Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Anxiety problems in young people with Asperger syndrome: a case series

It is now well established that the prevalence of mental health difficulties in individuals with autism spectrum disorders (ASD) is considerably higher than in the general population. With recent estimates of the prevalence of autism spectrum disorders being as high as one percent, increasing numbers of children and young people are presenting to local and specialist services with mental health problems in addition to a diagnosis of ASD. Many families report that the impact of the mental health problems can be as or more impairing than the autism spectrum difficulties themselves. Clinical services are frequently called upon to treat these difficulties; however, there is limited evidence for the effectiveness of treatments in this population. This paper reports a case series of children and adolescents with ASD and an anxiety disorder who were treated with a standard cognitive behaviour therapy (CBT) rationale adapted to take account of the neuropsychological features of ASD. Common features of the presentation of the disorders and also treatment processes are discussed.

Assessment of depression, anxiety and apathy in prodromal and early Huntington disease

The Functional Rating Scale Taskforce for pre-Huntington Disease (FuRST-pHD) is a multinational, multidisciplinary initiative with the goal of developing a data-driven, comprehensive, psychometrically sound, rating scale for assessing symptoms and functional ability in prodromal and early Huntington disease (HD) gene expansion carriers. The process involves input from numerous sources to identify relevant symptom domains, including HD individuals, caregivers, and experts from a variety of fields, as well as knowledge gained from the analysis of data from ongoing large-scale studies in HD using existing clinical scales. This is an iterative process in which an ongoing series of field tests in prodromal (prHD) and early HD individuals provides the team with data on which to make decisions regarding which questions should undergo further development or testing and which should be excluded. We report here the development and assessment of the first iteration of interview questions aimed to assess Depression, Anxiety and Apathy in prHD and early HD individuals.

Parent and child perspectives on the nature of anxiety in children and young people with Autism Spectrum Disorders: a focus group study

Anxiety disorders are common among children and young people with Autism Spectrum Disorders (ASD). Despite growing knowledge about the prevalence, phenomenology and treatment of anxiety disorders, relatively little is understood about the nature and impact of anxiety in this group and little is known about autism-specific factors that may play a role in the increased prevalence of anxiety disorders. In this exploratory study, we report on a series of 5 focus groups with 17 parents of children and adolescents with ASD and anxiety. Across groups, parents gave strikingly similar descriptions of the triggers and behavioural signs associated with anxiety. Another consistent finding was that many parents reported that their children had great difficulty expressing their worries verbally and most showed their anxiety through changes in their behaviour. The impact of anxiety was reported to often be more substantial than the impact of ASD itself. The implications of the focus group findings are discussed in relation to existing literature.

Response theory for equilibrium and non-equilibrium statistical mechanics: causality and generalized Kramers-Kronig relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

Doll Play narratives about starting school in children of socially anxious mothers, and their relation to subsequent child school-based anxiety

Background: Child social anxiety is common, and predicts later emotional and academic impairment. Offspring of socially anxious mothers are at increased risk. It is important to establish whether individual vulnerability to disorder can be identified in young children. Method: The responses of 4.5 year-old children of mothers with social phobia (N = 62) and non-anxious mothers (N = 60) were compared, two months before school entry, using a Doll Play (DP) procedure focused on the social challenge of starting school. DP responses were examined in relation to teacher reports of anxious-depressed symptoms and social worries at the end of the child’s first school term. The role of earlier child behavioral inhibition and attachment, assessed at 14 months, was also considered. Results: Compared to children of non-anxious mothers, children of mothers with social phobia were significantly more likely to give anxiously negative responses in their school DP (OR = 2.57). In turn, negative DP predicted teacher reported anxious-depressed and social worry problems. There were no effects of infant behavioral inhibition or attachment. Conclusion: Vulnerability in young children at risk of anxiety can be identified using Doll Play narratives.

Effects of psychotherapy for anxiety in children and adolescents: a meta-analytic review

This paper provides a comprehensive quantitative review of high quality randomized controlled trials of psychological therapies for anxiety disorders in children and young people. Using a systematic search for randomized controlled trials which included a control condition and reported data suitable for meta-analysis, 55 studies were included. Eligible studies were rated for methodological quality and outcome data were extracted and analyzed using standard methods. Trial quality was variable, many studies were underpowered and adverse effects were rarely assessed; however, quality ratings were higher for more recently published studies. Most trials evaluated cognitive behavior therapy or behavior therapy and most recruited both children and adolescents. Psychological therapy for anxiety in children and young people was moderately effective overall, but effect sizes were small to medium when psychological therapy was compared to an active control condition. The effect size for non-CBT interventions was not significant. Parental involvement in therapy was not associated with differential effectiveness. Treatment targeted at specific anxiety disorders, individual psychotherapy, and psychotherapy with older children and adolescents had effect sizes which were larger than effect sizes for treatments targeting a range of anxiety disorders, group psychotherapy, and psychotherapy with younger children. Few studies included an effective follow-up. Future studies should follow CONSORT reporting standards, be adequately powered, and assess follow-up. Research trials are unlikely to address all important clinical questions around treatment delivery. Thus, careful assessment and formulation will remain an essential part of successful psychological treatment for anxiety in children and young people.

