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By the Choquet theorem, distributions of random closed sets can be characterized by a certain class of set functions called capacity functionals. In this paper a generalization to the multivariate case is presented, that is, it is proved that the joint distribution of finitely many random sets can be characterized by a multivariate set function being completely alternating in each component, or alternatively, by a capacity functional defined on complements of cylindrical sets. For the special case of finite spaces a multivariate version of the Moebius inversion formula is derived. Furthermore, we use this result to formulate an existence theorem for set-valued stochastic processes.

Tuned mass dampers serve the purpose of damping vibrations of structures such as earthquake-induced vibrations. In their design, two types of uncertainty are relevant: the stochastic excitation (e.g. earthquake record) and the inherent uncertainty of internal parameters of the devices themselves. This paper presents a new framework that admits the combination of stochastic processes and interval-type parameter uncertainty, modelled by random sets. The approach is applied to show how the efficiency of tuned mass dampers can be realistically assessed in the presence of uncertainty.

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In a former paper, the author has investigated how copulas can be used to express the dependence relation between two random sets. It has been proven that a joint belief function is related to its marginal belief functions by a family of copulas and that, in general, a single copula is not sufficient. In this paper the results are investigated under the assumption that the involved belief functions are minitive which corresponds to the important case where the associated random sets are consonant. It is proven that under this additional assumption a single copula is sufficient to express the dependence relation. In other words, this means that Sklar's theorem remains valid if joint and marginal distribution functions are replaced by joint and marginal minitive belief functions.

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The methylotrophic yeast Pichia pastoris is known as an efficient host for the production of heterologous proteins. While N‐linked protein glycosylation is well characterized in P. pastoris there is less knowledge of the patterns of O‐glycosylation. O‐glycans produced by P. pastoris consist of short linear mannose chains, which in the case of recombinant biopharmaceuticals can trigger an immune response in humans. This study aims to reveal the influence of different cultivation strategies on O‐mannosylation profiles in P. pastoris. Sixteen different model proteins, produced by different P. pastoris strains, are analyzed for their O‐glycosylation profile. Based on the obtained data, human serum albumin (HSA) is chosen to be produced in fast and slow growth fed batch fermentations by using common promoters, PGAP and PAOX1. After purification and protein digestion, glycopeptides are analyzed by LC/ESI‐MS. In the samples expressed with PGAP it is found that the degree of glycosylation is slightly higher when a slow growth rate is used, regardless of the efficiency of the producing strain. The highest glycosylation intensity is observed in HSA produced with PAOX1. The results indicate that the O‐glycosylation level is markedly higher when the protein is produced in a methanol‐based expression system.