On the lattice structure of probability spaces in quantum mechanics

Let C be the set of all possible quantum states. We study the convex subsets of C with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models' approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416

Research Review: Do parent ratings of infant negative emotionality and self‐regulation predict psychopathology in childhood and adolescence? A systematic review and meta‐analysis of prospective longitudinal studies

Background Identifying low‐cost and easy to implement measures of infant markers of later psychopathology may improve targeting of early intervention for prevention. Because of their early manifestation, relative stability and overlap with constructs central to affect‐based dimensions of child and adolescent psychopathology, negative emotionality and self‐regulation have been the focus of this research. We conducted a meta‐analysis of longitudinal studies examining the prospective association between infant temperament measured with parent ratings and child/adolescent psychopathology. Methods A systematic literature search for prospective longitudinal studies, which included measures of questionnaire‐assessed infant temperament (negative emotionality, self‐regulation, behavioural inhibition, surgency/extraversion, activity level) and symptoms of child or adolescent mental health (externalising, internalising) and neurodevelopmental problems (attention deficit/hyperactivity disorder [ADHD], autism spectrum disorder [ASD]), was conducted. Standardised estimates of association were calculated and pooled in meta‐analyses. Results Twenty‐five studies (n = 28,425) met inclusion criteria. Small associations were seen between psychopathology aggregated across all domains and infant negative emotionality (r = .15; p < .001) and self‐regulation (r = −.19; p = .007). Effects were also significant but weaker for behavioural inhibition (r = .10; p = .027) and activity level (r = .08; p = .016). Surgency/extraversion was not significantly associated with psychopathology in general (r = −.04; p = .094); however, it was negatively associated with ASD (r = −.10, p = .015). Significant correlations were observed with some outcomes isomorphic with predictors, internalising problems and behavioural inhibition (r = .10; p = .013), ADHD symptoms and activity level (r = .19; p = .009). Conclusion Questionnaire‐based assessments of infant negative emotionality may have transdiagnostic potential to contribute to a risk index of later childhood psychopathology. Behavioural inhibition, surgency/extraversion and activity ratings may provide more specific predictive power. More data from prospective studies are required before the potential of self‐regulation and surgency/extraversion can be properly gauged