In this paper attention is given to the efficient numerical evaluation of the Pacific Earthquake Engineering Research (PEER) performance-based earthquake engineering framework equations. In particular, potential problems in determining an adequate yet efficient region of integration are discussed. An algorithm called "Magnitude-oriented Adaptive Quadrature" (MAQ) is developed, which is an integration algorithm with both locally and globally adaptive capabilities. MAQ allows efficient integration over the entire integration domain and requires only an error tolerance and maximum number of function evaluations to be specified. The advantages of utilizing the MAQ algorithm over other conventional integration methods such as Romberg integration and conventional adaptive quadrature are illustrated for the numerical computation of (1) expected annual loss; and (2) annual rate of collapse. It is shown that for determination of the expected annual loss a 4.5-to 8.8-fold reduction in the computational demand is obtained using MAQ compared to conventional integration methods. For annual rate of collapse the computational demand reductions range from 30% to two-fold. The computational reductions are a function of the error tolerance prescribed, with greater computational reductions as stricter tolerances are enforced. 2 KEYWORDSNumerical integration; performance-based earthquake engineering (PBEE); magnitudeoriented adaptive quadrature; Seismic loss estimation; Romberg Integration.

In many applications involving image reconstruction, signal observation time is limited. This emphasizes the requirement for optimal observation selection algorithms. A selection criterion using the trace of a matrix forms the basis of two existing algorithms, the Sequential Backward Selection and Sequential Forward Selection algorithms. Neither is optimal although both generally perform well. Here we introduce a trace row-exchange criterion to further improve the quality of the selected subset and introduce another observation selection criterion based upon the determinant of a matrix.

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Next to Magnet Resonance Elastography and Ultrasound Elastography, Digital Image Elasto-Tomography (DIET) is a new imaging-technique, using only motion data available on the boundary, to reconstruct mechanical material parameters, i.e. the interior stiffness of a domain, in order to diagnose tissue related disease such as breast cancer. Where classically Finite Element Methods have been employed to solve this inverse problem, this paper explores a new approach to the reconstruction of mechanical material properties of tissue and tissue defects by the use of Boundary Element Methods (BEM). Using the Boundary Integral Equations for Linear Elasticity in two dimensions within a Conjugate Gradients based inverse solver, material properties of healthy and malicious tissue could be determined from displacement data on the boundary. First simulation results are presented.

Previous work has investigated the feasibility of using Eigenimage-based enhancement tools to highlight abnormalities on chest X-rays (Butler et al in J Med Imaging Radiat Oncol 52:244-253, 2008). While promising, this approach has been limited by computational restrictions of standard clinical workstations, and uncertainty regarding what constitutes an adequate sample size. This paper suggests an alternative mathematical model to the above referenced singular value decomposition method, which can significantly reduce both the required sample size and the time needed to perform analysis. Using this approach images can be efficiently separated into normal and abnormal parts, with the potential for rapid highlighting of pathology.