Large deviations of the maximal eigenvalue of random matrices

We present detailed computations of the 'at least finite' terms (three dominant orders) of the free energy in a one-cut matrix model with a hard edge a, in beta-ensembles, with any polynomial potential. beta is a positive number, so not restricted to the standard values beta = 1 (hermitian matrices), beta = 1/2 (symmetric matrices), beta = 2 (quaternionic self-dual matrices). This model allows to study the statistic of the maximum eigenvalue of random matrices. We compute the large deviation function to the left of the expected maximum. We specialize our results to the gaussian beta-ensembles and check them numerically. Our method is based on general results and procedures already developed in the literature to solve the Pastur equations (also called "loop equations"). It allows to compute the left tail of the analog of Tracy-Widom laws for any beta, including the constant term.Comment: 62 pages, 4 figures, pdflatex ; v2 bibliography corrected ; v3 typos corrected and preprint added ; v4 few more numbers adde

The Dreyfus model of clinical problem-solving skills acquisition: a critical perspective

Context: The Dreyfus model describes how individuals progress through various levels in their acquisition of skills and subsumes ideas with regard to how individuals learn. Such a model is being accepted almost without debate from physicians to explain the ‘acquisition’ of clinical skills. Objectives: This paper reviews such a model, discusses several controversial points, clarifies what kind of knowledge the model is about, and examines its coherence in terms of problem-solving skills. Dreyfus’ main idea that intuition is a major aspect of expertise is also discussed in some detail. Relevant scientific evidence from cognitive science, psychology, and neuroscience is reviewed to accomplish these aims. Conclusions: Although the Dreyfus model may partially explain the ‘acquisition’ of some skills, it is debatable if it can explain the acquisition of clinical skills. The complex nature of clinical problem-solving skills and the rich interplay between the implicit and explicit forms of knowledge must be taken into consideration when we want to explain ‘acquisition’ of clinical skills. The idea that experts work from intuition, not from reason, should be evaluated carefully

18 Away from Delinquency and Crime: Resilience and Protective Factors

peer reviewedDelinquent and criminal behaviors are often the result of adverse conditions in the family and the neighborhood, or of affiliations with delinquent peers. However, case studies as well as large surveys have shown that even in adverse conditions, many children and adolescents do not engage in delinquency; they are “resilient.” In the explanation of criminal and antisocial behaviors, resilient individuals are those who have succeeded in overcoming at-risk circumstances. Resilience is also regarded as the process through which a person adjusts to at-risk situations in a successful manner. Promotive and protective factors stem from the community, family, school, peers, and individuals, and the configurations of these factors are important. In addition, protective factors are not universal. Risk factors and consequently, protective and resilience processes, may be different for children, adolescents, and adults, as well as for males and females. Finally, it is useful to distinguish primary resilience (i.e., as a preventive force in the onset of delinquency) from secondary resilience, which refers to a return to a crime-free life after a period of serious offending activity