This paper deals with the union set of a stationary Poisson process of cylinders in R n having an (n−m)-dimensional base and an m-dimensional direction space, where m ∈ {0, 1, . . . , n−1} and n ≥ 2. The concept simultaneously generalises those of a Boolean model and a Poisson hyperplane or m-flat process. Under very general conditions on the typical cylinder base a Berry-Esseen bound for the volume of the union set within a sequence of growing test sets is derived. Assuming convexity of the cylinder bases and of the window a similar result is shown for a broad class of geometric functionals, including the intrinsic volumes. In this context the asymptotic variance constant is analysed in detail, which in contrast to the Boolean model leads to a new degeneracy phenomenon. A quantitative central limit theory is developed in a multivariate set-up as well.

We present a new multi-layered annotation scheme for orthographic errors in freely written German texts produced by primary school children. The scheme is closely linked to the German graphematic system and defines categories for both general structural word properties and errorrelated properties. Furthermore, it features multiple layers of information which can be used to evaluate an error. The categories can also be used to investigate properties of correctly-spelled words, and to compare them to the erroneous spellings. For data representation, we propose the XML-format LearnerXML.

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Random union sets Z associated with stationary Poisson processes of k-cylinders in R d are considered. Under general conditions on the typical cylinder base a concentration inequality for the volume of Z restricted to a compact window is derived. Assuming convexity of the typical cylinder base and isotropy of Z a concentration inequality for intrinsic volumes of arbitrary order is established. A number of special cases are discussed, for example the case when the cylinder bases arise from a random rotation of a fixed convex body. Also the situation of expanding windows is studied. Special attention is payed to the case k = 0, which corresponds to the classical Boolean model.

We consider a class of dynamic random graphs known as preferential attachment models, where the probability that a new vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known that the distribution of a uniformly chosen vertex converges to a limiting distribution. Depending on the parameters, the tail of the limiting distribution may behave like a power law or a stretched exponential. Using Stein's method we provide rates of convergence to zero of the total variation distance between the finite distribution and its limit. Our proof uses the fact that the limiting distribution is the stationary distribution of a Markov chain together with the generator method of Barbour.