A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

The treatment of child anxiety disorders via guided parent-delivered cognitive-behavioural therapy: a randomised controlled trial

Background Promising evidence has emerged of clinical gains using guided self-help cognitive-behavioural therapy (CBT) for child anxiety and by involving parents in treatment; however, the efficacy of guided parent-delivered CBT has not been systematically evaluated in UK primary and secondary settings. Aims To evaluate the efficacy of low-intensity guided parent-delivered CBT treatments for children with anxiety disorders. Method A total of 194 children presenting with a current anxiety disorder, whose primary carer did not meet criteria for a current anxiety disorder, were randomly allocated to full guided parent-delivered CBT (four face-to-face and four telephone sessions) or brief guided parent-delivered CBT (two face-to-face and two telephone sessions), or a wait-list control group (trial registration: ISRCTN92977593). Presence and severity of child primary anxiety disorder (Anxiety Disorders Interview Schedule for DSM-IV, child/parent versions), improvement in child presentation of anxiety (Clinical Global Impression-Improvement scale), and change in child anxiety symptoms (Spence Children’s Anxiety Scale, child/parent version and Child Anxiety Impact scale, parent version) were assessed at post-treatment and for those in the two active treatment groups, 6 months post-treatment. Results Full guided parent-delivered CBT produced superior diagnostic outcomes compared with wait-list at post-treatment, whereas brief guided parent-delivered CBT did not: at post-treatment, 25 (50%) of those in the full guided CBT group had recovered from their primary diagnosis, compared with 16 (25%) of those on the wait-list (relative risk (RR) 1.85, 95% CI 1.14-2.99); and in the brief guided CBT group, 18 participants (39%) had recovered from their primary diagnosis post-treatment (RR = 1.56, 95% CI 0.89-2.74). Level of therapist training and experience was unrelated to child outcome. Conclusions Full guided parent-delivered CBT is an effective and inexpensive first-line

The parental overprotection scale: associations with child and parental anxiety

Background: Parental overprotection has commonly been implicated in the development and maintenance of childhood anxiety disorders. Overprotection has been assessed using questionnaire and observational methods interchangeably; however, the extent to which these methods access the same construct has received little attention. Edwards, 2008 and Edwards et al., 2010 developed a promising parent-report measure of overprotection (OP) and reported that, with parents of pre-school children, the measure correlated with observational assessments and predicted changes in child anxiety symptoms. We aimed to validate the use of the OP measure with mothers of children in middle childhood, and examine its association with child and parental anxiety. Methods: Mothers of 90 children (60 clinically anxious, 30 non-anxious) aged 7–12 years completed the measure and engaged in a series of mildly stressful tasks with their child. Results: The internal reliability of the measure was good and scores correlated significantly with observations of maternal overprotection in a challenging puzzle task. Contrary to expectations, OP was not significantly associated with child anxiety status or symptoms, but was significantly associated with maternal anxiety symptoms. Limitations: Participants were predominantly from affluent social groups and of non-minority status. Overprotection is a broad construct, the use of specific sub-dimensions of behavioural constructs may be preferable. Conclusions: The findings support the use of the OP measure to assess parental overprotection among 7–12 year-old children; however, they suggest that parental responses may be more closely related to the degree of parental rather than child anxiety.

Generalized Bayesian cloud detection for satellite imagery. part 1: technique and validation for night-time imagery over land and sea

Numerical Weather Prediction (NWP) fields are used to assist the detection of cloud in satellite imagery. Simulated observations based on NWP are used within a framework based on Bayes' theorem to calculate a physically-based probability of each pixel with an imaged scene being clear or cloudy. Different thresholds can be set on the probabilities to create application-specific cloud-masks. Here, this is done over both land and ocean using night-time (infrared) imagery. We use a validation dataset of difficult cloud detection targets for the Spinning Enhanced Visible and Infrared Imager (SEVIRI) achieving true skill scores of 87% and 48% for ocean and land, respectively using the Bayesian technique, compared to 74% and 39%, respectively for the threshold-based techniques associated with the validation dataset.

Longitudinal investigation of the role of temperament and stressful life events in childhood anxiety

The current study investigated the longitudinal relationships between BI, life events, and anxiety in a sample of 102 behaviourally inhibited (BI) and 100 uninhibited (BUI) children aged 3 to 4 years. Children’s parents completed questionnaires on BI, stressful life events, and anxiety symptoms, and were administered a diagnostic interview three times in a 5-year period. In line with our hypotheses, negative life events, and negative behaviour- dependent life events (i.e. life events that are related to the children’s own behaviours) in particular, and the impact of negative life events, were predictive of increases in subsequent anxiety symptoms, the likelihood of having an anxiety disorder, and increased number of anxiety diagnoses over the five year follow-up period. Experiencing more positive, behaviour-independent life events decreased the risk of being diagnosed with an anxiety disorder. Furthermore, differences were found in life events between BI and BUI children. That is, BI children experienced fewer positive and specifically positive behaviour-dependent life events, and the impact of these positive life events was also lower in BI children than in BUI children. However, BI did not interact with life events in the prediction of anxiety problems as hypothesized. Therefore, this study seems to indicate that BI and life events act as additive risk factors in the development of anxiety problems.

