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The aim of this paper is to describe an efficient strategy for descritizing ill-posed linear operator equations of the first kind: we consider Tikhonov-Phillips-regularization χ^δ α = (a * a + α I)^-1 A * y ^δ with a finite dimensional approximation A n instead of A. We propose a sparse matrix structure which still leads to optimal convergences rates but requires substantially less scalar products for computing A n compared with standard methods.
Contents: 1 Introduction 1.1 Tikhanov-Phillips Regularization of Ill-Posed Problems 1.2 A Compact Course to Wavelets 2 A Multilevel Iteration for Tikhonov-Phillips Regularization 2.1 Multilevel Splitting 2.2 The Multilevel Iteration 2.3 Multilevel Approach to Cone Beam Reconstuction 3 The use of approximating operators 3.1 Computing approximating families {Ah}
Projection methods based on wavelet functions combine optimal convergence rates with algorithmic efficiency. The proofs in this paper utilize the approximation properties of wavelets and results from the general theory of regularization methods. Moreover, adaptive strategies can be incorporated still leading to optimal convergence rates for the resulting algorithms. The so-called wavelet-vaguelette decompositions enable the realization of especially fast algorithms for certain operators.
Objective: There is a lack of brief rating scales for the reliable assessment of psychotherapeutic skills, which do not require intensive rater training and/or a high level of expertise. Thus, the objective is to validate a 14-item version of the Clinical Communication Skills Scale (CCSS-S).
Methods: Using a sample of N = 690 video-based ratings of role-plays with simulated patients, we calculated a confirmatory factor analysis and an exploratory structural equation modeling (ESEM), assessed convergent validities, determined inter-rater reliabilities and compared these with those who were either psychology students, advanced psychotherapy trainees, or experts.
Results: Correlations with other competence rating scales were high (rs > 0.86–0.89). The intraclass correlations ranged between moderate and good [ICC(2,2) = 0.65–0.80], with student raters yielding the lowest scores. The one-factor model only marginally replicated the data, but the internal consistencies were excellent (α = 0.91–95). The ESEM yielded a two-factor solution (Collaboration and Structuring and Exploration Skills).
Conclusion: The CCSS-S is a brief and valid rating scale that reliably assesses basic communication skills, which is particularly useful for psychotherapy training using standardized role-plays. To ensure good inter-rater reliabilities, it is still advisable to employ raters with at least some clinical experience. Future studies should further investigate the one- or two-factor structure of the instrument.
Zum dreißigjährigen Bestehen des Kommunalwissenschaftlichen Instituts an der Universität Potsdam vereint dieser Jubiläumsband kurze Aufsätze von ehemaligen und aktuellen Vorstandsmitgliedern, von Ehrenmitgliedern des Vorstands, langjährigen wissenschaftlichen Mitarbeitern des Instituts und aktuellen wissenschaftlichen Kooperationspartnern. Die insgesamt zwölf Beiträge befassen sich mit den Kommunalwissenschaften und der Geschichte des Kommunalwissenschaftlichen Instituts, mit aktuellen kommunalwissenschaftlichen Fragestellungen und wissenschaftlichen Kooperationen des KWI. Der vom KWI-Vorstand herausgegebene Band soll einen breiten Blick auf 30 Jahre Kommunalwissenschaften in Brandenburg und an der Universität Potsdam werfen und einen Ausblick auf zukünftige kommunalwissenschaftliche Forschung geben.