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Ground motion models (GMMs) are a key component in seismic hazard assessment and in seismic risk analysis. The consideration of both aleatory and epistemic sources of variability may have significant influence on the results and are vital because of their influence on the over- or under-estimation of the final assessment of losses. Recent research has shown that the commonly used framework of weighted logic trees for the choice of GMMs is not necessarily the best suited to account for epistemic uncertainty. Recently, a simple and alternative procedure has been proposed in which a GMM suite is defined with only three representative models (lower, central and upper) derived from available median models. This alternative model is equivalent to the use of multiple models, provided the same range of epistemic uncertainty is sampled. The representative suite approach was applied to the European context for developing a Pan-European GMM for EC8 ground type B and normal or strike slip faulting style for its implementation in risk analysis of critical infrastructures Europe wide, within the framework of the European funded project INFRARISK. The proposed new Pan-European representative GMM is based on the most recent GMMs developed using the common RESORCE strong-motion database of European and Near and Middle East acceleration records. It is shown to perform well when tested against new ground-motion observations from the ESM-Engineering Strong-Motion database and even slightly better than other available GMMs. The procedure is efficient and transparent limiting the sample space to three GMMs and reducing both complexity of the modelling and computational efforts. [ABSTRACT FROM AUTHOR]

A classic result known as the speed-up theorem in machine-independent complexity theory shows that there exist some computable functions that do not have best programs for them (Blum in J. ACM 14(2):322–336, and J. ACM 18(2):290–305, ). In this paper we lift this result into type-2 computations. Although the speed-up phenomenon is essentially inherited from type-1 computations, we observe that a direct application of the original proof to our type-2 speed-up theorem is problematic because the oracle queries can interfere with the speed of the programs and hence the cancellation strategy used in the original proof is no longer correct at type-2. We also argue that a type-2 analog of the operator speed-up theorem (Meyer and Fischer in J. Symb. Log. 37:55–68, ) does not hold, which suggests that this curious speed-up phenomenon disappears in higher-typed computations beyond type-2. The result of this paper adds one more piece of evidence to support the general type-2 complexity theory under the framework proposed in Li (Proceedings of the Third International Conference on Theoretical Computer Science, pp. 471–484, and Proceedings of Computability in Europe: Logical Approach to Computational Barriers, pp. 182–192, ) and Li and Royer (On type-2 complexity classes: Preliminary report, pp. 123–138, ) as a reasonable setup. [ABSTRACT FROM AUTHOR]