectional analysis using data from 6640 adults participating in the Health Workers’ Cohort Study. Factor analysis was performed to identify beverage patterns using sex-specific Framingham prediction algorithms to estimate CHD risk. The prevalence of moderate to high CHD risk was 17·8 %. We identified four major beverage consumption patterns, which were categorised as alcohol, coffee/tea, soft drinks and low-fat milk. We observed a lower risk of CHD (OR=0·61; 95 % CI 0·46, 0·80; and OR=0·58; 95 % CI 0·43, 0·79, respectively) among participants in the upper quintile of alcohol or low-fat milk consumption compared with those in the bottom quintile. In contrast, a higher consumption of soft drinks was positively associated with CHD risk (OR=1·64; 95 % CI 1·21, 2·20) when compared with other extreme quintiles. Finally, coffee/tea consumption was not significantly associated with CHD risk. Our findings suggest that a beverage pattern characterised by a higher intake of sugar-sweetened beverages may be associated with an increased risk of CHD among the Mexican adult population, whereas patterns of moderate alcohol intake and low-fat milk may be associated with a reduced risk. [ABSTRACT FROM AUTHOR]

BackgroundThe number of separable cognitive dimensions in schizophrenia has been debated. Guided by the extant factor analytic literature, the NIMH Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) initiative selected seven cognitive domains relevant to treatment studies in schizophrenia: speed of processing, attention/vigilance, working memory, verbal learning, visual learning, reasoning and problem solving, and social cognition. These domains are assessed in the MATRICS Consensus Cognitive Battery (MCCB). The aim of this study was to conduct a confirmatory factor analysis (CFA) of the beta battery of the MCCB to compare the fit of the MATRICS consensus seven-domain model to other models in the current literature on cognition in schizophrenia.MethodUsing data from 281 schizophrenia outpatients, we compared the seven correlated factors model with alternative models. Specifically, we compared the 7-factor model to (a) a single-factor model, (b) a three correlated factors model including speed of processing, working memory, and general cognition, and (c) a hierarchical model in which seven first-order factors loaded onto a second-order general cognitive factor.ResultsMultiple fit indices indicated the seven correlated factors model was the best fit for the data and provided significant improvement in model fit beyond the comparison models.ConclusionsThese results support the assessment of these seven cognitive dimensions in clinical trials of interventions to improve cognition in schizophrenia. Because these cognitive factors are separable to some degree, it is plausible that specific interventions may have differential effects on the domains. [ABSTRACT FROM AUTHOR]