Approximation Theory of Multivariate Spline Functions in Sobolev Spaces

In this paper we study some approximation theory questions which arise from the analysis of the discretization error associated with the use of the Rayleigh-Ritz-Galerkin method for approximating the solutions to various types of boundary value problems, cf. [13, [2], [33, [43, [7], [8], [93, [12], [143, [18], [19], [20] and [22]. In particular, we consider upper and lower bounds for the error in approximation of certain families of functions in Sobolev spaces, cf. [15], by functions in finite-dimensional "polynomial spline types" subspaces, cf. [16]. In doing this, we directly generalize, improve, and extend the corresponding results of[1], [17], [18], [19], [20], and [21]. Throughout this paper, the symbol K will be used repeatedly to denote a positive constant, not necessarily the same at each occurrence and the symbol μ will be used repeatedly to denote a nonnegative, continuous function on [0,∞], not necessarily the same at each occurrence

L∞-Multivariate approximation theory

This paper is concerned with multivariate analogues of many standard results in the L∞-approximation theory of functions of one real variable, cf. [12], [13], [14], [20], [21] and [24]. In particular, asymptotic bounds are given for the distance of a given smooth function from various finite-dimensional spaces such as multivariate trigonometric polynomials, multivariate algebraic polynomials and multivariate polynomial spline functions

Developing a Holistic Competence Model for Telenursing Practice: Perspectives from Telenurses and Managers of Telemedical Service Centres

Telenurse’s work performance determines the quality and the efficiency of the service and strongly influences the acceptance of patients and healthcare professionals. Considering this important role, qualification and training of telenurses is of utmost importance for the success of telemedicine providers and the future of telemedicine. However, in Germany the profession “telenurse” is not yet established, nor is there a standardised education programme for telenurses. Purpose: In our study, we seek to identify and describe needed competencies from the perspectives of employees and employers in telemedicine service centres. We develop a systematic competencies concept fundamental for a specific telenurse education curriculum. Methods: We designed an exploratory study as a series of semi-standardised interviews with telenurses and the management of telenursing centres, focusing on knowledge, skills and attitudes needed in telenursing practice. Results: By including the perspectives of employers and employees, we provide a broad view on the skills and competencies needed. We show that telenursing requires a great variety of competencies that can be structured into four categories: professional, methodological, personal and social competencies. Conclusion: Our study provides a comprehensive approach to key competencies of telenurses. The results set out a framework for the development of skills and competencies considering the perception of the telenurse-workplace not only from employers but also from employee’s perspective

Choice mechanisms for past, temporally extended outcomes.

Accurate retrospection is critical in many decision scenarios ranging from investment banking to hedonic psychology. A notoriously difficult case is to integrate previously perceived values over the duration of an experience. Failure in retrospective evaluation leads to suboptimal outcome when previous experiences are under consideration for revisit. A biologically plausible mechanism underlying evaluation of temporally extended outcomes is leaky integration of evidence. The leaky integrator favours positive temporal contrasts, in turn leading to undue emphasis on recency. To investigate choice mechanisms underlying suboptimal outcome based on retrospective evaluation, we used computational and behavioural techniques to model choice between perceived extended outcomes with different temporal profiles. Second-price auctions served to establish the perceived values of virtual coins offered sequentially to humans in a rapid monetary gambling task. Results show that lesser-valued options involving successive growth were systematically preferred to better options with declining temporal profiles. The disadvantageous inclination towards persistent growth was mitigated in some individuals in whom a longer time constant of the leaky integrator resulted in fewer violations of dominance. These results demonstrate how focusing on immediate gains is less beneficial than considering longer perspectives.This research was supported by the Wellcome Trust Grants 095495 and 093270 and European Research Council Advanced Grant ERC-2011-AdG 293549.This is the final version. It was first published by Royal Society Publishing at http://rspb.royalsocietypublishing.org/content/282/1810/20141766