Cognitive, affective and behavioural characteristics of mothers with anxiety disorders in the context of child anxiety disorder

Parental emotional distress, particularly high maternal anxiety, is one of the most consistent predictors of child anxiety treatment outcome. In order to identify the cognitive, affective and behavioural parenting characteristics of mothers of children with anxiety disorders who themselves have an anxiety disorder, we assessed the expectations and appraisals of 88 mothers of anxious children (44 not anxious (NONANX) and 44 with a current anxiety disorder (ANX)) before and after interacting with their 7-12 year old children. There were no observed differences in anxiety and avoidance among children of ANX and NONANX mothers, but, compared to NONANX mothers, ANX mothers held more negative expectations and differed on observations of intrusiveness, expressed anxiety, warmth and the quality of the relationship. Associations were moderated by the degree to which children expressed anxiety during the tasks. Maternal reported negative emotions during the task significantly mediated the association between maternal anxiety status and the observed quality of the relationship. These findings suggest that maternal anxiety disorder is associated with reduced tolerance of children’s negative emotions. This may interfere with the maintenance of a positive, supportive mother-child interaction under conditions of stress, and as such impede optimum treatment outcomes. The findings identify potential cognitive, affective and behavioural targets to improve treatment outcomes for children with anxiety disorders in the context of a current maternal anxiety disorder.

Predicting outcomes following cognitive behavior therapy in child anxiety disorders: the influence of genetic, demographic and clinical information

Background. Within a therapeutic gene by environment (GxE) framework, we recently demonstrated that variation in the Serotonin Transporter Promoter Polymorphism; 5HTTLPR and marker rs6330 in Nerve Growth Factor gene; NGF is associated with poorer outcomes following cognitive behaviour therapy (CBT) for child anxiety disorders. The aim of this study was to explore one potential means of extending the translational reach of G×E data in a way that may be clinically informative. We describe a ‘risk-index’ approach combining genetic, demographic and clinical data and test its ability to predict diagnostic outcome following CBT in anxious children. Method. DNA and clinical data were collected from 384 children with a primary anxiety disorder undergoing CBT. We tested our risk model in five cross-validation training sets. Results. In predicting treatment outcome, six variables had a minimum mean beta value of 0.5: 5HTTLPR, NGF rs6330, gender, primary anxiety severity, comorbid mood disorder and comorbid externalising disorder. A risk index (range 0-8) constructed from these variables had moderate predictive ability (AUC = .62-.69) in this study. Children scoring high on this index (5-8) were approximately three times as likely to retain their primary anxiety disorder at follow-up as compared to those children scoring 2 or less. Conclusion. Significant genetic, demographic and clinical predictors of outcome following CBT for anxiety-disordered children were identified. Combining these predictors within a risk-index could be used to identify which children are less likely to be diagnosis free following CBT alone or thus require longer or enhanced treatment. The ‘risk-index’ approach represents one means of harnessing the translational potential of G×E data.

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Interpretation and expectation in childhood anxiety disorders: age effects and social specificity

Theory and treatment for childhood anxiety disorders typically implicates children’s negative cognitions, yet little is known about the characteristics of thinking styles of clinically anxious children. In particular, it is unclear whether differences in thinking styles between children with anxiety disorders and non-anxious children vary as a function of child age, whether particular cognitive distortions are associated with childhood anxiety disorders at different child ages, and whether cognitive content is disorder-specific. The current study addressed these questions among 120 7 - 12 year old children (53% female) who met diagnostic criteria for social anxiety disorder, other anxiety disorder, or who were not currently anxious. Contrary to expectations, threat interpretation was not inflated amongst anxious compared to non-anxious children at any age, although older (10 - 12 year old) anxious children did differ from non-anxious children on measures of perceived coping. The notion of cognitive-content specificity was not supported across the age-range. The findings challenge current treatment models of childhood anxiety, and suggest that a focus on changing anxious children’s cognitions is not warranted in mid-childhood, and in late childhood cognitive approaches may be better focussed on promoting children’s perceptions of control rather than challenging threat interpretations.