In this paper, we extend the implicit-explicit (IMEX) methods of Peer type recently developed in [Lang, Hundsdorfer, J. Comp. Phys., 337:203-215, 2017] to a broader class of two-step methods that allow the construction of superconvergent IMEX-Peer methods with A-stable implicit part. IMEX schemes combine the necessary stability of implicit and low computational costs of explicit methods to efficiently solve systems of ordinary differential equations with both stiff and non-stiff parts included in the source term. To construct superconvergent IMEX-Peer methods with favourable stability properties, we derive necessary and sufficient conditions on the coefficient matrices and apply an extrapolation approach based on already computed stage values. Optimised super-convergent IMEX-Peer methods of order s + 1 for s = 2, 3, 4 stages are given as result of a search algorithm carefully designed to balance the size of the stability regions and the extrapolation errors. Numerical experiments and a comparison to other IMEX-Peer methods are included.

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Dynamical systems with sub-processes evolving on many different time scales are ubiquitous in applications. Their efficient solution is greatly enhanced by automatic time step variation. This paper is concerned with the theory, construction and application of IMEX-Peer methods that are super-convergent for variable step sizes and A-stable in the implicit part. IMEX schemes combine the necessary stability of implicit and low computational costs of explicit methods to efficiently solve systems of ordinary differential equations with both stiff and non-stiff parts included in the source term. To construct super-convergent IMEX-Peer methods which keep their higher order for variable step sizes and exhibit favourable linear stability properties, we derive necessary and sufficient conditions on the nodes and coefficient matrices and apply an extrapolation approach based on already computed stage values. New super-convergent IMEX-Peer methods of order s + 1 for s = 2, 3, 4 stages are given as result of additional order conditions which maintain the super-convergence property independent of step size changes. Numerical experiments and a comparison to other super-convergent IMEX-Peer methods show the potential of the new methods when applied with local error control.

Artificial intelligence can be used to realise new types of protective devices and assistance systems, so their importance for occupational safety and health is continuously increasing. However, established risk mitigation measures in software development are only partially suitable for applications in AI systems, which only create new sources of risk. Risk management for systems that for systems using AI must therefore be adapted to the new problems. This work objects to contribute hereto by identifying relevant sources of risk for AI systems. For this purpose, the differences between AI systems, especially those based on modern machine learning methods, and classical software were analysed, and the current research fields of trustworthy AI were evaluated. On this basis, a taxonomy could be created that provides an overview of various AI-specific sources of risk. These new sources of risk should be taken into account in the overall risk assessment of a system based on AI technologies, examined for their criticality and managed accordingly at an early stage to prevent a later system failure.

In this paper, we present a computational model of the elicitation and the dynamics of affective states in autonomous agents based on fuzzy methodology. Fuzzy logic has been used in computational modelling of affect for 15 years, but has not yet been employed to bridge the particular benefits of fuzzy modelling with dynamical systems approaches to understanding emotions. The information-processing architecture scheme we propose for the calculations which are involved in affective processes can be instantiated in a distributed fashion. This enables 'programming' of the agent's affective interpretation of its relationship with its environment with respect to different objects and their behavior towards the agent, as well as its own internal motivational states. In our simulations, we emphasize dynamic properties of affective processes and behaviors resulting therefrom. In addition, we sketch theoretical ideas of internal effects of different affective states that we are currently implementing.