Showing papers by "Volker Schmidt published in 2005"

Simulation of typical Cox–Voronoi cells with a special regard to implementation tests

Abstract: We consider stationary Poisson line processes in the Euclidean plane and analyze properties of Voronoi tessellations induced by Poisson point processes on these lines. In particular, we describe and test an algorithm for the simulation of typical cells of this class of Cox–Voronoi tessellations. Using random testing, we validate our algorithm by comparing theoretical values of functionals of the zero cell to simulated values obtained by our algorithm. Finally, we analyze geometric properties of the typical Cox–Voronoi cell and compare them to properties of the typical cell of other well-known classes of tessellations, especially Poisson–Voronoi tessellations. Our results can be applied to stochastic–geometric modelling of networks in telecommunication and life sciences, for example. The lines can then represent roads in urban road systems, blood arteries or filament structures in biological tissues or cells, while the points can be locations of telecommunication equipment or vesicles, respectively.

Quantitative analysis of keratin filament networks in scanning electron microscopy images of cancer cells

Abstract: The keratin filament network is an important part of the cytoskeleton. It is involved in the regulation of shape and viscoelasticity of epithelial cells. The morphology of keratin networks depends on post-translational modifications of keratin monomers. In-vitro studies indicated that network characteristics, such as filament crosslink density, determines the biophysical properties of the filament network. This report presents a quantitative method for the morphological analysis of keratin filament networks. Visualization of filaments was based on prefixation extraction of epithelial cells and scanning electron microscopy (SEM). SEM images were processed by a skeletonization algorithm to obtain a graph structure that represents individual filaments as well as their connections. This method was applied to investigate the effects of transforming growth factor alpha (TGFalpha) on the morphology of keratin networks in pancreatic cancer cells. TGFalpha contributes to pancreatic cancer progression and activates signalling pathways phosphorylating keratin monomers. Using this new method, a significant alteration to the keratin network morphology could be detected in response to TGFalpha.

Statistical analysis of the three‐dimensional structure of centromeric heterochromatin in interphase nuclei

Abstract: Translocation of genes into the pericentromeric heterochromatin occurs during cellular differentiation and leads to a long-term silencing of these genes. Consequently, a structural remodelling of this heterochromatin compartment is observed during differentiation but this remains to be defined from a topological point of view. In a previous study, we analysed the three-dimensional (3D) distribution patterns of centromere clusters (chromocentres) by confocal scanning laser microscopy and found that differentiation of the promyelocytic leukaemia cell line NB4 along the neutrophil lineage is associated with a progressive clustering of centromeres. This clustering was reflected by a decreased number of detectable chromocentres, i.e. groups of centromeres with a distance below the diffraction-limited resolution of optical microscopy. The purpose of this study was to perform a statistical analysis of the 3D distribution of chromocentres in NB4 cells. Several point field characteristics (Ripley's K-function, L-function, pair correlation function, nearest-neighbour distribution function) were investigated to describe the topology of chromocentres during differentiation of NB4 cells. The pair correlation function revealed a higher frequency of chromocentre distances between 350 nm and 800 nm in undifferentiated NB4 cells as compared with differentiated cells. The L-function and the nearest-neighbour distribution function confirmed these results. These data imply the existence of intranuclear heterochromatin zones formed by functionally related centromeric regions. In view of the observed decrease in the number of detectable chromocentres during differentiation, we hypothesize that these zones with a diameter of 350-800 nm in undifferentiated NB4 cells contract into zones with a diameter below 350 nm in differentiated cells.

Limit theorems for stationary tessellations with random inner cell structures

Abstract: We consider stationary and ergodic tessellations X = { n }n> in Rd, where X is observed in a bounded and convex sampling window W, C IRd. It is assumed that the cells En of X possess random inner structures, examples of which include point patterns, fibre systems, and tessellations. These inner cell structures are generated, both independently of each other and independently of the tessellation X, by generic stationary random sets that are related to a stationary random vector measure Jo acting on Rd. In particular, we study the asymptotic behaviour of a multivariate random functional, which is determined both by X and by the individual cell structures contained in W,, as W, f Rd. It turns out that this functional provides an unbiased estimator for the intensity vector associated with Jo. Furthermore, under natural restrictions, strong laws of large numbers and a multivariate central limit theorem of the normalized functional are proven. Finally, we discuss in detail some numerical examples and applications, for which the inner structures of the cells of X are induced by iterated Poisson-type tessellations.

On the Local Connectivity Number of Stationary Random Closed Sets

Abstract: Random closed sets (RACS) in the d—dimensional Euclidean space are considered, whose realizations belong to the extended convex ring. A family of nonparametric estimators is investigated for the simultaneous estimation of the vector of all specific Minkowski functionals (or, equivalently, the specific intrinsic volumes) of stationary RACS. The construction of these estimators is based on a representation formula for the expected local connectivity number of stationary RACS intersected with spheres, whose radii are small in comparison with the size of the whole sampling window. Asymptotic properties of the estimators are given for unboundedly increasing sampling windows. Numerical results are provided as well.