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This paper presents a probabilistic learning method on random manifolds for building and updating statistical surrogate models using small datasets. The approach accounts for various types of variables, including random, controlled, and latent, forming a random manifold that links quantities of interest to controlled variables. This paper consolidates the Probabilistic Learning on Manifolds (PLoM) methodology, previously dispersed across multiple publications, and demonstrates its effectiveness through three diverse applications: Molecular dynamics, nonlinear elasticity, and updating under-observed nonlinear dynamic system with incomplete data. These examples illustrate the robustness of the method in managing complex and uncertain problems.

A fully parallel algorithm for updating and downdating the singular value decompositions (SVD’s) of an m-by-n(m≥n) matrix A is described. The algorithm uses similar chasing techniques for modifying the SVD’s described in [3], but requires fewer plane rotations, and can be implemented almost identically for both updating and downdating. Both cyclic and consecutive storage schemes are considered in parallel implementation. We show that the latter scheme outperforms the former on a distributed memory MIMD multiprocessor. We present the experimental results on the 32-node Connection Machine (CM-5).

This paper evaluates performance of three representative single-person walking excitation models which can be used to check vibration levels of high-frequency building floors accommodating highly sensitive equipment. The three models calculate vibration responses by harmonic, transient and spectral analyses, respectively.

The evaluation was based on a combined experimental and analytical work comprising modal testing of a prototype floor, repeated measurements of walking-induced vibrations, finite element modelling and model updating to match the measured modal properties. The updated and verified model was then used for the application of the three walking models results of which were then compared with their experimental counterparts.

It was found that all three models were on the "safe" side and overestimated responses measured in all response tests. However, the harmonic model which assumes high-frequency floor resonance caused by the 7th or 8th harmonic of the walking resulted in over-conservative response estimates order of magnitude higher than the maximum measured values in all response tests. Nevertheless, the model which describes walking across a high-frequency floor as pulses representing footfalls consistently overestimated responses by just about 20% and is, therefore, recommended for vibration serviceability checks of this type of floors.

The IREC system aims to control the evolution of Eiffel classes to enable not only versionning, but also the most possible automatic reactualization of dependent entities: client or heir classes, instances migration, library merging…These reactualizations need a very sharp knowledge of classes' structure and semantics in order to compute deltas, to determine the consequences of changes from different points of view, to dynamically evaluate class invariants…in a both compiled and interpreted framework. This paper presents the reflexive representation chosen in IREC to give the needed knowledge for previous handling. It is presented in the form of an Eiffel language components library, which describes in a distributed way every structural and semantic aspect, from classes up to Eiffel language tokens. Each of these components is equipped with handling methods for the different life cycle phases of the application or library classes. The modularity of the representation and factorisations by inheritance enable to consider of other handlings and the adaptation of current components to other languages.