Touching points of s star-shaped set with an affine subspace

AbstractThe paper studies the following problem. Given a linear subspace L ⊂ Rn of dimension k, 1 ⩽ k ⩽ n – 1, the point x ∃ Rn, x ∉ L, and a star-shaped set A ⊂ Rn, characterize those τ> 0 for which L + x touches τA, and, if this is the case, describe the set τ cl(A)∩(L + x). Here A is star-shaped if λA ⊆ A for all 0 ⩽ λ ⩽ 1, L + x touches τA if L + x meets τA only on the boundary, and cl(A) means the closure of A. The problem is solved for two kinds of sets: convex A such that the origin θ is contained in the relative interior of A, and A equals to the closed unit ɭp-ball Gp for some 0 < p < 1. For convex A the set L⊥ ∩ A∗ plays a crucial role, where A∗ ≔ {z ∃ Rn:⇄z,y↩ ⩽ 1 for all y ∈ A} is the polar of A, and L⊊ is the orthogonal complement subspace to L. For Gp the problem is solved by a special geometrical construction based on “coordinate” subspaces RT such that L ∩ RT = {θ}

The Predictive Utility Of Drinking Refusal Self-Efficacy And Alcohol Expectancy: A Diary-Based Study Of Tension Reduction

The potential tension reduction effects of alcohol may be most appropriately tested by examining the role of alcohol related beliefs regarding alcohol's anxiolytic properties. The relationship between affective change drinking refusal self-efficacy, tension reduction alcohol expectancies, and ongoing drinking behavior was examined amongst 57 regular drinkers. Alcohol consumption, antecedent, and consequent mood states were monitored prospectively by diary. Social leaming theory hypothesizes that low drinking refusal self-efficacy when experiencing a negative mood state should be associated with more frequent drinking when tense. Strong alcohol expectancies of tension reduction were hypothesized to predict subsequent tension reduction. Contrary to this hypothesis, the present study found that alcohol expectancies were more strongly related to antecedent mood states. Only a weak relationship between drinking refusal self-efficacy and predrinking tension, and between alcohol expectancy and subsequent tension reduction, was evident

The Psychobiological Correlates Of Panic Attacks During In Vivo Exposure

This study examined in detail the psychobiological correlates of panic attacks experienced in panic disorder with agoraphobia. The cognitions, affect, and physiology of the six patients were monitored during in vivo exposure to their phobic situations. The results from these case studies showed that catastrophic cognitions are the key component of panic attacks. However, there was no clear-cut evidence to support an interaction among cognitions, affect, and physiology, which has been postulated by cognitive theories to be the central component of panic attacks and panic disorder with agoraphobia

Effectiveness of a self-help cognitive behavioural treatment program for problem gamblers: a randomised controlled trial

The study aimed to strengthen the scarce literature on self-help treatments for Problem Gambling (PG) by comparing the effectiveness of a Self-Help Cognitive Behavioral Treatment (SHCBT) program (n\ua0=\ua023) with a 6-week Waitlist condition (n\ua0=\ua032) in problem gamblers. Participants were community volunteers with gambling problems and were randomly allocated to the Waitlist and treatment conditions. Results showed significant improvements at post-treatment in gambling behaviors including frequency of gambling, average amount gambled per day and PG symptoms as well as a number of gambling correlates including psychological states (e.g., depression, anxiety and stress), gambling cognitions, gambling urges, gambling related self-efficacy, satisfaction with life, and quality of life among those who completed the SHCBT program, when compared with the waitlist condition. The effect size (partial η) ranged from .25 to .57 for all assessed outcomes that showed significant improvement from pre- to post-treatment. It was concluded that a self-help CBT program can be beneficial for treating community problem gamblers

Confirmatory Factor Analysis of the COPE Questionnaire on Community Drinkers and An Alcohol-Dependent Sample