Informing early intervention: preschool predictors of anxiety disorders in middle childhood

Background: To inform early intervention practice, the present research examines how child anxiety, behavioural inhibition, maternal overinvolvement, maternal negativity, mother-child attachment and maternal anxiety, as assessed at age four, predict anxiety at age nine. Method: 202 children (102 behaviourally inhibited and 100 behaviourally uninhibited) aged 3–4 years were initially recruited and the predictors outlined above were assessed. Diagnostic assessments, using the Anxiety Disorders Interview Schedule, were then conducted five years later. Results: Behavioural inhibition, maternal anxiety, and maternal overinvolvement were significant predictors of clinical anxiety, even after controlling for baseline anxiety (p,.05). No significant effect of negativity or attachment security was found over and above baseline anxiety (p..1). Conclusions: Preschool children who show anxiety, are inhibited, have overinvolved mothers and mothers with anxiety disorders are at increased risk for anxiety in middle childhood. These factors can be used to identify suitable participants for early intervention and can be targeted within intervention programs.

Interpretation bias in preschool children at risk for anxiety: a prospective study

A story-stem paradigm was used to assess interpretation bias in preschool children. Data were available for 131 children. Interpretation bias, behavioural inhibition (BI) and anxiety were assessed when children were aged between 3 years 2 months and 4 years 5 months. Anxiety was subsequently assessed 12-months, 2-years and 5-years later. A significant difference in interpretation bias was found between participants who met criteria for an anxiety diagnosis at baseline, with clinically anxious participants more likely to complete the ambiguous story-stems in a threat-related way. Threat interpretations significantly predicted anxiety symptoms at 12-month follow-up, after controlling for baseline symptoms, but did not predict anxiety symptoms or diagnoses at either 2-year or 5- year follow-up. There was little evidence for a relationship between BI and interpretation bias. Overall, the pattern of results was not consistent with the hypothesis that interpretation bias plays a role in the development of anxiety. Instead, some evidence for a role in the maintenance of anxiety over relatively short periods of time was found. The use of a story-stem methodology to assess interpretation bias in young children is discussed along with the theoretical and clinical implications of the findings.

Beyond behaviour: is social anxiety low in Williams syndrome

Individuals with Williams syndrome (WS) exhibit striking social behaviour that may be indicative of abnormally low social anxiety. The present research aimed to determine whether social anxiety is unusually low in WS and to replicate previous findings of increased generalised anxiety in WS using both parent and self report. Fifteen individuals with WS aged 12-28 years completed the Spence Children’s Anxiety Scale (SCAS) and the Children’s Automatic Thoughts Scale (CATS). Their responses were compared to clinically anxious and community comparison groups matched on mental age. The findings suggest that WS is not associated with unusually low social anxiety but that generalised anxiety symptoms and physical threat thoughts are increased in WS, relative to typically developing children.

Self-ratings and observer-ratings of social skill: a manipulation of state social anxiety in anxious and non-anxious children

The role of state and trait anxiety on observer ratings of social skill and negatively biased self-perception of social skill was examined. Participants were aged between 7 and 13 years (mean=9.65; sd=1.77; N=102), 47 had a current anxiety diagnosis and 55 were non-anxious controls. Participants were randomly allocated to a high or low anxiety condition and asked to complete social tasks. Task instructions were adjusted across conditions to manipulate participants’ state anxiety. Observers rated anxious participants as having poorer social skills than non-anxious controls but there was no evidence that anxious participants exhibited a negative self-perception bias, relative to controls. However, as participants’ ratings of state anxiety increased, their perception of their performance became more negatively biased. The results suggest that anxious children may exhibit real impairments in social skill and that high levels of state anxiety can lead to biased judgements of social skills in anxious and non-anxious children.

Temperament, family environment and anxiety in preschool children

This research examines the relationship between behavioural inhibition (BI), family environment (overinvolved and negative parenting, parental anxiety and parent-child attachment) and anxiety in a sample of 202 preschool children. Participants were aged between 3 years 2 months and 4 years 5 months, 101 were male. A thorough methodology was used that incorporated data from multiple observations of behaviour, diagnostic interviews and questionnaire measures. The results showed that children categorised as behaviourally inhibited were significantly more likely to meet criteria for a range of anxiety diagnoses. Furthermore, a wide range of family environment factors, including maternal anxiety, parenting and attachment were significantly associated with BI, with inhibited children more likely to experience adverse family environment factors. No interactions between temperament and family environment were found for child anxiety. However, a significant relationship between current maternal anxiety and child anxiety was found consistently even after controlling for BI. Additionally, there was some evidence of a relationship between maternal negativity and child anxiety, after controlling for BI. The results may suggest that temperament and family environment operate as additive, rather than interactive risk factors for child anxiety. This is discussed in the context of theoretical models of child anxiety and directions for future research.

