On products of long cycles: short cycle dependence and separation probabilities

We present various results on multiplying cycles in the symmetric group. One result is a generalisation of the following theorem of Boccara (1980): the number of ways of writing an odd permutation in the symmetric group on n symbols as a product of an n-cycle and an (n - 1)-cycle is independent of the permutation chosen. We give a number of different approaches of our generalisation. One partial proof uses an inductive method which we also apply to other problems. In particular, we give a formula for the distribution of the number of cycles over all products of cycles of fixed lengths. Another application is related to the recent notion of separation probabilities for permutations introduced by Bernardi, Du, Morales and Stanley (2014)

Can mental health diagnoses in administrative data be used for research? A systematic review of the accuracy of routinely collected diagnoses

BACKGROUND: There is increasing availability of data derived from diagnoses made routinely in mental health care, and interest in using these for research. Such data will be subject to both diagnostic (clinical) error and administrative error, and so it is necessary to evaluate its accuracy against a reference-standard. Our aim was to review studies where this had been done to guide the use of other available data. METHODS: We searched PubMed and EMBASE for studies comparing routinely collected mental health diagnosis data to a reference standard. We produced diagnostic category-specific positive predictive values (PPV) and Cohen’s kappa for each study. RESULTS: We found 39 eligible studies. Studies were heterogeneous in design, with a wide range of outcomes. Administrative error was small compared to diagnostic error. PPV was related to base rate of the respective condition, with overall median of 76 %. Kappa results on average showed a moderate agreement between source data and reference standard for most diagnostic categories (median kappa = 0.45–0.55); anxiety disorders and schizoaffective disorder showed poorer agreement. There was no significant benefit in accuracy for diagnoses made in inpatients. CONCLUSIONS: The current evidence partly answered our questions. There was wide variation in the quality of source data, with a risk of publication bias. For some diagnoses, especially psychotic categories, administrative data were generally predictive of true diagnosis. For others, such as anxiety disorders, the data were less satisfactory. We discuss the implications of our findings, and the need for researchers to validate routine diagnostic data. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12888-016-0963-x) contains supplementary material, which is available to authorized users

Meditation or Medication? Mindfulness training versus medication in the treatment of childhood ADHD: a randomized controlled trial

Background Attention-Deficit-Hyperactivity-Disorder (ADHD) is, with a prevalence of 5 %, a highly common childhood disorder, and has severe impact on the lives of youngsters and their families. Medication is often the treatment of choice, as it currently is most effective. However, medication has only short-term effects, treatment adherence is often low and most importantly; medication has serious side effects. Therefore, there is a need for other interventions for youngsters with ADHD. Mindfulness training is emerging as a potentially effective training for children and adolescents with ADHD. The aim of this study is to compare the (cost) effectiveness of mindfulness training to the (cost) effectiveness of methylphenidate in children with ADHD on measures of attention and hyperactivity/impulsivity. Methods/design A multicenter randomized controlled trial with 2 follow-up measurements will be used to measure the effects of mindfulness training versus the effects of methylphenidate. Participants will be youngsters (aged 9 to 18) of both sexes diagnosed with ADHD, referred to urban and rural mental healthcare centers. We aim to include 120 families. The mindfulness training, using the MYmind protocol, will be conducted in small groups, and consists of 8 weekly 1.5-h sessions. Youngsters learn to focus and enhance their attention, awareness, and self-control by doing mindfulness exercises. Parents will follow a parallel mindful parenting training in which they learn to be fully present in the here and now with their child in a non-judgmental way, to take care of themselves, and to respond rather than react to difficult behavior of their child. Short-acting methylphenidate will be administered individually and monitored by a child psychiatrist. Assessments will take place at pre-test, post-test, and at follow-up 1 and 2 (respectively 4 and 10 months after the start of treatment). Informants are parents, children, teachers, and researchers. Discussion This study will inform mental health care professionals and health insurance companies about the clinical and cost effectiveness of mindfulness training for children and adolescents with ADHD and their parents compared to the effectiveness of methylphenidate. Limitations and several types of bias that are anticipated for this study are discussed

Lower semicontinuity of the feasible set mapping of linear systems relative to their domains

This paper deals with stability properties of the feasible set of linear inequality systems having a finite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, affecting respectively, all of the data, the left-hand side data, or the right-hand side coefficients.This research was partially supported by the MICINN grant MTM2011-29064-C03-01 and -02 (Spain). The second and third authors are Partner Investigators in the Australian Research Council Discovery Projects DP120100467 and DP110102011, respectively. The research of the fourth author was partially supported by the MIUR project “Variational and Topological Methods in the Study of Nonlinear Phenomena” (2009)

Discretization of information collecting situations and continuity of compensation rules

A canonical procedure is described, which associates to each infinite information collecting situation a related information collecting situation with finite state and action spaces, in such a way that the two corresponding IC-games are near to each other.Compensations for informants are then also near to each other in the two IC-situations, if they are based on continuous compensation rules.