Objective: The COPE questionnaire has often been used as an efficient method of assessing a range of coping dimensions in many areas, including alcohol research. To date, however, this questionnaire has not been validated for use in community drinkers or alcohol-dependent samples. This study aimed to rectify this shortcoming in the literature. Method: Confirmatory factor analyses (CFA) were performed for 600 Australians (315 men, 285 women; 300 community drinkers and 300 individuals dependent on alcohol; all Ss aged 18-60 yrs), in an attempt to confirm the 14 primary factors and the higher-order factor structure of the COPE. Results: The results of the CFA show that, whereas a 14-factor primary structure and the popular 3-factor higher-order structure were confirmed in the sample of community drinkers, the 4-factor model (COPE) was not confirmed. No support for any factor solution was found in the alcohol-dependent sample. Conclusion: It was concluded that the COPE has good psychometric properties when assessing community drinkers, but it is not an adequate tool for assessing dimensions of coping in an alcohol-dependent sample and should be used with extreme caution

Positive effects of Individual Cognitive Behavior Therapy for patients with unipolar mood disorders with suicidal ideation in Malaysia: a randomised controlled trial

The aim of this study was to investigate the effectiveness of Individual Cognitive Behavior Therapy (ICBT) in treating patients with mood disorders with suicidal ideation. A total of 69 patients (48 females, 21 males) with the diagnoses above were randomly allocated to either the group of Treatment As Usual (TAU)+ICBT (n=33) or the TAU group (n=36). All participants completed the Beck Depression Inventory (BDI), Beck Scale for Suicide Ideation (BSS), Positive and Negative Suicide Ideation Inventory (PANSI), Beck Hopelessness Scale (BHS), and Depression Anxiety Stress Scale-21 (DASS-21). These questionnaires were administered at pre-treatment, midway through treatment (week 4), post-treatment (week 8), and at follow-ups after three months (week 20) and six months (week 32). Factorial ANOVA results showed that the TAU+ICBT patients improved significantly and at faster rate as compared to the TAU group, which showed improvement only from pre to mid treatment on DASS-D and BHS-T measures. The effect size (Cohen's d), for the TAU+ICBT group showed large effect (1.47) for depressive symptoms and suicidal ideation (1.00). These findings suggest that ICBT used in addition to the TAU, was effective in enhancing treatment outcome of patients with unipolar mood disorders as well as, reducing risk for suicide behavior

Genicular artery embolization as a novel treatment for mild to moderate knee osteoarthritis:protocol design of a randomized sham-controlled clinical trial

INTRODUCTION: Knee osteoarthritis is a common disease with pain as the most prevalent symptom. Previous cohort studies have shown genicular artery embolization to reduce pain symptoms in patients with mild to moderate knee osteoarthritis. Patients resistant to conservative therapy but not eligible yet for surgical treatment due to young age or comorbidities may profit from an effective and sustained pain reduction treatment. This study is a randomized sham-controlled trial to evaluate the efficacy of genicular artery embolization in patients with knee osteoarthritis. METHODS AND ANALYSIS: Fifty-eight patients with mild-to-moderate knee osteoarthritis will be recruited and randomly allocated to the treatment or control group in a 1:1 ratio. Participants in the treatment group will undergo genicular artery embolization. Patients in the control group will undergo sham treatment. Outcome measurements will be assessed at baseline and after 1, 4, 8, and 12 months with questionnaires, pressure pain threshold testing, and MR imaging. The MR imaging protocol is designed to (semi)quantitatively assess osteoarthritis in the knee joint. The primary outcome is the change from baseline of the Knee injury and Osteoarthritis Outcome Score (KOOS) pain subscale after 4 months. Secondary outcomes include change in osteoarthritis-related questionnaires, pressure pain threshold, and OA-related MRI features, particularly synovitis and bone marrow lesions. ETHICS AND DISSEMINATION: This trial will determine the efficacy of genicular artery embolization compared to a sham treatment. This is of importance to assess before proceeding to larger-scale efficiency studies and, ultimately, implementing this treatment into day to day clinical practice. TRIAL REGISTRATION: ClinicalTrials.gov NCT03884049. Registered on 21 March 201