On the generalized eigenvalue problem for the Rossby wave vertical velocity in the presence of mean flow and topography

In a series of papers, Killworth and Blundell have proposed to study the effects of a background mean flow and topography on Rossby wave propagation by means of a generalized eigenvalue problem formulated in terms of the vertical velocity, obtained from a linearization of the primitive equations of motion. However, it has been known for a number of years that this eigenvalue problem contains an error, which Killworth was prevented from correcting himself by his unfortunate passing and whose correction is therefore taken up in this note. Here, the author shows in the context of quasigeostrophic (QG) theory that the error can ulti- mately be traced to the fact that the eigenvalue problem for the vertical velocity is fundamentally a non- linear one (the eigenvalue appears both in the numerator and denominator), unlike that for the pressure. The reason that this nonlinear term is lacking in the Killworth and Blundell theory comes from neglecting the depth dependence of a depth-dependent term. This nonlinear term is shown on idealized examples to alter significantly the Rossby wave dispersion relation in the high-wavenumber regime but is otherwise irrelevant in the long-wave limit, in which case the eigenvalue problems for the vertical velocity and pressure are both linear. In the general dispersive case, however, one should first solve the generalized eigenvalue problem for the pressure vertical structure and, if needed, diagnose the vertical velocity vertical structure from the latter.

Emotional reasoning and anxiety sensitivity: associations with social anxiety disorder in childhood

Background Two specific cognitive constructs that have been implicated in the development and maintenance of anxiety symptoms are anxiety sensitivity and emotional reasoning, both of which relate to the experience and meaning of physical symptoms of arousal or anxiety. The interpretation of physical symptoms has been particularly implicated in theories of social anxiety disorder, where internal physical symptoms are hypothesized to influence the individual's appraisals of the self as a social object. Method The current study compared 75 children on measures of anxiety sensitivity and emotional reasoning: 25 with social anxiety disorder, 25 with other anxiety disorders, and 25 nonanxious children (aged 7–12 years). Results Children with social anxiety disorder reported higher levels of anxiety sensitivity and were more likely than both other groups to view ambiguous situations as anxiety provoking, whether physical information was present or not. There were no group differences in the extent to which physical information altered children's interpretation of hypothetical scenarios. Limitations This study is the first to investigate emotional reasoning in clinically anxious children and therefore replication is needed. In addition, those in both anxious groups commonly had comorbid conditions and, consequently, specific conclusions about social anxiety disorder need to be treated with caution. Conclusion The findings highlight cognitive characteristics that may be particularly pertinent in the context of social anxiety disorder in childhood and which may be potential targets for treatment. Furthermore, the findings suggest that strategies to modify these particular cognitive constructs may not be necessary in treatments of some other childhood anxiety disorders.

Child anxiety and parenting in England and Italy: the moderating role of maternal warmth

BACKGROUND: Parenting factors have been implicated in the aetiology and maintenance of child anxiety. Most research has been correlational with little experimental or longitudinal work. Cross-cultural comparison could be illuminating. A comparison of Italian and British children and their mothers was conducted. METHODS: A sample of 8- to 10-year old children, 60 Italian and 49 English, completed the Spence Child Anxiety Scale. Mothers also completed two questionnaires of parenting: the Skills of Daily Living Checklist (assessing maternal autonomy granting) and the Parent-Child Interaction Questionnaire (assessing maternal intrusiveness). Parenting was assessed in two video-recorded blindly rated mother-child interaction tasks, the 'belt-buckling tasks and the 'etch-a-sketch', providing objective indices of overcontrol, warmth, lack of autonomy granting, and overprotection. RESULTS: There were no differences between the children in overall anxiety and specific forms of anxiety. Parenting, however, was markedly different for the two countries. Compared to English mothers, on the two questionnaires, Italian mothers were significantly less autonomy granting and more intrusive; and in terms of the observed indices, a significantly greater proportion of the Italian mothers displayed a high level of both overprotection and overcontrol, and a low level of autonomy granting. Notably, Italian mothers evidenced significantly more warmth than English mothers; and maternal warmth was found to moderate the impact of self-reported maternal intrusiveness on the level of both overall child anxiety and the level of child separation anxiety; and it also moderated the relationship between both observed maternal intrusiveness and overall child anxiety and observed maternal overprotectiveness and child separation anxiety. CONCLUSIONS: Although, compared to the British mothers, the Italian mothers were more likely to evidence high levels of parenting behaviours previously found to be anxiogenic, the high levels of warmth displayed by these mothers to their children appears to have neutralised the adverse impact of these behaviours.