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103 results

Page 1 of 6

Matrix Positivity
  • Matrix Positivity
  • Charles R. Johnson, Ronald L. Smith, Michael J. Tsatsomeros
  • Published online: 11 September 2020
  • Print publication: 01 October 2020
  • View description
    Matrix positivity is a central topic in matrix theory: properties that generalize the notion of positivity to matrices arose from a large variety of applications, and many have also taken on notable theoretical significance, either because they are natural or unifying. This is the first book to provide a comprehensive and up-to-date reference of important material on matrix positivity classes, their properties, and their relations. The matrix classes emphasized in this book include the classes of semipositive matrices, P-matrices, inverse M-matrices, and copositive matrices. This self-contained reference will be useful to a large variety of mathematicians, engineers, and social scientists, as well as graduate students. The generalizations of positivity and the connections observed provide a unique perspective, along with theoretical insight into applications and future challenges. Direct applications can be found in data analysis, differential equations, mathematical programming, computational complexity, models of the economy, population biology, dynamical systems and control theory.
  • Imagery-enhanced v. verbally-based group cognitive behavior therapy for social anxiety disorder: a randomized clinical trial
  • Peter M. McEvoy, Matthew P. Hyett, Samantha R. Bank, David M. Erceg-Hurn, Andrew R. Johnson, Michael J. Kyron, Lisa M. Saulsman, Michelle L. Moulds, Jessica R. Grisham, Emily A. Holmes, David A. Moscovitch, Ottmar V. Lipp, Bruce N. C. Campbell, Ronald M. Rapee
  • Journal: Psychological Medicine , First View
  • Published online by Cambridge University Press: 11 September 2020, pp. 1-10
  • View abstract
    Background

    Cognitive behavior therapy (CBT) is effective for most patients with a social anxiety disorder (SAD) but a substantial proportion fails to remit. Experimental and clinical research suggests that enhancing CBT using imagery-based techniques could improve outcomes. It was hypothesized that imagery-enhanced CBT (IE-CBT) would be superior to verbally-based CBT (VB-CBT) on pre-registered outcomes.

    Methods

    A randomized controlled trial of IE-CBT v. VB-CBT for social anxiety was completed in a community mental health clinic setting. Participants were randomized to IE (n = 53) or VB (n = 54) CBT, with 1-month (primary end point) and 6-month follow-up assessments. Participants completed 12, 2-hour, weekly sessions of IE-CBT or VB-CBT plus 1-month follow-up.

    Results

    Intention to treat analyses showed very large within-treatment effect sizes on the social interaction anxiety at all time points (ds = 2.09–2.62), with no between-treatment differences on this outcome or clinician-rated severity [1-month OR = 1.45 (0.45, 4.62), p = 0.53; 6-month OR = 1.31 (0.42, 4.08), p = 0.65], SAD remission (1-month: IE = 61.04%, VB = 55.09%, p = 0.59); 6-month: IE = 58.73%, VB = 61.89%, p = 0.77), or secondary outcomes. Three adverse events were noted (substance abuse, n = 1 in IE-CBT; temporary increase in suicide risk, n = 1 in each condition, with one being withdrawn at 1-month follow-up).

    Conclusions

    Group IE-CBT and VB-CBT were safe and there were no significant differences in outcomes. Both treatments were associated with very large within-group effect sizes and the majority of patients remitted following treatment.

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